Canonical modified signed-digit arithmetic using opto-electronics symbolic substitution

Two-step electro-optical early-free addition/subtraction units are designed using a new canonical algorithm for the modified signed-digit (MSD) numbers. The canonical algorithm applied to the MSD numbers provides an optical parallel addition/subtraction operations in one step. It will be shown that the canonical MSD has a significant reduced number of the symbolic substitution based optical content-addressable-memory (OCAM) system.