Binary Coded Decimal

  Binary coded decimal (BCD) is a method for implementing lossless decimal arithmetic (including decimal fractions) on a binary computer. The most obvious uses involve money amounts where round-off error from using binary approximations is unacceptable. Some early computers used BCD exclusively.

    Decimal digits (0-9) can be encoded in a nibble (half a byte), with some left over bit patterns (hexadecimal A-F). In BCD operations, the processor performs ordinary binary computations, then adjusts the result to conform to BCD. For example, if you add the binary number 5 (bit pattern 0101) to binary number 6 (bit pattern 0110), you get the binary result of 11 (bit pattern 1011, or hexadecimal B). With BCD arithmetic, the processor would adjust the result to make it into a valid BCD result (which in this case would be bit pattern 0001 0001).

    BCD arithmetic includes BCD addition, BCD subtraction, BCD multiplication, BCD division, and BCD negate.

    The Intel 80x86 series uses a two step approach for BCD arithmetic. Instead of having separate BCD instructions, the normal binary addition and subtraction instructions are used, then hardware instructions are used to adjust the results to correct BCD results. There are instuctions for both packed and unpacked adjustments. The advantage of this approach is greater flexibility (more addressing modes and choices of arithmetic operations because of the use of regular binary integer instructions in the first step). The disadvantage of this approach is that it is slower and takes more memory.

    Pack (Motorola 680x0) converts byte encoded numeric data (such as ASCII or EBCDIC characters) into binary coded decimals. Unpack (Motorola 680x0) converts binary coded decimals into byte encoded numeric data (such as ASCII or EBCDIC characters). The ASCII adjustment field is $3030; the EBCDIC adjustment field is $F0F0.

• ABCD Add Decimal with Extend; Motorola 680x0, Motorola 68300; performs binary coded decimal addition of source plus destination plus extend bit, source and destination can be two data registers or two locations in memory with the two address pointer registers being predecremented; sets or clears flags
• SBCD Subtract Decimal with Extend; Motorola 680x0; performs binary coded decimal subtraction of source and extend bit from destination, source and destination can be two data registers or two locations in memory with the two address pointer registers being predecremented; sets or clears flags
• NBCD Negate Decimal with Extend; Motorola 680x0, Motorola 68300; performs tens complement of contents of a data register or memory location by performing decimal coded binary subtraction of destination and extend bit from zero; sets or clears flags
• DAA Decimal Adjust after Addition; Intel 80x86; adjusts the result of adding two valid packed decimal operands in AL register; sets or clears flags
• DAS Decimal Adjust after Subtraction; Intel 80x86; adjusts the result of subtracting two valid packed decimal operands in AL register; sets or clears flags
• AAA ASCII Adjust after Addition; Intel 80x86; changes the contents of register AL to a valid unpacked decimal number, and zeros the top 4 bits; sets or clears flags
• AAS ASCII Adjust after Subtraction; Intel 80x86; changes the contents of register AL to a valid unpacked decimal number, and zeros the top 4 bits; sets or clears flags
• AAM ASCII Adjust after Multiplication; Intel 80x86; corrects the result of a multiplication of two valid unpacked decimal numbers, the high order digit is left in AH, the low order digit in AL; sets or clears flags
• AAD ASCII Adjust before Division; Intel 80x86; modifies the numerator in AH and AL to prepare for the division of two valid unpacked decimal operands so that the quotient produced by the division will be a valid unpacked decimal number, AH should contain the high-order digit and AL the low-order digit, this instruction adjusts the value and places the result in AL, AH will contain zero.; sets or clears flags
• PACK Pack; Motorola 680x0; converts converts byte encoded numeric data (such as ASCII or EBCDIC characters) into binary coded decimals using an adjustment field ($3030 for ASCII, $F0F0 for EBCDIC), either from data register to data register or memory location to memory location with predecrement of address pointers; does not modify flags
• UNPK Unpack; Motorola 680x0; converts converts converts binary coded decimals into byte encoded numeric data (such as ASCII or EBCDIC characters) using an adjustment field ($3030 for ASCII, $F0F0 for EBCDIC), either from data register to data register or memory location to memory location with predecrement of address pointers; does not modify flags