# Number Representation

### How do we represent negative numbers?

### Option 3: Two's Complement ☜ ✓ ★ ☺

- Flip every bit to represent the number's negative value, then
add one

(Note: surprisingly, this also works both ways!)
- Left-most bit still represents the sign
- Examples:
`00000001`

= +1
`11111111`

= -1 (two's complement)
`00000101`

= +5
`11111011`

= -5 (two's complement)
`01111111`

= +127
`10000001`

= -127 (two's complement)

- Problem 1 Solved!
`00000000`

= +0
`00000000`

= -0 (two's complement)

- Problem 2 Solved!
` 00000101`

5
` 11111111`

+ -1
` --------`

-----
`100000100`

4 (ignore overflow)

Alyce Brady, Kalamazoo College