Abstract

The problem of comparing n-bit two's complement numbers is closely related to the problem of detecting whether a carry is generated from the sum of two numbers. A faster solution to the carry generation problem immediately yields a faster solution to the comparison problem. We use a variation of the boolean circuit model to present a new upper bound to the solution of both problems. The new solution uses half-adders and a parallel prefix-and circuit to find the unique significant carry bit, and tristate buffers to pass the value of the significant bit to the output. Two implementations are presented: the bit prefix-and method, which is suitable for small n, and the group prefix-and method, which is just as fast but uses less hardware for moderate to large n. Both methods have simple and regular layouts, and are faster and require less area than existing methods.

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