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Adder circuits are fundamental building blocks of computer arithmetic. Every processor uses adders to perform addition, and understanding how they work from basic logic gates is a core part of the OCR H446 specification.
Binary addition follows the same rules as decimal addition, but with only two digits (0 and 1):
| A | B | Sum | Carry |
|---|---|---|---|
| 0 + 0 | 0 | 0 | |
| 0 + 1 | 1 | 0 | |
| 1 + 0 | 1 | 0 | |
| 1 + 1 | 0 | 1 |
When both bits are 1, the sum is 0 with a carry of 1 (just like 5 + 5 = 10 in decimal — the "0" stays and the "1" carries to the next column).
A half adder adds two single-bit inputs (A and B) and produces a sum (S) and a carry (C).
Truth table:
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