====== 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:

{{ :reference:twosComplementEquation.png?600 |Two's Complement Equation}}

With this equation in mind, one can see how the two tables from [[http://en.wikipedia.org/wiki/Two%27s_complement|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