Conditional symbolic modified signed-digit arithmetic using optical content-addressable memory logic elements

A new conditional symbolic substitution rule for modified signed-digit arithmetic computation is introduced. Using this substitution rule, the numbers to be added or subtracted are first replaced by a pair of new equivalent strings, which in a second step are then subject to another substitution to generate both the addition or subtraction result and its complement. For an optical implementation, a holographic contentaddressable memory is used. Correspondingly, the input encoding, the logic reduction, and the optical processing techniques are described.