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Stolen base

In baseball, a stolen base occurs when a runner advances to a base unaided by other actions and the official scorer rules that the advance should be credited to the action of the runner. The umpires determine whether the runner is safe or out at the next base, but the official scorer rules on the question of credit or blame for the advance under Rule 10 (Rules of Scoring) of the MLB's Official Rules.

A stolen base most often occurs when a base runner advances to the next base while the pitcher is pitching the ball to home plate.

Successful base stealers must be fast and have good timing.

Background
Ned Cuthbert, playing for the Philadelphia Keystones in either 1863 or 1865, was the first player to steal a base in a baseball game, although the term stolen base was not used until 1870. For a time in the 19th century, stolen bases were credited when a baserunner reached an extra base on a base hit from another player. For example, if a runner on first base reached third base on a single, it counted as a steal. In 1887, Hugh Nicol set a still-standing Major League record with 138 stolen bases, many of which would not have counted under modern rules. Modern steal rules were fully implemented in 1898.

Base stealing was popular in the game's early decades, with speedsters such as Ty Cobb and Clyde Milan stealing nearly 100 bases in a season. But the tactic fell into relative disuse after Babe Ruth introduced the era of the home run – in 1955, for example, no one in baseball stole more than 25 bases, and Dom DiMaggio won the AL stolen base title in 1950 with just 15. However, in the late 1950s and early 1960s, base-stealing was brought back to prominence primarily by Luis Aparicio and Maury Wills, who broke Cobb's modern single-season record by stealing 104 bases in 1962. Wills’ record was broken in turn by Lou Brock in 1974 and Rickey Henderson in 1982. The stolen base remained a popular tactic through the 1980s, perhaps best exemplified by Vince Coleman and the St. Louis Cardinals, but began to decline again in the 1990s as the frequency of home runs reached record heights and the steal-friendly artificial turf ballparks began to disappear.

Base stealing is an important characteristic of the "small ball" managing style (or "manufacturing runs"). Such managers emphasize "doing the little things" (including risky running plays like base-stealing) to advance runners and score runs, often relying on pitching and defense to keep games close. The Los Angeles Dodgers of the 1960s, led by pitcher Sandy Koufax and speedy shortstop Maury Wills, were a successful example of this style. The antithesis of this is reliance on power hitting, exemplified by the Baltimore Orioles of the 1970s, which aspired to score most of its runs via home runs. Often the "small ball" model is associated with the National League, while power hitting is associated with the American League. However, some successful recent American League teams, including the 2002 Anaheim Angels, the 2001 Seattle Mariners, the 2005 Chicago White Sox, and the 2015 Kansas City Royals, have excelled at "small ball." The Royals in particular embodied this style within the last decade, leading the league in stolen bases but finishing last in home runs in 2013 and 2014, leading to a berth in two consecutive World Series, one of which they won. Successful teams often combine both styles, with speedy runners complementing power hitters—such as the 2005 White Sox, who hit 200 home runs, which was fifth most in the majors, and had 137 stolen bases, which was fourth.

Base-stealing technique
Baseball's Rule 8 (The Pitcher) specifies the pitching procedure in detail. For example, in the Set Position, the pitcher must "com[e] to a complete stop"; thereafter, "any natural motion associated with his delivery of the ball to the batter commits him to the pitch without alteration or interruption." A runner intending to "steal on the pitcher" breaks for the next base the moment the pitcher commits to pitch to home plate. The pitcher cannot abort the pitch and try to put the runner out; this is a balk under Rule 8.

If the runner breaks too soon (before the pitcher is obliged to complete a pitch), the pitcher may throw to a base rather than pitch, and the runner is usually picked off by being tagged out between the bases. Past this moment, any delay in the runner's break makes it more likely that the catcher, after receiving the pitch, will be able to throw the runner out at the destination base.

Before the pitch, the runner takes a lead, walking several steps away from the base as a head start toward the next base. Even a runner who does not intend to steal takes a secondary lead of a few more steps, once the pitcher has legally committed to complete the pitch.

The pitcher may throw to the runner's base. The runner must return to that base or risk being tagged out. As well as putting the runner out, an underlying goal is to dissuade the runner from too big a lead; that is, to hold the runner on the original base. (Historically, this gambit could be used without limit. An MLB rules change in 2023 limited the pitcher to two throws; the pitcher must then pitch to the batter.)

The more adept base stealers are proficient at reading the pickoff, meaning that they can detect certain tells (tell-tale signs) in a pitcher's pre-pitch movements or mannerisms that indicate the pickoff attempt is or is not imminent. For example, one experienced base stealer noted that careless pitchers dig the toes on their back foot into the ground when they are about to pitch in order to get a better push off, but when they intend to turn and throw a pickoff, they do not.

If a batted ball is caught on the fly, the runner must return to his original base. In this case, a runner trying to steal is more likely to be caught off his original base, resulting in a double play. This is a minor risk of a steal attempt. It is offset by the fact that a ground ball double play is less likely.

Plays involving baserunning
In the hit-and-run play, coaches coordinate the actions of runner and batter. The runner tries to steal and the batter swings at almost any pitch, if only to distract the catcher. If the batter makes contact, the runner has a greater chance of reaching the next base; if the batter gets a base hit, the runner will likely be able to take an extra base. If the batter fails to hit the ball, the hit-and-run becomes a pure steal attempt.

The less common cousin to the hit and run is the "run and hit" play. In the run and hit, the base runner attempts to advance when the pitcher commits the pitch to home plate, but the batter is instead directed to exercise his judgement as to whether or not to swing at the pitch. If the batter feels it is not advantageous to swing, AND he believes the base runner is very likely to succeed in the steal attempt, he does not swing. This play is typically utilized with elite base stealers and skilled batters only, wherein a highly experienced batsman is trusted to decide whether or not to "protect" the base runner. If the batter chooses not to swing, it becomes a pure steal attempt.

In the delayed steal, the runner does not take advantage of the pitcher's duty to complete a pitch, but relies on surprise and takes advantage of any complacency by the fielders. The runner gives the impression he is not trying to steal, and does not break for the next base until the ball crosses the plate. It is rare for Major League defenses to be fooled, but the play is used effectively at the college level. The first delayed steal on record was performed by Miller Huggins in 1903. The delayed steal was famously practiced by Eddie Stanky of the Brooklyn Dodgers.

Second base is the base most often stolen, because once a runner is on second base he is considered to be in scoring position, meaning that he is expected to be able to run home and score on most routine singles hit into the outfield. Second base is also the easiest to steal, as it is farthest from home plate and thus a longer throw from the catcher is required to prevent it. Third base is a shorter throw for the catcher, but the runner is able to take a longer lead off second base and can leave for third base earlier against a left-handed pitcher. A steal of home plate is the riskiest, as the catcher only needs to tag out the runner after receiving the ball from the pitcher. It is difficult for the runner to cover the distance between the bases before the ball arrives home. Ty Cobb holds the records for most steals of home in a single season (8) as well as for a career (54). Steals of home are not officially recorded statistics, and must be researched through individual game accounts. Thus Cobb's totals may be even greater than is recorded. Jackie Robinson famously stole home in Game 1 of the 1955 World Series. Thirty-five games have ended with a runner stealing home, but only two have occurred since 1980. In a variation on the steal of home, the batter is signaled to simultaneously execute a sacrifice bunt, which results in the squeeze play. The suicide squeeze is a squeeze in which the runner on third begins to steal home without seeing the outcome of the bunt; it is so named because if the batter fails to bunt, the runner will surely be out. In contrast, when the runner on third does not commit until seeing that the ball is bunted advantageously, it is called a safety squeeze.

In more recent years, most steals of home involve a delayed double steal, in which a runner on first attempts to steal second, while the runner on third breaks for home as soon as the catcher throws to second base. If it is important to prevent the run from scoring, the catcher may hold on to the ball (conceding the steal of second) or may throw to the pitcher; this may deceive the runner at third and the pitcher may throw back to the catcher for the out.

Statistics
In baseball statistics, stolen bases are denoted by "SB". Attempts to steal that result in the baserunner being out are caught stealing ("CS"). The sum of these statistics is steal attempts. Successful steals as a percentage of total steal attempts is called the success rate.

The rule on stolen bases states that:
 * Advances that are credited to some other play are not steal attempts. For example, on a wild pitch or a passed ball, the official scorer must notice whether the runner broke for the next base before the pitch got away.
 * As usual, statistics in the case of a defensive error are based on error-free play. If a runner would have been out, but for the error, it is scored as "caught stealing, safe on the error." A catcher does not commit an error by throwing poorly to the destination base, but if any runner takes an extra base on the bad throw, it is "stolen base plus error."
 * There is no steal attempt on a dead ball, whether the runner is sent back to the original base (as on a foul ball) or is awarded the next base (as on a hit batsman). On a base award when the ball is live (such as a walk), the runner could make a steal attempt beyond the base awarded.
 * Cases where the defense intentionally allows the runner to advance without attempting to put him out are scored as defensive indifference, also called fielder's indifference, and do not count as stolen bases. This is usually only scored late in games when it is clear that the defense's priority is getting the batter out. The lack of a putout attempt does not by itself indicate defensive indifference; the official scorer must also factor in the game situation and the defensive players' actions.

Relative skill at stealing bases can be judged by evaluating either a player's total number of steals or the success rate. Noted statistician Bill James has argued that unless a player has a high success rate (67–70% or better), attempting to steal a base is detrimental to a team.

Comparing skill against players from other eras is problematic, because the definition has not been constant. Caught stealing was not recorded regularly until the middle of the 20th century. Ty Cobb, for example, was known as a great base-stealer, with 892 steals and a success rate of over 83%. However, the data on Cobb's caught stealing is missing from 12 seasons, strongly suggesting he was unsuccessful many more times than his stats indicate. Carlos Beltrán, with 286 steals, has the highest career success rate of all players with over 300 stolen base attempts, at 88.3%.

Evolution of rules and scoring
The first mention of the stolen base as a statistic was in the 1877 scoring rules adopted by the National League, which noted credit toward a player's total bases when a base is stolen. It was not until 1886 that the stolen base appeared as something to be tracked, but was only to "appear in the summary of the game".

In 1887, the stolen base was given its own individual statistical column in the box score, and was defined for purposes of scoring: "...every base made after first base has been reached by a base runner, except for those made by reason of or with the aid of a battery error (wild pitch or passed ball), or by batting, balks or by being forced off. In short, shall include all bases made by a clean steal, or through a wild throw or muff of the ball by a fielder who is directly trying to put the base runner out while attempting to steal." The next year, it was clarified that any attempt to steal must be credited to the runner, and that fielders committing errors during this play must also be charged with an error. This rule also clarified that advancement of another base(s) beyond the one being stolen is not credited as a stolen base on the same play, and that an error is charged to the fielder who permitted the extra advancement. There was clarification that a runner is credited with a steal if the attempt began before a battery error. Finally, batters were credited with a stolen base if they were tagged out after over running the base.

In 1892, a rule credited runners with stolen bases if a base runner advanced on a fly out, or if they advanced more than one base on any safe hit or attempted out, providing an attempt was made by the defense to put the runner out. The rule was rescinded in 1897.

In 1898, stolen base scoring was narrowed to no longer include advancement in the event of a fielding error, or advancement caused by a hit batsman.

1904 saw an attempt to reduce the already wordy slew of rules governing stolen bases, with the stolen base now credited when "the baserunner [sic] advances a base unaided by a base hit, a put out, (or) a fielding or batter error."

1910 saw the first addressing of the double and triple steal attempts. Under the new rule, when any runner is thrown out, and the other(s) are successful, the successful runners will not be credited with a stolen base.

Without using the term, 1920 saw the first rule that would be referred to today as defensive indifference, as stolen bases would not be credited, unless an effort was made to stop the runner by the defense. This is usually called if such is attempted in the ninth inning while that player's team is trailing, unless the runner represents the potential tying run.

1931 saw a further narrowing of the criteria for awarding a stolen base. Power was given to the official scorer, in the event of a muff by the catcher in throwing, that in the judgment of the scorer the runner would have been out, to credit the catcher with an error, and not credit the runner with a stolen base. Further, any successful steal on a play resulting in a wild pitch, passed ball, or balk would no longer be credited as a steal, even if the runner had started to steal before the play.

One of the largest rewrites to the rules in history came in 1950. The stolen base was specifically to be credited "to a runner whenever he advances one base unaided by a base hit, a putout, a forceout, a fielder's choice, a passed ball, a wild pitch, or a balk."

There were noted exceptions, such as denying a stolen base to an otherwise successful steal as a part of a double or triple steal, if one other runner was thrown out in the process. A stolen base would be awarded to runners who successfully stole second base as a part of a double steal with a man on third, if the other runner failed to steal home, but instead was able to return safely to third base. Runners who are tagged out oversliding the base after an otherwise successful steal would not be credited with a stolen base. Indifference was also credited as an exception. Runners would now be credited with stolen bases if they had begun the act of stealing, and the resulting pitch was wild, or a passed ball. Finally, for 1950 only, runners would be credited with a stolen base if they were "well advanced" toward the base they were attempting to steal, and the pitcher is charged with a balk, with the further exception of a player attempting to steal, who would otherwise have been forced to advance on the balk by a runner behind them. This rule was removed in 1951.

A clarification came in 1955 that awarded a stolen base to a runner even if he became involved in a rundown, provided he evaded the rundown and advanced to the base he intended to steal.

The criteria for "caught stealing" were fine-tuned in 1979, with a runner being charged with being caught if he is put out while trying to steal, overslides a base (otherwise successfully stolen), or is picked off a base and tries to advance to the next base. It is explicitly not caught stealing to be put out after a wild pitch or passed ball.

"Stealing first"
While not recorded as a stolen base, the same dynamic between batter/runner and defense is on display in the case of an uncaught third strike. The batter/runner can avoid an out and become a baserunner by reaching first base ahead of the throw. This case is a strikeout that is not an out; the batter/runner's acquisition of first base is scored as a passed ball, a wild pitch, or an error.

In baseball's earlier decades, a runner on second base could "steal" first base, perhaps with the intention of drawing a throw that might allow a runner on third to score (a tactic famously employed by Germany Schaefer). However, such a tactic was not recorded as a stolen base. MLB rules now forbid running clockwise on the basepaths to "confuse the defense or make a travesty of the game". Further, after the pitcher assumes the pitching position, runners cannot return to any previous base.

In a game on August 16, 1987, Toronto Blue Jays center fielder Lloyd Moseby successfully stole second base on a throwing error by Chicago White Sox catcher Carlton Fisk that went well into center field. However, shortstop Ozzie Guillen faked as if the batter had hit a popfly, which would have required Moseby to return to first base to avoid getting doubled off. Moseby made it back to first base, but another throwing error sent the ball to the infield wall, giving Moseby another chance to steal second, which he did. This chaos led the announcer to say, "He doesn't know where the throw is; he's going back to first base! Is he going to steal first? He steals first! Now he's going to steal second again! I've never seen it before!" This bizarre play was officially scored as a baserunner advancing on a throwing error by the center fielder, ironically resulting in neither a stolen base awarded nor an error charged to the catcher.

In a game on April 19, 2013, Milwaukee Brewers shortstop Jean Segura stole second base in the bottom of the eighth inning. After the batter up, Ryan Braun, walked, Segura broke early for third base and the pitcher, Shawn Camp of the Chicago Cubs, threw ahead of him. As Segura was chased back to second base, Braun advanced to second as well and was tagged out. Segura, thinking he was out, began to return to the home dugout behind first base, but first base coach Garth Iorg directed him to stand at first. Segura had not intentionally run the bases backwards as a deception or mockery, but no fielder tried to tag him out. Later in the inning, he attempted to steal second for the second time, but was thrown out by catcher Welington Castillo.

The expression "You can't steal first base" is sometimes used in reference to a player who is fast but not very good at getting on base in the first place. Former Pittsburgh Pirates and Seattle Mariners manager Lloyd McClendon is jokingly referred to as having "stolen first" in a June 26, 2001 game as the manager of the Pirates: after being ejected for disputing a call at first base, he yanked the base out of the ground and left the field with it, delaying the game. Of the incident, McClendon said "I told him he wasn't using it, so I thought I'd take it." When a groundskeeper came out to replace the bag, the crowd booed him.

The independent Atlantic League instituted a new rule for the second half of the 2019 season, allowing batters to become runners on any pitch not "caught in flight" by the catcher, as they can throughout baseball after most uncaught third strikes. On July 13, 2019, outfielder Tony Thomas of the Southern Maryland Blue Crabs became the first player to reach first base under this rule. The press described this as "stealing first base", though it is scored as described above.

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Plate appearance

In baseball, a player is credited with a plate appearance (denoted by PA) each time he completes a turn batting. Under Rule 5.04(c) of the Official Baseball Rules, a player completes a turn batting when he is put out or becomes a runner. This happens when he strikes out or is declared out before reaching first base; or when he reaches first base safely or is awarded first base (by a base on balls, hit by pitch, catcher's interference, or obstruction); or when he hits a fair ball which causes a preceding runner to be put out for the third out before he himself is put out or reaches first base safely (see also left on base, fielder's choice, force play). A very similar baseball statistic, at bats, counts a subset of plate appearances that end under certain circumstances.

Use as batting record qualifier
At bats - rather than plate appearances - are used to calculate batting averages, slugging percentages. However, starting in 1957, at season's end a player must have accumulated 3.1 times the number of games scheduled for each team (502 plate appearances for a 162-game season) during a season to be ranked as a league-leader in certain statistical categories. For example, Player A gets 100 hits in 400 at bats over 510 plate appearances, which works out to a .250 batting average (equivalent to one hit in every four at-bats). Alternatively, Player B gets 110 hits in 400 at bats over 490 plate appearances during the same season, finishing with a .275 batting average. Player B, even though he had the same amount of at bats as Player A and even though his batting average is higher, will not be eligible for certain percentage-based season-ending rankings because he did not accumulate the required 502 plate appearances, while Player A did and therefore will be eligible. There is, however, an exception:

Exception for batting titles
Rule 9.22(a) of the Official Baseball Rules make a single allowance to the minimum requirement of 502 plate appearances for the purposes of determining the batting, slugging or on-base percentage title. If a player:

 * leads the league in one of the statistics;
 * does not have the required 502 plate appearances; and
 * would still lead the league in that statistic if as many at bats (without hits or reaching base) were added to his records as necessary to meet the requirement,

he will win that title, but with his original statistic (before the extra at bats were added).

In the example above, Player B is 12 plate appearances short of the required 502, but were he be charged with 12 additional unproductive at bats, he would go 110-for-412 for a batting average of .267. If no one else has a batting average (similarly modified if appropriate) higher than .267, player B will be awarded the batting title (with his original batting average of .275) despite the lack of 502 plate appearances.

In a real-life example, in 2012, Melky Cabrera, then of the San Francisco Giants, finished the season with a league-high .346 batting average, but he had only 501 plate appearances, one short of the required 502. Per the rule, he would have won the batting title because after an extra at bat is added and his batting average recalculated, he still would have led the league in batting average. Cabrera's case, however, turned out differently. The reason Cabrera finished the season with only 501 plate appearances was because he was suspended in mid-August when he tested positive for illegal performance-enhancing drugs. Cabrera was still eligible for that extra at bat, but he requested that the extra at bat not be added to his total, and that he not be considered for the batting crown, because he admitted that his use of performance-enhancing drugs had given him an unfair advantage over other players. As a result, Cabrera's name is nowhere to be found on the list of 2012 National League batting leaders.

Scoring
A batter is not credited with a plate appearance if, while batting, a preceding runner is put out on the basepaths for the third out in a way other than by the batter putting the ball into play (i.e., picked off, caught stealing). In this case, the same batter continues his turn batting in the next inning with no balls or strikes against him.

A batter is not credited with a plate appearance if, while batting, the game ends as the winning run scores from third base on a balk, stolen base, wild pitch or passed ball.

A batter may or may not be credited with a plate appearance (and possibly at bat) in the rare instance when he is replaced by a pinch hitter after having already started his turn at bat. Under Rule 9.15(b), the pinch hitter would receive the plate appearance (and potential of an at-bat) unless the original batter is replaced when having 2 strikes against him and the pinch hitter subsequently completes the strikeout, in which case the plate appearance and at-bat are charged to the first batter.

Relation to at bat
Under Official Baseball Rule 9.02(a)(1), an at bat results from a completed plate appearance, unless the batter:

 * hits a sacrifice bunt or sacrifice fly; or
 * is awarded first base on four called balls; or
 * is hit by a pitched ball; or
 * is awarded first base because of interference or obstruction.

In common parlance, the term "at bat" is sometimes used to mean "plate appearance" (for example, "he fouled off the ball to keep the at bat alive"). The intent is usually clear from the context, although the term "official at bat" is sometimes used to explicitly refer to an at bat as distinguished from a plate appearance. However, terms such as turn at bat or time at bat are synonymous with plate appearance.

"Time at bat" in the rulebook
Official Baseball Rule 5.06(c) provides that "[a] batter has legally completed his time at bat when he is put out or becomes a runner" (emphasis added). The "time at bat" defined in this rule is more commonly referred to as a plate appearance, and the playing rules (Rules 1 through 8) uses the phrase "time at bat" in this sense (e.g. Rule 5.04(a)(3), which states that "[t]he first batter in each inning after the first inning shall be the player whose name follows that of the last player who legally completed his time at bat in the preceding inning" (emphasis added)). In contrast, the scoring rules uses the phrase "time at bat" to refer to the statistic at bat, defined in Rule 9.02(a)(1), but sometimes uses the phrase "official time at bat" or refers back to Rule 9.02(a)(1) when mentioning the statistic. The phrase "plate appearance" is used in Rules 9.22 and 9.23 dealing with batting titles and hitting streaks, and in Rule 5.10(g) Comment in relation to the Three-Batter Minimum: "[t]o qualify as one of three consecutive batters, the batter must complete his plate appearance, which ends only when the batter is put out or becomes a runner." (emphasis added) The term is not elsewhere defined in the rulebook.

In on-base percentage
Plate appearances are a primary component in calculating on-base percentage (OBP), an alternative measurement of a player's offensive performance, but are not the only one in determining its denominator.

By rule, certain plate appearances, such as times reached base via either catcher's interference or fielder's obstruction or sacrifice bunts, are excluded from it, leaving the denominator determined instead as the sum of at-bats, walks, hit-by-pitches, and sacrifice flies. And the numerator represented by a batter's times on base (composed of the sum of hits, base on balls, and times hit by pitch).

Other uses
Plate appearances are used by scorers for "proving" a box score. Under Rule 9.03(c), the following two items should be equal for each team, because each is equal to the team's total number of plate appearances:

 * The sum of the team's at bats, walks, hit by pitches, sacrifices (both bunts and flies), and times awarded first base on interference or obstruction.
 * The sum of the team's runs, runners left on base, and men put out.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

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Games played

Games played (GP) is a statistic used in team sports to indicate the total number of games in which a player has participated (in any capacity); the statistic is generally applied irrespective of whatever portion of the game is contested.

Association football
In association football, a game played is counted if a player is in the starting 11, or if a reserve player enters the game before full-time.

Baseball
In baseball, the statistic applies to players, who prior to a game, are included on a starting lineup card or are announced as an ex ante substitute, whether or not they play. For pitchers only, the statistic games pitched is used.

A notable example of the application of the above rule is pitcher Larry Yount, who suffered an injury while throwing warmup pitches after being summoned as a reliever in a Major League Baseball (MLB) game on September 15, 1971. He did not face a batter, but was credited with an appearance because he had been announced as a substitute. Yount never appeared in (or actually played in) any other MLB game.

Basketball
Robert Parish has the NBA record for most regular season games played, with 1,611. A.C. Green has the NBA record for most consecutive games played, with 1,192.

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Boogie Down Productions

Boogie Down Productions (BDP) was an American hip hop group originally composed of KRS-One, D-Nice, and DJ Scott La Rock. DJ Scott La Rock was murdered on August 27, 1987, five months after the release of BDP's debut album, Criminal Minded. The name of the group, Boogie Down, derives from a nickname for the South Bronx section of New York City. The group pioneered the fusion of dancehall reggae and hip hop music and their debut LP Criminal Minded contained frank descriptions of life in the South Bronx during the late 1980s, thus setting the stage for what would eventually become gangsta rap.

Members
BDP's membership changed throughout its existence, the only constant being KRS-One. The group was founded by KRS-One and DJ Scott La Rock, with producer Lee Smith, who was essential in the production of the songs on Criminal Minded, being added as a member shortly after. From those beginnings, BDP members and collaborators included Ced Gee of Ultramagnetic MC's, Lee Smith, Scott La Rock, D-Nice, Henry Wilkerson PoppyDa, Kenny Parker (KRS-One's younger brother), Just-Ice, ICU, McBoo, Ms. Melodie, Heather B., Scottie Morris, Tony Rahsan, Willie D., RoboCop, Harmony, DJ Red Alert, Jay Kramer, D-Square, Rebekah Foster, Scott Whitehill, Scott King, Chris Tait and Sidney Mills. BDP as a group essentially ended because KRS-One began recording and performing under his own name rather than the group name. Lee Smith, who has co-producer credit on the original 12" "South Bronx" single, was the first to be jettisoned by KRS-One and the future new label after Scott's death.

In the liner notes on BDP's 1992 album Sex and Violence, KRS-One writes: "BDP in 1992 is KRS-One, Willie D, and Kenny Parker! BDP is not D-Nice, Jamal-Ski, Harmony, Ms. Melodie, and Scottie Morris. They are not down with BDP so stop frontin'." Steve "Flash" Juon of RapReviews.com claimed that this initiated the ultimate breakup of the group.

"The Bridge Wars"
A conflict arose in the late 1980s concerning the origins of hip-hop, and BDP made conscious efforts in its early work to establish its interpretation of the issue. The origins of hip-hop to many, including BDP, are believed to be from the Bronx. A rival hip-hop collective, known as the Juice Crew's lyrics, were misunderstood to contain a claim in the song "The Bridge" that hip hop was directly a result of artists originating from Queensbridge. Boogie Down and KRS retorted angrily with songs such as "The Bridge is Over" and "South Bronx," which started one of the first notable hip hop wars as MC Shan, Marley Marl, Roxanne Shanté and Blaq Poet all released songs featuring verses personally attacking KRS and Scott La Rock. But the Bridge Wars were short-lived, and after Scott La Rock's death, KRS began to concentrate on socially conscious music.

While Criminal Minded contained vivid descriptions of South Bronx street life, BDP changed after Scott's death. Lee Smith was dropped and KRS-One adopted the Teacha moniker and made a deliberate attempt at creating politically and socially conscious hip-hop. BDP was influential in provoking political and social consciousness in hip-hop, for example in "Stop The Violence" on 1988's By All Means Necessary.

Jamaican inspirations
The Jamaican influence in Criminal Minded is well illustrated by the use of the "Mad Mad" or "Diseases" riddim started in 1981 with reggae star Yellowman's song "Zunguzunguzeng." BDP used this riff in the song "Remix for P is Free," and it was later resampled by artists such as Black Star and dead prez. As an album regarded by many as the start of the gangsta rap movement, Criminal Minded played an important role in reaffirming the social acceptance of having Jamaican roots. BDP referenced reggae in a way that helped to solidify Jamaica's place in modern hip-hop culture.

Political and social activism
From its start, BDP affected the development of hip-hop and gave a sincere voice to the reality of life in the South Bronx, a section of New York City clouded with poverty and crime. With Criminal Minded, the group combined the sounds of LaRock's harsh, spare, reggae-influenced beats and KRS-One's long-winded rhyme style on underground classics such as "9mm Goes Bang" and "South Bronx," the album's gritty portrait of life on the streets (as well as the firearms that adorned its cover) influenced the gangsta rap movement that began in earnest two years later.

BDP's influence in the creation and development of gangsta rap highlights the cultural significance and impact of the type of music BDP and other early hip-hop artists like it created. This subgenre of hip-hop is most closely associated with hard-core hip-hop and is widely misinterpreted as promoting violence and gang activity. This misinterpretation or stigma is closely related to Boogie Down Productions and the general purpose behind their underlying themes of violence. For instance, the cover art of Criminal Minded displays the two artists in the group brandishing drawn guns and displaying other firearms. This is not an encouragement of the violence described in BDP's music, but a portrayal of the violence in the South Bronx as a means of expression, escape, and even condemnation. This album art is not meant to advocate violence but to challenge the conception of a criminal, to assert that those who are really criminally minded are those who hold power.

BDP's music became significantly more politically astute after Scott La Rock's death. KRS-One published four more albums under the title Boogie Down Productions, and each was increasingly innovative and expanded from the thuggish imagery of Criminal Minded, exploring themes like black-on-black crime and black radicalism, using a riff on the words of Malcolm X, "by any means necessary", which became the title of the second BDP album, and remains one of the most political hip-hop albums to date. It was in this album that KRS defined himself as the "teacha" or "teacher", symbolizing his emphasis on educating his audience members and fans about relevant social issues surrounding the African-American experience.

During his time in association with Boogie Down Productions, KRS-One joined other rappers to create the Stop the Violence Movement, which addressed many of the issues brought up in BDP's music and is the most conscious effort displayed by KRS-One and BDP of political activism and engagement. The movement created the single "Self-Destruction" in 1989 through the collaboration of BDP (KRS-One, D-Nice & Ms. Melodie), Stetsasonic (Delite, Daddy-O, Wise, and Frukwan), Kool Moe Dee, MC Lyte, Doug E. Fresh, Just-Ice, Heavy D, Biz Markie, and Public Enemy (Chuck D & Flavor Flav), with the aim of spreading awareness about violence in African-American and hip-hop communities. All proceeds from this effort went to the National Urban League.

Studio albums

 * Criminal Minded (1987)
 * By All Means Necessary (1988)
 * Ghetto Music: The Blueprint of Hip Hop (1989)
 * Edutainment (1990)
 * Sex and Violence (1992)

title: Boogie Down Productions


text:
Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow).

In byte-oriented systems (i.e. most modern computers), the term unpacked BCD usually implies a full byte for each digit (often including a sign), whereas packed BCD typically encodes two digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9. The precise four-bit encoding, however, may vary for technical reasons (e.g. Excess-3).

The ten states representing a BCD digit are sometimes called tetrades (the nibble typically needed to hold them is also known as a tetrade) while the unused, don't care-states are named,     pseudo-decimals or pseudo-decimal digits.

BCD's main virtue, in comparison to binary positional systems, is its more accurate representation and rounding of decimal quantities, as well as its ease of conversion into conventional human-readable representations. Its principal drawbacks are a slight increase in the complexity of the circuits needed to implement basic arithmetic as well as slightly less dense storage.

BCD was used in many early decimal computers, and is implemented in the instruction set of machines such as the IBM System/360 series and its descendants, Digital Equipment Corporation's VAX, the Burroughs B1700, and the Motorola 68000-series processors.

BCD per se is not as widely used as in the past, and is unavailable or limited in newer instruction sets (e.g., ARM; x86 in long mode). However, decimal fixed-point and decimal floating-point formats are still important and continue to be used in financial, commercial, and industrial computing, where the subtle conversion and fractional rounding errors that are inherent in binary floating point formats cannot be tolerated.

Background
BCD takes advantage of the fact that any one decimal numeral can be represented by a four-bit pattern. An obvious way of encoding digits is Natural BCD (NBCD), where each decimal digit is represented by its corresponding four-bit binary value, as shown in the following table. This is also called "8421" encoding.

This scheme can also be referred to as Simple Binary-Coded Decimal (SBCD) or BCD 8421, and is the most common encoding. Others include the so-called "4221" and "7421" encoding – named after the weighting used for the bits – and "Excess-3". For example, the BCD digit 6, 0110'b in 8421 notation, is 1100'b in 4221 (two encodings are possible), 0110'b in 7421, while in Excess-3 it is 1001'b ($$6 + 3 = 9$$).

The following table represents decimal digits from 0 to 9 in various BCD encoding systems. In the headers, the " " indicates the weight of each bit. In the fifth column ("BCD 84−2−1"), two of the weights are negative. Both ASCII and EBCDIC character codes for the digits, which are examples of zoned BCD, are also shown.

As most computers deal with data in 8-bit bytes, it is possible to use one of the following methods to encode a BCD number:
 * Unpacked: Each decimal digit is encoded into one byte, with four bits representing the number and the remaining bits having no significance.
 * Packed: Two decimal digits are encoded into a single byte, with one digit in the least significant nibble (bits 0 through 3) and the other numeral in the most significant nibble (bits 4 through 7).

As an example, encoding the decimal number  using unpacked BCD results in the following binary pattern of two bytes: Decimal:        9         1 Binary : 0000 1001 0000 0001

In packed BCD, the same number would fit into a single byte: Decimal:   9    1 Binary : 1001 0001

Hence the numerical range for one unpacked BCD byte is zero through nine inclusive, whereas the range for one packed BCD byte is zero through ninety-nine inclusive.

To represent numbers larger than the range of a single byte any number of contiguous bytes may be used. For example, to represent the decimal number  in packed BCD, using big-endian format, a program would encode as follows: Decimal:   0    1    2    3    4    5 Binary : 0000 0001 0010 0011 0100 0101

Here, the most significant nibble of the most significant byte has been encoded as zero, so the number is stored as  (but formatting routines might replace or remove leading zeros). Packed BCD is more efficient in storage usage than unpacked BCD; encoding the same number (with the leading zero) in unpacked format would consume twice the storage.

Shifting and masking operations are used to pack or unpack a packed BCD digit. Other bitwise operations are used to convert a numeral to its equivalent bit pattern or reverse the process.

Packed BCD
In packed BCD (or packed decimal ), each nibble represents a decimal digit. Packed BCD has been in use since at least the 1960s and is implemented in all IBM mainframe hardware since then. Most implementations are big endian, i.e. with the more significant digit in the upper half of each byte, and with the leftmost byte (residing at the lowest memory address) containing the most significant digits of the packed decimal value. The lower nibble of the rightmost byte is usually used as the sign flag, although some unsigned representations lack a sign flag.

As an example, a 4-byte value consists of 8 nibbles, wherein the upper 7 nibbles store the digits of a 7-digit decimal value, and the lowest nibble indicates the sign of the decimal integer value. Standard sign values are 1100 (hex C) for positive (+) and 1101 (D) for negative (−). This convention comes from the zone field for EBCDIC characters and the signed overpunch representation.

Other allowed signs are 1010 (A) and 1110 (E) for positive and 1011 (B) for negative. IBM System/360 processors will use the 1010 (A) and 1011 (B) signs if the A bit is set in the PSW, for the ASCII-8 standard that never passed. Most implementations also provide unsigned BCD values with a sign nibble of 1111 (F). ILE RPG uses 1111 (F) for positive and 1101 (D) for negative. These match the EBCDIC zone for digits without a sign overpunch. In packed BCD, the number 127 is represented by 0001 0010 0111 1100 (127C) and −127 is represented by 0001 0010 0111 1101 (127D). Burroughs systems used 1101 (D) for negative, and any other value is considered a positive sign value (the processors will normalize a positive sign to 1100 (C)).

No matter how many bytes wide a word is, there is always an even number of nibbles because each byte has two of them. Therefore, a word of n bytes can contain up to (2n)−1 decimal digits, which is always an odd number of digits. A decimal number with d digits requires $1⁄2$(d+1) bytes of storage space.

For example, a 4-byte (32-bit) word can hold seven decimal digits plus a sign and can represent values ranging from ±9,999,999. Thus the number −1,234,567 is 7 digits wide and is encoded as: 0001 0010 0011 0100 0101 0110 0111 1101 1   2    3    4    5    6    7    −

Like character strings, the first byte of the packed decimal – that with the most significant two digits –  is usually stored in the lowest address in memory, independent of the endianness of the machine.

In contrast, a 4-byte binary two's complement integer can represent values from −2,147,483,648 to +2,147,483,647.

While packed BCD does not make optimal use of storage (using about 20% more memory than binary notation to store the same numbers), conversion to ASCII, EBCDIC, or the various encodings of Unicode is made trivial, as no arithmetic operations are required. The extra storage requirements are usually offset by the need for the accuracy and compatibility with calculator or hand calculation that fixed-point decimal arithmetic provides. Denser packings of BCD exist which avoid the storage penalty and also need no arithmetic operations for common conversions.

Packed BCD is supported in the COBOL programming language as the "COMPUTATIONAL-3" (an IBM extension adopted by many other compiler vendors) or "PACKED-DECIMAL" (part of the 1985 COBOL standard) data type. It is supported in PL/I as "FIXED DECIMAL". Beside the IBM System/360 and later compatible mainframes, packed BCD is implemented in the native instruction set of the original VAX processors from Digital Equipment Corporation and some models of the SDS Sigma series mainframes, and is the native format for the Burroughs Medium Systems line of mainframes (descended from the 1950s Electrodata 200 series).

Ten's complement representations for negative numbers offer an alternative approach to encoding the sign of packed (and other) BCD numbers. In this case, positive numbers always have a most significant digit between 0 and 4 (inclusive), while negative numbers are represented by the 10's complement of the corresponding positive number.

As a result, this system allows for 32-bit packed BCD numbers to range from −50,000,000 to +49,999,999, and −1 is represented as 99999999. (As with two's complement binary numbers, the range is not symmetric about zero.)

Fixed-point packed decimal
Fixed-point decimal numbers are supported by some programming languages (such as COBOL and PL/I). These languages allow the programmer to specify an implicit decimal point in front of one of the digits.

For example, a packed decimal value encoded with the bytes 12 34 56 7C represents the fixed-point value +1,234.567 when the implied decimal point is located between the fourth and fifth digits: 12 34 56 7C 12 34.56 7+

The decimal point is not actually stored in memory, as the packed BCD storage format does not provide for it. Its location is simply known to the compiler, and the generated code acts accordingly for the various arithmetic operations.

Higher-density encodings
If a decimal digit requires four bits, then three decimal digits require 12 bits. However, since 210 (1,024) is greater than 103 (1,000), if three decimal digits are encoded together, only 10 bits are needed. Two such encodings are Chen–Ho encoding and densely packed decimal (DPD). The latter has the advantage that subsets of the encoding encode two digits in the optimal seven bits and one digit in four bits, as in regular BCD.

Zoned decimal
Some implementations, for example IBM mainframe systems, support zoned decimal numeric representations. Each decimal digit is stored in one byte, with the lower four bits encoding the digit in BCD form. The upper four bits, called the "zone" bits, are usually set to a fixed value so that the byte holds a character value corresponding to the digit. EBCDIC systems use a zone value of 1111 (hex F); this yields bytes in the range F0 to F9 (hex), which are the EBCDIC codes for the characters "0" through "9". Similarly, ASCII systems use a zone value of 0011 (hex 3), giving character codes 30 to 39 (hex).

For signed zoned decimal values, the rightmost (least significant) zone nibble holds the sign digit, which is the same set of values that are used for signed packed decimal numbers (see above). Thus a zoned decimal value encoded as the hex bytes F1 F2 D3 represents the signed decimal value −123: F1 F2 D3 1 2 −3

EBCDIC zoned decimal conversion table
(*) Note: These characters vary depending on the local character code page setting.

Fixed-point zoned decimal
Some languages (such as COBOL and PL/I) directly support fixed-point zoned decimal values, assigning an implicit decimal point at some location between the decimal digits of a number.

For example, given a six-byte signed zoned decimal value with an implied decimal point to the right of the fourth digit, the hex bytes F1 F2 F7 F9 F5 C0 represent the value +1,279.50: F1 F2 F7 F9 F5 C0 1 2  7  9. 5 +0

Addition
It is possible to perform addition by first adding in binary, and then converting to BCD afterwards. Conversion of the simple sum of two digits can be done by adding 6 (that is, 16 − 10) when the five-bit result of adding a pair of digits has a value greater than 9. The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 24 = 16), but only 10 values are valid (0000 through 1001). For example: 1001 + 1000 = 10001   9 +    8 =    17 10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit. To correct this, 6 (0110) is added to the total, and then the result is treated as two nibbles: 10001 + 0110 = 00010111 => 0001 0111   17 +    6 =       23       1    7 The two nibbles of the result, 0001 and 0111, correspond to the digits "1" and "7". This yields "17" in BCD, which is the correct result.

This technique can be extended to adding multiple digits by adding in groups from right to left, propagating the second digit as a carry, always comparing the 5-bit result of each digit-pair sum to 9. Some CPUs provide a half-carry flag to facilitate BCD arithmetic adjustments following binary addition and subtraction operations. The Intel 8080, the Zilog Z80 and the CPUs of the x86 family provide the opcode DAA (Decimal Adjust Accumulator).

Subtraction
Subtraction is done by adding the ten's complement of the subtrahend to the minuend. To represent the sign of a number in BCD, the number 0000 is used to represent a positive number, and 1001 is used to represent a negative number. The remaining 14 combinations are invalid signs. To illustrate signed BCD subtraction, consider the following problem: 357 − 432.

In signed BCD, 357 is 0000 0011 0101 0111. The ten's complement of 432 can be obtained by taking the nine's complement of 432, and then adding one. So, 999 − 432 = 567, and 567 + 1 = 568. By preceding 568 in BCD by the negative sign code, the number −432 can be represented. So, −432 in signed BCD is 1001 0101 0110 1000.

Now that both numbers are represented in signed BCD, they can be added together: 0000 0011 0101 0111  0    3    5    7 + 1001 0101 0110 1000   9    5    6    8 = 1001 1000 1011 1111   9    8    11   15 Since BCD is a form of decimal representation, several of the digit sums above are invalid. In the event that an invalid entry (any BCD digit greater than 1001) exists, 6 is added to generate a carry bit and cause the sum to become a valid entry. So, adding 6 to the invalid entries results in the following: 1001 1000 1011 1111  9    8    11   15 + 0000 0000 0110 0110   0    0    6    6 = 1001 1001 0010 0101   9    9    2    5 Thus the result of the subtraction is 1001 1001 0010 0101 (−925). To confirm the result, note that the first digit is 9, which means negative. This seems to be correct since 357 − 432 should result in a negative number. The remaining nibbles are BCD, so 1001 0010 0101 is 925. The ten's complement of 925 is 1000 − 925 = 75, so the calculated answer is −75.

If there are a different number of nibbles being added together (such as 1053 − 2), the number with the fewer digits must first be prefixed with zeros before taking the ten's complement or subtracting. So, with 1053 − 2, 2 would have to first be represented as 0002 in BCD, and the ten's complement of 0002 would have to be calculated.

IBM
IBM used the terms Binary-Coded Decimal Interchange Code (BCDIC, sometimes just called BCD), for 6-bit alphanumeric codes that represented numbers, upper-case letters and special characters. Some variation of BCDIC alphamerics is used in most early IBM computers, including the IBM 1620 (introduced in 1959), IBM 1400 series, and non-decimal architecture members of the IBM 700/7000 series.

The IBM 1400 series are character-addressable machines, each location being six bits labeled B, A, 8, 4, 2 and 1, plus an odd parity check bit (C) and a word mark bit (M). For encoding digits 1 through 9, B and A are zero and the digit value represented by standard 4-bit BCD in bits 8 through 1. For most other characters bits B and A are derived simply from the "12", "11", and "0" "zone punches" in the punched card character code, and bits 8 through 1 from the 1 through 9 punches. A "12 zone" punch set both B and A, an "11 zone" set B, and a "0 zone" (a 0 punch combined with any others) set A. Thus the letter A, which is (12,1) in the punched card format, is encoded (B,A,1). The currency symbol $, (11,8,3) in the punched card, was encoded in memory as (B,8,2,1). This allows the circuitry to convert between the punched card format and the internal storage format to be very simple with only a few special cases. One important special case is digit 0, represented by a lone 0 punch in the card, and (8,2) in core memory.

The memory of the IBM 1620 is organized into 6-bit addressable digits, the usual 8, 4, 2, 1 plus F, used as a flag bit and C, an odd parity check bit. BCD alphamerics are encoded using digit pairs, with the "zone" in the even-addressed digit and the "digit" in the odd-addressed digit, the "zone" being related to the 12, 11, and 0 "zone punches" as in the 1400 series. Input/output translation hardware converted between the internal digit pairs and the external standard 6-bit BCD codes.

In the decimal architecture IBM 7070, IBM 7072, and IBM 7074 alphamerics are encoded using digit pairs (using two-out-of-five code in the digits, not BCD) of the 10-digit word, with the "zone" in the left digit and the "digit" in the right digit. Input/output translation hardware converted between the internal digit pairs and the external standard 6-bit BCD codes.

With the introduction of System/360, IBM expanded 6-bit BCD alphamerics to 8-bit EBCDIC, allowing the addition of many more characters (e.g., lowercase letters). A variable length packed BCD numeric data type is also implemented, providing machine instructions that perform arithmetic directly on packed decimal data.

On the IBM 1130 and 1800, packed BCD is supported in software by IBM's Commercial Subroutine Package.

Today, BCD data is still heavily used in IBM databases such as IBM Db2 and processors such as z/Architecture and POWER6 and later Power ISA processors. In these products, the BCD is usually zoned BCD (as in EBCDIC or ASCII), packed BCD (two decimal digits per byte), or "pure" BCD encoding (one decimal digit stored as BCD in the low four bits of each byte). All of these are used within hardware registers and processing units, and in software.

Other computers
The Digital Equipment Corporation VAX series includes instructions that can perform arithmetic directly on packed BCD data and convert between packed BCD data and other integer representations. The VAX's packed BCD format is compatible with that on IBM System/360 and IBM's later compatible processors. The MicroVAX and later VAX implementations dropped this ability from the CPU but retained code compatibility with earlier machines by implementing the missing instructions in an operating system-supplied software library. This is invoked automatically via exception handling when the defunct instructions are encountered, so that programs using them can execute without modification on the newer machines.

Many processors have hardware support for BCD-encoded integer arithmetic. For example the 6502, the Motorola 68000 series, and the x86 series. The Intel x86 architecture supports a unique 18-digit (ten-byte) BCD format that can be loaded into and stored from the floating point registers, from where computations can be performed.

In more recent computers such capabilities are almost always implemented in software rather than the CPU's instruction set, but BCD numeric data are still extremely common in commercial and financial applications.

There are tricks for implementing packed BCD and zoned decimal add–or–subtract operations using short but difficult to understand sequences of word-parallel logic and binary arithmetic operations. For example, the following code (written in C) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations:

BCD in electronics
BCD is common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor. By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub-circuit.

This matches much more closely the physical reality of display hardware—a designer might choose to use a series of separate identical seven-segment displays to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing with such a display would require complex circuitry. Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to an overall simpler system than converting to and from binary. Most pocket calculators do all their calculations in BCD.

The same argument applies when hardware of this type uses an embedded microcontroller or other small processor. Often, representing numbers internally in BCD format results in smaller code, since a conversion from or to binary representation can be expensive on such limited processors. For these applications, some small processors feature dedicated arithmetic modes, which assist when writing routines that manipulate BCD quantities.

Advantages

 * Scaling by a power of 10 is simple.
 * Rounding at a decimal digit boundary is simpler. Addition and subtraction in decimal do not require rounding.
 * The alignment of two decimal numbers (for example 1.3 + 27.08) is a simple, exact shift.
 * Conversion to a character form or for display (e.g., to a text-based format such as XML, or to drive signals for a seven-segment display) is a simple per-digit mapping, and can be done in linear (O(n)) time. Conversion from pure binary involves relatively complex logic that spans digits, and for large numbers, no linear-time conversion algorithm is known (see ).
 * Many non-integral values, such as decimal 0.2, have an infinite place-value representation in binary (.001100110011...) but have a finite place-value in binary-coded decimal (0.0010). Consequently, a system based on binary-coded decimal representations of decimal fractions avoids errors representing and calculating such values. This is useful in financial calculations.

Disadvantages

 * Practical existing implementations of BCD are typically slower than operations on binary representations, especially on embedded systems, due to limited processor support for native BCD operations.
 * Some operations are more complex to implement. Adders require extra logic to cause them to wrap and generate a carry early. Also, 15 to 20 per cent more circuitry is needed for BCD add compared to pure binary. Multiplication requires the use of algorithms that are somewhat more complex than shift-mask-add (a binary multiplication, requiring binary shifts and adds or the equivalent, per-digit or group of digits is required).
 * Standard BCD requires four bits per digit, roughly 20 per cent more space than a binary encoding (the ratio of 4 bits to log210 bits is 1.204). When packed so that three digits are encoded in ten bits, the storage overhead is greatly reduced, at the expense of an encoding that is unaligned with the 8-bit byte boundaries common on existing hardware, resulting in slower implementations on these systems.

Representational variations
Various BCD implementations exist that employ other representations for numbers. Programmable calculators manufactured by Texas Instruments, Hewlett-Packard, and others typically employ a floating-point BCD format, typically with two or three digits for the (decimal) exponent. The extra bits of the sign digit may be used to indicate special numeric values, such as infinity, underflow/overflow, and error (a blinking display).

Signed variations
Signed decimal values may be represented in several ways. The COBOL programming language, for example, supports five zoned decimal formats, with each one encoding the numeric sign in a different way:

Telephony binary-coded decimal (TBCD)
3GPP developed TBCD, an expansion to BCD where the remaining (unused) bit combinations are used to add specific telephony characters, with digits similar to those found in telephone keypads original design.

The mentioned 3GPP document defines TBCD-STRING with swapped nibbles in each byte. Bits, octets and digits indexed from 1, bits from the right, digits and octets from the left. bits 8765 of octet n encoding digit 2n

bits 4321 of octet n encoding digit 2(n – 1) + 1

Meaning number, would become   in TBCD.

Alternative encodings
If errors in representation and computation are more important than the speed of conversion to and from display, a scaled binary representation may be used, which stores a decimal number as a binary-encoded integer and a binary-encoded signed decimal exponent. For example, 0.2 can be represented as 2.

This representation allows rapid multiplication and division, but may require shifting by a power of 10 during addition and subtraction to align the decimal points. It is appropriate for applications with a fixed number of decimal places that do not then require this adjustment—particularly financial applications where 2 or 4 digits after the decimal point are usually enough. Indeed, this is almost a form of fixed point arithmetic since the position of the radix point is implied.

The Hertz and Chen–Ho encodings provide Boolean transformations for converting groups of three BCD-encoded digits to and from 10-bit values that can be efficiently encoded in hardware with only 2 or 3 gate delays. Densely packed decimal (DPD) is a similar scheme that is used for most of the significand, except the lead digit, for one of the two alternative decimal encodings specified in the IEEE 754-2008 floating-point standard.

Application
The BIOS in many personal computers stores the date and time in BCD because the MC6818 real-time clock chip used in the original IBM PC AT motherboard provided the time encoded in BCD. This form is easily converted into ASCII for display.

The Atari 8-bit computers use a BCD format for floating point numbers. The MOS Technology 6502 processor has a BCD mode for the addition and subtraction instructions. The Psion Organiser 1 handheld computer's manufacturer-supplied software also uses BCD to implement floating point; later Psion models use binary exclusively.

Early models of the PlayStation 3 store the date and time in BCD. This led to a worldwide outage of the console on 1 March 2010. The last two digits of the year stored as BCD were misinterpreted as 16 causing an error in the unit's date, rendering most functions inoperable. This has been referred to as the Year 2010 problem.

Legal history
In the 1972 case Gottschalk v. Benson, the U.S. Supreme Court overturned a lower court's decision that had allowed a patent for converting BCD-encoded numbers to binary on a computer.

The decision noted that a patent "would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself". This was a landmark judgement that determined the patentability of software and algorithms.

title: Binary-coded decimal


text:
BCD

BCD may refer to:

Computing

 * Binary-coded decimal, a representation of decimal digits in binary
 * BCD (character encoding), a 6-bit superset of binary-coded decimal derived from the binary encoding of the same name
 * Boot Configuration Data, the configuration data required to boot Microsoft Windows Vista and later
 * Bipolar-CMOS-DMOS, a type of BiCMOS semiconductor technology

Organisations

 * Basnahira Cricket Dundee, a Sri Lankan cricket team
 * BCD Tofu House, a Los Angeles-based Korean restaurant chain
 * BCD Travel, a provider of global corporate travel management
 * Belarusian Christian Democracy, a Christian-democratic political party in Belarus.
 * Berkshire Country Day School, an independent school in Lenox, Massachusetts, US
 * Bid Closing Date The closing date for a bid is a specific date (and usually a specific time) when the bid is closed to the public for bid submissions. At this point, only the submitted proposals will be considered eligible.
 * The British Columbia Dragoons, a Canadian Forces armoured regiment
 * Battlefield Coordination Detachment, is the senior United States Army liaison element of the Army Air Ground System.

Places

 * Bacolod–Silay International Airport (IATA code), Silay City, Philippines
 * Beirut Central District, Beirut, Lebanon

Other uses

 * Bad conduct discharge, a form of discharge from US military service, sometimes referred to colloquially as a "big chicken dinner".
 * Barrels per calendar day, a unit for measuring output of oil refineries
 * Blue compact dwarf galaxy, a small galaxy which contains large clusters of young, hot, massive stars
 * Board-certified diplomate, in the list of credentials in psychology
 * Buoyancy control device, in scuba diving
 * Bolt circle diameter, for example, of a crankset, of a bicycle disc brake, or in wheel sizing
 * "Behind closed doors", a marketing term for previewing a product to a select audience

title: BCD


text:
Binary

Binary may refer to:

Mathematics

 * Binary number, a representation of numbers using only two digits (0 and 1)
 * Binary function, a function that takes two arguments
 * Binary operation, a mathematical operation that takes two arguments
 * Binary relation, a relation involving two elements
 * Binary-coded decimal, a method for encoding for decimal digits in binary sequences
 * Finger binary, a system for counting in binary numbers on the fingers of human hands

Computing

 * Binary code, the representation of text and data using only the digits 1 and 0
 * Bit, or binary digit, the basic unit of information in computers
 * Binary file, composed of something other than human-readable text
 * Executable, a type of binary file that contains machine code for the computer to execute
 * Binary tree, a computer tree data structure in which each node has at most two children

Astronomy

 * Binary star, a star system with two stars in it
 * Binary planet, two planetary bodies of comparable mass orbiting each other
 * Binary asteroid, two asteroids orbiting each other

Biology

 * Binary fission, the splitting of a single-celled organism into two daughter cells

Chemistry

 * Binary phase, a chemical compound containing two different chemical elements

Arts and entertainment

 * Binary (Doctor Who audio)

Marvel Comics

 * Binary, the name of two superheroines in the Marvel Universe
 * Binary (Carol Danvers), a Marvel Comics character
 * Binary (Marvel Cinematic Universe), or Maria Rambeau, a Marvel Cinematic Universe character

Music

 * Binary form, a way of structuring a piece of music
 * Binary (Ani DiFranco album), 2017
 * Binary (Kay Tse album), 2008
 * "Binary" (song), a 2007 single by Assemblage 23

Novel

 * Binary (novel), a 1972 novel by Michael Crichton (writing as John Lange)
 * Binary, an evil organization in the novel InterWorld

Other uses

 * Binary opposition, polar opposites, often ignoring the middle ground
 * Gender binary, the classification of sex and gender into two distinct and disconnected forms of masculine and feminine

title: Binary


text:
Bumin Qaghan

Bumin Qaghan (𐰉𐰆𐰢𐰣:𐰴𐰍𐰣, also known as Illig Qaghan (Chinese: 伊利可汗, Pinyin: Yīlì Kèhán, Wade–Giles: i-li k'o-han) or Yamï Qaghan (𐰖𐰢𐰃:𐰴𐰍𐰣, died 552 AD) was the founder of the Turkic Khaganate. He was the eldest son of Ashina Tuwu (吐務 / 吐务). He was the chieftain of the Turks under the sovereignty of Rouran Khaganate.   He is also mentioned as Tumen (,, commander of ten thousand ) of the Rouran Khaganate.

Early life and reign
According to History of Northern Dynasties and Zizhi Tongjian, in 545 Tumen's tribe started to rise and frequently invaded the western frontier of Wei. The chancellor of Western Wei, Yuwen Tai, sent An Nuopanto (安諾盤陀, Nanai-Banda, a Sogdian from Bukhara, ) as an emissary to the Göktürk chieftain Tumen, in an attempt to establish a commercial relationship. In 546, Tumen paid tribute to the Western Wei state. In that same year, Tumen put down a revolt of the Tiele tribes against the Rouran Khaganate, their overlords. Following this, Tumen felt entitled to request of the Rouran a princess as his wife. The Rouran khagan, Anagui, sent a message refusing this request and adding: "You are my blacksmith slave. How dare you utter these words?" Bumin got angry, killed Anagui's emissary, and severed relations with the Rouran Khaganate. Anagui's "blacksmith" (鍛奴 / 锻奴, Pinyin: duàn nú, Wade–Giles: tuan-nu) insult was recorded in Chinese chronicles. Some sources state that members of the Turks (referred as "Tujue" in Chinese sources) did serve as blacksmiths for the Rouran elite,  and that "blacksmith slavery" may refer to a kind of vassalage that prevailed in Rouran society. Nevertheless, after this incident Bumin emerged as the leader of the revolt against Rouran. In 551, Bumin requested a Western Wei princess in marriage. Yuwen Tai permitted it and sent Princess Changle(長樂公主) of Western Wei to Bumin. In the same year when Emperor Wen of Western Wei died, Bumin sent mission and gave two hundred horses.

The beginning of formal diplomatic relations with China propped up Bumin's authority among the Turks. He eventually united the local Turkic tribes and threw off the yoke of the Rouran domination. In 552 Bumin's army defeated Anagui's forces at the north of Huaihuang and then Anagui committed suicide. With their defeat Bumin proclaimed himself "Illig Qaghan" and made his wife qaghatun. "Illig" means Ilkhan (i.e. ruler of people) in Old Turkic. According to the Bilge Qaghan's memorial complex and the Kul Tigin's memorial complex, Bumin and Istemi ruled people by Turkic laws and they developed them.

Death and family
Bumin died within several months after proclaiming himself Illig Qaghan. He was married to Princess Changle of Western Wei.

Issue:

 * Ashina Keluo (阿史那科罗) - Issig Qaghan
 * Ashina Qijin (阿史那俟斤) - Muqan Qaghan
 * Taspar Qaghan
 * Ashina Kutou (阿史那庫頭) - Ditou Qaghan (appointed by Muqan Qaghan to be lesser khagan of eastern wing of Turkic Empire)
 * Mahan Tigin - Lesser khagan appointed by Taspar Qaghan
 * Rudan Qaghan (褥但可汗)
 * Böri Qaghan (步離可汗) - Lesser khagan of appointed by Taspar Qaghan

Legacy
He was succeeded by his younger brother Istemi in the western part and by his son Issik Qaghan in the eastern part. In less than one century, his khaganate expanded to comprise most of Central Asia.

title: Bumin Qaghan


text:
Bilge Qaghan

Bilge Qaghan (𐰋𐰃𐰠𐰏𐰀:𐰴𐰍𐰣; ; 683 – 25 November 734) was the fourth Qaghan of the Second Turkic Khaganate. His accomplishments were described in the Orkhon inscriptions.

Names
As was the custom, his personal name and the name after assuming the title Qaghan were different. His personal name was recorded in Chinese characters as 阿史那默棘連. His name after assuming the title was Bilgä Qaγan. (𐰋𐰃𐰠𐰏𐰀 𐰴𐰍𐰣, ).

Early years
He was born in 683, in the early years of the khaganate. He campaigned alongside his father from early childhood. He was created as Tardush shad and given command over the western wing of the empire in 697 by Qapaghan. He managed to annihilate Wei Yuanzhong's army in 701 with his brother. He also reconquered Basmyl tribes in 703. He also subdued Yenisei Kyrgyz forces in 709, after their disobedience had to reconquer and kill their Qaghan in 710. He killed Türgesh khagan Suoge at Battle of Bolchu.

In later years of Qapaghan, he had to fight four battles in a year starting from 714, resubduing tribes and nearly was killed in an ambush from Uyghur forces in 716.

Reign
In 716, Qapaghan Qaghan, the second Qaghan, was killed in his campaign against the Toquz Oghuz alliance and his severed head was sent to Chang'an. Although his son Inel Khagan succeeded him, Bilgä's brother Kul Tigin and Tonyukuk carried out a coup d'état against Inel Qaghan. They killed him and made him Bilgä Qaghan. His name literally means "wise king".

He appointed his brother Kul Tigin to be Left Wise Prince, which made second most powerful person in realm. He re-subdued Huige in 716. He also appointed his father-in-law Tonyukuk to be Master Strategist.

New reforms and stabilization of the regime, caused tribes that fled Tujue to come back. Tang chancellor Wang Jun, believing that the Göktürks who surrendered would try to flee back to the Göktürk state, suggested that they be forcibly moved into the heart of the empire to prevent them from doing so. Before Wang's suggestion could be acted upon, however, there was an uprising by the Göktürks who surrendered, under the leadership of Xiedie Sitai (𨁂跌思泰) and Axilan (阿悉爛). Xue and Wang tried to intercept them and dealt them defeats, but they were able to flee back to the Göktürk state anyway. This defeat led to Xue Ne's retirement.

Religious policy
At some point in his life, he thought about converting to Buddhism and settling in cities. However, Tonyukuk discouraged him from this, citing the Turks' few numbers and vulnerability to Chinese attacks. While the Turks' power rested on their mobility, conversion to Buddhism would bring pacifism among the population. Therefore, sticking to Tengrism was necessary for survival.

Later reign
In 720, Wang believed that the Pugu (僕固) and Xiedie tribes of the region were planning to defect to Eastern Tujue and attack with Eastern Tujue troops. He thus held a feast and invited the chieftains, and, at the feast, massacred them. He then attacked the Pugu and Xiedie tribes in the area, nearly wiping them out. He then proposed a plan to attack Qaghan along with the Baximi, Xi, and Khitan. Emperor Xuanzong also recruited Qapaghan Khagan's sons Bilgä Tigin and Mo Tigin, Yenisei Kyrgyz Qaghan Kutluk Bilgä Qaghan and Huoba Guiren to fight against Tujue. Tonyukuk cunningly launched first attack on Baximi in 721 autumn, completely crushing them. Meanwhile, Bilgä raided Gansu, taking much of the livestock. Later that year Khitans, next year Xi were also crushed.

In 726, his father-in-law and chancellor Tonyukuk died.

In 727, he sent Buyruk Chor as an emissary to Xuanzong with 30 horses as a gift. He also warned him of Me Agtsom's proposal of an anti-Tang alliance. This alarm proved to be true when Tibetan general We Tadra Khonglo invaded Tang China in 727, sacked Guazhou (瓜州, in modern Gansu), Changle (常樂, in south of modern Guazhou County), Changmenjun (長門軍, in north of modern Yumen) and Anxi (安西, modern Lintan).

On 27 February 731, Kul Tigin died, for which Qaghan mourned and ordered a great funeral ceremony.

In 733, he defeated rebellious Khitan tribes.

Death
Just after sending an emissary to Xuanzong to gain heqin alliance, he was poisoned by Buyruk Chor. He did not die immediately and he had time to punish the family of Buyruk Chor with death. He died on 25 November 734, his burial ceremony took place on 22 June 735.

Family
He was married to El Etmish Bilge Khatun, Tonyukuk's daughter. He had several children:

 * Ashina Yiran (阿史那伊然)
 * Ashina Kutluk (阿史那骨咄)
 * 2 unnamed sons who both became puppet Qaghans under Kutluk Yabgu Khagan
 * A daughter who was married to Suluk
 * Po Beg - submitted to Tang after 744.

Legacy
After his death from poisoning, several steles were erected in the capital area by the Orkhon River. These Orkhon inscriptions are the first known texts in the Old Turkic language.

In popular culture

 * Bilge Qaghan is portrayed by Kang Jae-ik in the 2006-2007 KBS TV series Dae Jo-yeong.

title: Bilge Qaghan