Binary-coded decimal: Difference between revisions

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==Packed BCD==

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In '''packed BCD''' (or simply '''packed decimal'''<ref name="Dewar-Smosna_1990"/>), each [[nibble]] represent a decimal digit.<ref group="nb" name="Packed_chars"/> 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 ([[hexadecimal|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).<ref name="IBM_1980_POP"/><ref name="DEC_1983_PDP11"/><ref name="DEC_1985_VAX11"/> ILE RPG uses 1111 (F) for positive and 1101 (D) for negative.<ref name="ILE-RPG"/> 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)).