# Two's Compliment

Twos complement is a commonly used technique in binary coding to represent both positive and negative values. Luckily, its pretty easy to determine what the corresponding decimal value is by using the following equation:

With this equation in mind, one can see how the two tables from Wikipedia's page on Two's Complement were derived.

3-bits two's-complement integers
Bits Unsigned Value 2's Complement Value
011¹ 3 3
010 2 2
001 1 1
000 0 0
111 7 -1
110 6 -2
101² 5 -3
100 4 -4

¹ Example calculation would work out to be –> 3 - (0)*(7+1) = 3
² Example calculation would work to be –> 5 - (1)*(7+1) = -3

8-bits two's-complement integers
Bits Unsigned Value 2's Complement Value
0111 1111 127 127
0111 1110¹ 126 126
0000 0010 2 2
0000 0001 1 1
0000 0000 0 0
1111 1111 255 -1
1111 1110² 254 -2
1000 0010 130 -126
1000 0010 129 -127
1000 0010 128 -128

¹ Example calculation would work out to be –> 126 - (0)*(255+1) = 126
² Example calculation would work out to be –> 254 - (1)*(255+1) = -2