In signed 2's complement representation of 4-bit positive binary numbers are:
- 0000 -> +0
- 0001 -> +1
- 0010 -> +2
…. - 0111 -> +7
Negative binary numbers(from -1 to -7) are obtained by taking 2's complement of this positive binary numbers(from +1 to +7). But there is -8 in this system. Where did -8 come from? Because there is no +8 in 4-bit system so that we can take 2's complement of it to result this -8.
Best Answer
This is why:
0000 -> 0111 = 0 -> 7
1111 -> 1000 = -1 -> -8
both series can represent 8 numbers, the positive series already include the 0 so the negative serie doesn't have to do this.