## Lecture 1 (12:00) - Twos Compliment

- First field becomes -128
- Overflow happens when:
	- Both numbers are positive or negative
	- Sign is different to sign of input

| -128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | Output |
|------|----|----|----|---|---|---|---|--------|
| 0    | 0  | 0  | 0  | 1 | 0 | 1 | 0 | 10     |
|      |    |    |    |   |   |   |   |        |
| 1    | 1  | 1  | 1  | 0 | 1 | 0 | 1 | Invert |
|      |    |    |    |   |   |   | 1 | 1      |
|      |    |    |    |   |   | 1 |   | Overflow |
| 1    | 1  | 1  | 1  | 0 | 1 | 1 | 0 | -10    |

-10x10 = -10 x (8+2) = (-10 x 8) + (-10 x 2)

| -128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |      |
|------|----|----|----|---|---|---|---|------|
| 1    | 1  | 1  | 1  | 0 | 1 | 1 | 0 | -10  |
| 1    | 0  | 1  | 1  | 0 | 0 | 0 | 0 | <<<  |
|      |    |    |    |   |   |   |   |      |
| 1    | 1  | 1  | 1  | 0 | 1 | 1 | 0 | -10  |
| 1    | 1  | 1  | 0  | 1 | 1 | 0 | 0 | <    |
|      |    |    |    |   |   |   |   |      |
| 1    | 0  | 1  | 1  | 0 | 0 | 0 | 0 | -80 |
| 1    | 1  | 1  | 0  | 1 | 1 | 0 | 0 | -20 |
| 1    | 1  |    |    |   |   |   |   | Overflow |
| 1    | 0  | 0  | 1  | 1 | 1 | 0 | 0 | -100 |