Optical carry-free addition and borrow-free subtraction based on redundant signed-digit numbers

A single-step electro-optical or two-step all optical carry-free addition and borrow-free subtraction units are designed using a new recoding algorithm for the signed-digits redundant numbers. A new recording truth-table which has a symmetrical complemented relationship between the input minterms (entries that produce an output of 1 or 1) and their corresponding output bits is developed. Using the new recording scheme, an efficient adder/subtracter units are implemented using optical symbolic substitution based content-addressable memory (CAM). It is shown that the new recoded signed-digit based adder/subtracter has much less symbolic substitution rules and its superiority is established over all other two-step based-symbolic substitution optical implementations.<
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