Binary-Coded Decimal Addition

Binary-Coded Decimal Addition

Binary-coded decimal (BCD) represents each decimal digit separately using a 4-bit binary group. When adding BCD numbers, the goal is to perform normal binary addition on each digit group, then correct any group that is not a valid decimal digit.

Method

1. Add the digits as binary. Work from right to left, just as in ordinary addition.
2. Check each 4-bit group. A valid BCD digit must be from 0000 to 1001 (0 to 9).
3. Apply the BCD correction if needed. If a group is greater than 1001, or if a carry appears from that group, add 0110 to that group.
4. Pass the carry leftward. Any carry created by the correction moves to the next group.
5. Repeat for all groups. Continue until every digit group is valid.

How to check your result

Convert each final 4-bit group back to a decimal digit. The combined digits should match the decimal sum of the original numbers. If a group is outside the BCD range, the addition is not finished correctly.

Good habit

After finishing, read the answer digit by digit rather than as one binary number. BCD is meant to preserve decimal digits, so the final form should be a clean decimal-style result encoded in binary groups.