Determine the binary encoding for a system that uses two’s complement of the base-10 quantities negative six and six for a digital system where all binary numbers are represented by four bits, one where all numbers are represented by eight bits (one byte).

4 bits:

6 = 0110

-6 = 1010

8 bits:

6 = 00000110

-6 = 11111010

Explanation:

2's complement is easier to implement, because it only has one representation of 0 and starts counting backwards from the highest number you can represent with the available bits.

e.g.,

7 = 0111

6 = 0110

5 = 0101

4 = 0100

3 = 0011

2 = 0010

1 = 0001

0 = 0000

-1 = 1111

-2 = 1110

-3 = 1101

-4 = 1100

-5 = 1011

-6 = 1010

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