Adder
An adder is a logic circuit that adds binary numbers. It takes an input of two bits, and outputs two bits in sum and carry terms.
A half adder produces the sum of the two inputs as a sum bit and carry out bit.
| A | B | Sum | Carry Out |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
A full adder also considers the carry input, the sum of three inputs as a sum bit and carry out bit.
| Carry In | A | B | Sum | Carry Out |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
You can string multiple full adders together to create a ripple carry adder. The Carry Out bit of the previous adder stage will be the Carry In bit of the next adder stage. - However, this method is slow - you have to wait for the carry to propagate all the way through to the last stage
To reduce the delay on the carry, we can calculate the carries in parallel. Distributing the terms is known as a prefix adder.