Edge detection schemes based on Prewitt, Sobel, and Roberts operators are realized using optical symbolic substitution. The corresponding optical systems are compared in terms of hardware and performance.

An efficient symbolic substitution scheme for modified-signed digit arithmetic operations is introduced. In this technique, an additional bit is used along with each pair of the input bits so that the nth additional bit is a characteristic of the (n - 1)th pair of input bits. The truth table minimization thereby shows that relatively fewer minterms are to be included in the corresponding optical content-addressable memory.

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A general design algorithm is presented for the multioutput polarization-encoded optical shadow-casting scheme. A set of POSC equations is obtained from the truth table of the desired logic unit and is solved in terms of four possible pixel characteristics (transparent, opaque, vertically polarized, and horizontally polarized) and four possible source characteristics (off, unpolarized, vertically polarized, and horizontally polarized). To demonstrate its feasibility, the algorithm is used to determine the input pixel characteristics of a full adder and a full subtracter.

Symmetrically recoded modified signed-digit number algorithms are proposed for carry-free arithmetic. The superiority of the new algorithms is established over all other two-step-based symbolic-substitution optical implementations.