Building Blocks

REPRESENTING NEGATIVE NUMBERS The most commonly used representation is called two's complement. [**]

The representation of a negative number B in this format, is performed by computing (K-B) where K = 2ⁿ such that n is the number of digits (bits) in B, that is n = floor(log₂|B|) + 1. Rather than performing this computation, we can simulate it by the following algorithm:

To find the representation of a negative integer B, complement the bits of the representation of B, and add 1,
where complement: if (bit = 0) then bit <- 1 else bit <- 0

WHY?

Examples (assuming 8 bits):
                      33₁₀ is 0010 0001₂
                     -33₁₀ is 1101 1110₂
                                              +1
                   --------------------------
                                  1101 1111
                   --------------------------
                        -1 is 1111 1111
                        -2 is 1111 1110
                        -3 is 1111 1101
                                    ::
                                    ::
                    -128 is 1000 0000
                     127 is 0111 1111
                                    ::
                                    ::
                        2 is 0000 0010
                        1 is 0000 0001
                        0 is 0000 0000

More Tutorial Help:
See the Case Western Reserve University explanation. .

One's Complement:
One's complement is simply the complement of the number representation (without the addition of 1).

CS1104 Main Page
Last Updated 09/21/2000
© L.Heath, 2000

More Tutorial Help:

One's Complement: