Binary-coded decimal

In byte-oriented systems (i.e. most modern computers), the term unpacked BCD[1] 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.

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.

[11] BCD takes advantage of the fact that any one decimal numeral can be represented by a four-bit pattern.

This scheme can also be referred to as Simple Binary-Coded Decimal (SBCD) or BCD 8421, and is the most common encoding.

For example, to represent the decimal number 12345 in packed BCD, using big-endian format, a program would encode as follows: Here, the most significant nibble of the most significant byte has been encoded as zero, so the number is stored as 012345 (but formatting routines might replace or remove leading zeros).

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.

Denser packings of BCD exist which avoid the storage penalty and also need no arithmetic operations for common conversions.

Some implementations, for example IBM mainframe systems, support zoned decimal numeric representations.

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).

One important special case is digit 0, represented by a lone 0 punch in the card, and (8,2) in core memory.

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).

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.

[47] 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.

[48] 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.

[49] For example, the following code (written in C) computes an unsigned 8-digit packed BCD addition using 32-bit binary operations: 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.

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.

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.

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).

The COBOL programming language, for example, supports five zoned decimal formats, with each one encoding the numeric sign in a different way: 3GPP developed TBCD,[53] an expansion to BCD where the remaining (unused) bit combinations are used to add specific telephony characters,[54][55] with digits similar to those found in telephone keypads original design.

This format is used in modern mobile telephony to send dialed numbers, as well as operator ID (the MCC/MNC tuple), IMEI, IMSI (SUPI), et.c.

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.

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.