Abstract

A high-accuracy fixed-point optical adder that operates in parallel on many long words and that uses a pipelined correlator architecture is described. A symbolic substitution algorithm with the modified signed-digit number representation is used to perform fixed-point additions with limited carries. A new set of substitution rules and encodings is developed to combine the recognition and substitution steps into one correlation operation. This reduces hardware requirements, improves throughput by reducing the space–bandwidth product needed, and reduces latency (the delay between when data enter the processor and when the final output is available) by a factor of 2. This algorithm and our new modified signed-digit encodings and substitution rules improve the performance of other correlator and noncorrelator optical numeric computing architectures.

© 1994 Optical Society of America

Modified signed-digit trinary arithmetic by using optical symbolic substitution

A. A. S. Awwal, M. N. Islam, and M. A. Karim
Appl. Opt. 31(11) 1687-1694 (1992)

High-accuracy pipelined iterative-tree optical multiplication

Khaled Al-Ghoneim and David Casasent
Appl. Opt. 33(8) 1517-1527 (1994)

Optoelectronic recoded and nonrecoded trinary signed-digit adder that uses optical correlation

Abdallah K. Cherri, Mahmoud K. Habib, and Mohammad S. Alam
Appl. Opt. 37(11) 2153-2163 (1998)

Optical processing based on conditional higher-order trinary modified signed-digit symbolic substitution

M. S. Alam, M. A. Karim, A. A. S. Awwal, and J. J. Westerkamp
Appl. Opt. 31(26) 5614-5621 (1992)

Digital optical processing based on higher-order modified signed-digit symbolic substitution

Mohammad S. Alam, Abdul Ahad S. Awwal, and Mohammad A. Karim
Appl. Opt. 31(14) 2419-2425 (1992)