Editing Binary-coded decimal (section)

=== Subtraction ===
Subtraction is done by adding the ten's complement of the [[subtrahend]] to the [[minuend]]. To represent the sign of a number in BCD, the number 0000 is used to represent a [[positive number]], and 1001 is used to represent a [[negative number]]. The remaining 14 combinations are invalid signs. To illustrate signed BCD subtraction, consider the following problem: 357 − 432.

In signed BCD, 357 is 0000 0011 0101 0111. The ten's complement of 432 can be obtained by taking the [[nine's complement]] of 432, and then adding one. So, 999 − 432 = 567, and 567 + 1 = 568. By preceding 568 in BCD by the negative sign code, the number −432 can be represented. So, −432 in signed BCD is 1001 0101 0110 1000.

Now that both numbers are represented in signed BCD, they can be added together:
   0000 0011 0101 0111
   0    3    5    7
 + 1001 0101 0110 1000
   9    5    6    8
 = 1001 1000 1011 1111
   9    8    11   15
Since BCD is a form of decimal representation, several of the digit sums above are invalid. In the event that an invalid entry (any BCD digit greater than 1001) exists, 6 is added to generate a carry bit and cause the sum to become a valid entry. So, adding 6 to the invalid entries results in the following:
   1001 1000 1011 1111
   9    8    11   15
 + 0000 0000 0110 0110
   0    0    6    6
 = 1001 1001 0010 0101
   9    9    2    5
Thus the result of the subtraction is 1001 1001 0010 0101 (−925). To confirm the result, note that the first digit is 9, which means negative. This seems to be correct since 357 − 432 should result in a negative number. The remaining nibbles are BCD, so 1001 0010 0101 is 925. The ten's complement of 925 is 1000 − 925 = 75, so the calculated answer is −75.

If there are a different number of nibbles being added together (such as 1053 − 2), the number with the fewer digits must first be prefixed with zeros before taking the ten's complement or subtracting. So, with 1053 − 2, 2 would have to first be represented as 0002 in BCD, and the ten's complement of 0002 would have to be calculated.