Question

Find the eight bit two’s complement of
-123

Answer 1

Simply find the base two representation and add a leading zero

11510=1110011=0111001111510=1110011=01110011

The number in base two uses 7 bits, so we need to add a leading zero to use all eight bits, and the leading zero then conveys that the number is positive.

Do you know how to express −11510−11510? Flip zeros for ones in the 8-bit representation of 11510,11510, and vice versa, then add 1 bit:

−11510=10001100+00000001=10001101−11510=10001100+00000001=10001101

Note that this process of reversing 1's and 0's guarantees the the leading bit is equal to 11, which conveys that the decimal number represented is negative.