Two’s-Complement Addition

Two’s-Complement Addition

Two’s-complement addition works like ordinary binary addition, but you must pay attention to the fixed bit-width and the sign bit.

1) Add bit by bit

Write the numbers in the same number of bits. Add from right to left just as in decimal addition, carrying when needed.

2) Keep only the allowed width

In two’s-complement, the result is interpreted using the same fixed number of bits as the inputs. If a carry goes beyond the leftmost bit, discard it.

3) Read the sign correctly

• If the leftmost bit is 0, the result is nonnegative.
• If the leftmost bit is 1, the result is negative in two’s-complement form.

4) Simplify the final answer

Leave the result in its final two’s-complement form unless the exercise asks for a decimal value.

Check your work

A useful check is to convert the result to decimal and verify that it matches the sum of the original values, as long as the addition stays within the representable range. If the result seems inconsistent, recheck the carries and the bit-width used.