A three-step modified signed-digit (MSD) adder is proposed which can be optically implmented using binary logic gates. The proposed scheme depends on encoding each MSD digits into a pair of binary digits using a two-state and multi-position based encoding scheme. The design algorithm depends on constructing the addition truth table of binary-coded MSD numbers and then using Karnaugh map to achieve output minimization. The functions associated with the optical binary logic gates are achieved by simply programming the decoding masks of an optical shadow-casting logic system.
R. S. Fyath,
A. A. W. Alsaffar,
M. S. Alam,
"Optical three-step binary-logic-gate-based MSD arithmetic", Proc. SPIE 5202, Optical Information Systems, (23 October 2003); doi: 10.1117/12.503869; https://doi.org/10.1117/12.503869