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Representation Properties

The two's complement representation has several properties, familiar to designers of digital logic, that are responsible for its near-universal use in general purpose computers. For convenience we now introduce some formal notation for binary representations and review the relevant properties.

The unsigned interpretation of a vector of n bits is given by


Rather than give a bit-by-bit definition of the representation function it will suffice to define it as the inverse of the interpretation function:


for non-negative x.

The two's complement (signed) representation can be defined by concatenating a sign bit onto an unsigned bit vector:


The interpretation function for the two's complement representation was given in equation (2); it can also be defined in terms of the unsigned interpretation function:


Stephen W. Nuchia
Mon Dec 11 17:02:42 CST 2000