Binary-coded decimal

In <a href="/facts/Computing/Kghtm9fX">computing</a> and <a href="/facts/Electronics/E4JhgISq">electronic</a> systems, binary-coded decimal (BCD) is a class of <a href="/facts/Binary_number/a6JDSRPs">binary</a> encodings of <a href="/facts/Decimal/7omfVNIM">decimal</a> numbers where each <a href="/facts/Numerical_digit/JJdLBoGT">digit</a> is represented by a fixed number of <a href="/facts/Bit/S972NSaD">bits</a>, usually four or eight. Sometimes, special bit patterns are used for a <a href="/facts/Sign_(mathematics)/z0xollg1">sign</a> or other indications (e.g. error or overflow).
In <a href="/facts/Byte/BNHUp9Qq">byte</a>-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. <a href="/facts/Excess-3/shAvgBtQ">Excess-3</a>).
The ten states representing a BCD digit are sometimes called <a href="/facts/Tetrade_(computing)/PUaqCEVw">tetrades</a> (the <a href="/facts/Nibble/PUaqCEVw">nibble</a> typically needed to hold them is also known as a tetrade) while the unused, <a href="/facts/Don%27t_care/kvQuwYMK">don't care</a>-states are named pseudo-tetrad(e)s[de], pseudo-decimals, or pseudo-decimal digits.
BCD's main virtue, in comparison to binary <a href="/facts/Positional_system/31DECoN4">positional systems</a>, 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 <a href="/facts/Decimal_computer/03q4eQAA">decimal computers</a>, and is implemented in the instruction set of machines such as the <a href="/facts/IBM_System/360/7znvpy4K">IBM System/360</a> series and its descendants, <a href="/facts/Digital_Equipment_Corporation/ztxs6keA">Digital Equipment Corporation</a>'s <a href="/facts/VAX/N3r13IHH">VAX</a>, the <a href="/facts/Burroughs_B1700/80aExR2b">Burroughs B1700</a>, and the Motorola <a href="/facts/68000/3p2wt2D6">68000</a>-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., <a href="/facts/ARM_architecture_family/SALsYA79">ARM</a>; <a href="/facts/X86/Kypq5fgu">x86</a> in <a href="/facts/Long_mode/ITshSuE6">long mode</a>). However, decimal <a href="/facts/Fixed-point_arithmetic/pd3RU72P">fixed-point</a> and decimal <a href="/facts/Floating-point/eIckahxe">floating-point</a> formats are still important and continue to be used in financial, commercial, and industrial computing, where the subtle conversion and fractional <a href="/facts/Round-off_error/aF9N8X4I">rounding errors</a> that are inherent in binary floating point formats cannot be tolerated.

Binary-coded decimal open-in-new

Binary-coded decimal