Number representation effects in truth-table look-up processing: 8-bit addition example.

The parallelism and interconnectivity of optical systems may provide important advantages for these systems in massively parallel processing applications. Electronic systems, however, retain all the advantages of a highly developed technology that has been widely applied with excellent success. In both of these technologies, the methods of direct truth-table look-up processing are becoming increasingly important as the need grows for increased speed and throughput. A major 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 direct binary are also performed using truth-table look-up methods. For the direct binary representation, a total of 2545 gates (2519 holograms) are required. For the residue representation, a total of 1764 gates (1686 holograms) are required. For the modified signed-digit representation, a total of 4142 gates (4052 holograms) are required.