# Number Representation

### How do we represent negative numbers?

### Option 2: One's Complement

- Flip every bit to represent the number's negative value

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

= +1
`11111110`

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

= +5
`11111010`

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

= +127
`10000000`

= -127 (one's complement)

- Problem 1:
`00000000`

= +0
`11111111`

= -0 (one's complement)

- Problem 2:
` 00000101`

5
` 11111110`

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

-----
`100000011`

overflow ???

Alyce Brady, Kalamazoo College