Comparison of number systems in truth-table look-up processing

Abstract

An important issue in truth-table look-up processing is the number representation used for data. In this paper, the effects of number representation are investigated for the important case of 8-bit addition as a specific example. The inputs are two 8-bit binary numbers together with an input carry. The output is a full-precision 9-bit binary sum. For the intermediate processing, three number representations are treated: binary, residue, and modified signed digit. The numbers in all three representations are in binary-coded form throughout the processing. The critically important steps of encoding the numbers into the residue and modified signed digit systems and then decoding the results back into the direct binary are also performed by applying truth-table look-up methods. For each case, the complexity has been found by listing all the required reference patterns (minterms) and reducing this list using logical minimization techniques. Also, for the binary number case, analytic expressions have been derived for the number of reduced reference patterns. It is shown that the residue processor is superior in required hardware while the binary processor is the fastest.