Editing Binary-coded decimal (section)

=== Addition ===
It is possible to perform [[addition]] by first adding in binary, and then converting to BCD afterwards. Conversion of the simple sum of two digits can be done by adding 6 (that is, 16 − 10) when the five-bit result of adding a pair of digits has a value greater than 9. The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 2<sup>4</sup> = 16), but only 10 values are valid (0000 through 1001). For example:
 1001 + 1000 = 10001
    9 +    8 =    17
10001 is the binary, not decimal, representation of the desired result, but the most significant 1 (the "carry") cannot fit in a 4-bit binary number. In BCD as in decimal, there cannot exist a value greater than 9 (1001) per digit. To correct this, 6 (0110) is added to the total, and then the result is treated as two nibbles:
 10001 + 0110 = 00010111 => 0001 0111
    17 +    6 =       23       1    7
The two nibbles of the result, 0001 and 0111, correspond to the digits "1" and "7". This yields "17" in BCD, which is the correct result.

This technique can be extended to adding multiple digits by adding in groups from right to left, propagating the second digit as a carry, always comparing the 5-bit result of each digit-pair sum to 9. 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).