Algorithms for optoelectronic implementation of modified signed-digit division, square-root, logarithmic, and exponential functions

Abstract

Algorithms for computing complex elementary functions based on the modified signed-digit (MSD) number system representations are proposed. An arithmetic unit that performs parallel one-step addition (subtraction), multiplication, and division is proposed to achieve the computation of complex functions such as the square-root, logarithm, exponential, and other related operations. An optoelectronic correlator-based architecture is suggested for implementing the proposed MSD algorithms to compute the above-mentioned elementary functions. We utilized the symbolic substitution technique to reduce the number of computation rules involved.

© 2001 Optical Society of America

Designs of optoelectronic trinary signed-digit multiplication by use of joint spatial encodings and optical correlation

Abdallah K. Cherri
Appl. Opt. 38(5) 828-837 (1999)

Recoded and nonrecoded trinary signed-digit adders and multipliers with redundant-bit representations

Abdallah K. Cherri and Mohammed S. Alam
Appl. Opt. 37(20) 4405-4418 (1998)

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)

Modified signed-digit arithmetic based on redundant bit representation

Hongxin Huang, Masahide Itoh, and Toyohiko Yatagai
Appl. Opt. 33(26) 6146-6156 (1994)

Digital optical arithmetic

Earl Swartzlander
Appl. Opt. 25(18) 3021-3032 (1986)