#### Biased Notation

##### Format

Biased notation stores a signed number N as an unsigned value N+B, where B is the bias. B is usually half the unsigned range, though we could in theory choose any bias we want.

For example, to store the value -3 in 4-bit bias-7 notation, we simply add -3 + 7 = 4 and store it as unsigned binary 0100.

To find out what 1110 represents in 4-bit bias-7 notation, we convert the binary representation to decimal and subtract the bias: 11102 = 2 + 4 + 8 = 14 - 7 = +7.

```Binary      0000 0111 1000 1111
Unsigned       0    7    8   15
Bias-7        -7    0    1    8
Two's comp     0    7   -8   -1
```
##### Negation

Subtract twice the value. E.g., to negate +6, subtract 12. To negate -6, subtract -12.

Complicated.

##### Range

The range is simply 0-bias to (maximum unsigned)-bias.

##### Comparison

Numbers stored in biased notation can be compared in the same way as unsigned numbers. Unlike two's complement, which uses what would be the higher unsigned values to represent negative numbers (0000 to 0111 are positive and 1000 to 1111 are negative), biased notation keeps the values in the same order, but simply shifts the number line.

### Note

Be sure to thoroughly review the instructions in Section 2, “Practice Problem Instructions” before doing the practice problems below.
1. Perform the following conversions.

1. 11111111 8-bit bias-127 to decimal

2. 01111111 8-bit bias-127 to decimal

3. -7 decimal to 8-bit bias-127

2. What is an advantage of biased notation over two's complement?

3. What is an advantage of two's complement over biased notation?