Editing Binary-coded decimal (section)

{{Short description|System of digitally encoding numbers}}
{{redirect|BCD code|BCD character sets|BCD (character encoding)||}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
{{Use list-defined references|date=January 2022}}
{{anchor|Compressed}}<!-- parked anchor for redirects -->
[[File:Binary clock.svg|250px|thumbnail|right|A [[binary clock]] might use [[Light-emitting diode|LED]]s to express binary values. In this clock, each column of LEDs shows a binary-coded decimal numeral of the traditional [[sexagesimal]] time.]]

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

In [[byte]]-oriented systems (i.e. most modern computers), the term ''unpacked'' BCD<ref name="Intel_IA32"/> 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]]).

{{anchor|Pseudo-tetrade}}The ten states representing a BCD digit are sometimes called ''[[tetrade (computing)|tetrade]]s''<ref name="Klar_1970"/><ref name="Klar_1989"/> (the [[nibble]] typically needed to hold them is also known as a tetrade) while the unused, [[don't care]]-states are named ''pseudo-tetrad(e)s''{{small|{{bracket|[[:de:Pseudotetrade|de]]}}}},<ref name="Schneider_1986"/><ref name="Tafel_1971"/><ref name="Steinbuch-Weber-Heinemann_1974"/><ref name="Tietze-Schenk_2013"/><ref name="Kowalski_1070"/> ''pseudo-decimals'',<ref name="Klar_1989"/> or ''pseudo-decimal digits''.<ref name="Ferretti_2013"/><ref name="Speiser_1965"/><ref group="nb" name="Pseudo-tetrades"/>

BCD's main virtue, in comparison to binary [[positional system]]s, is its more accurate representation and rounding of decimal quantities, as well as its ease of conversion into conventional<!-- many among us can read hexidecimal just fine, though we don't ordinarily memorize the hexadecimal times table --> 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 computer]]s, 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 architecture family|ARM]]; [[x86]] in [[long mode]]). However, decimal [[Fixed-point arithmetic|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 [[round-off error|rounding errors]] that are inherent in binary floating point formats cannot be tolerated.<ref name="Cowlishaw_GDA" />