Abstract
A family of redundant binary number representations, obtained by generalization of the RB (redundant binary) number representation, is introduced. All these number representations are suitable for optical computing and have properties similar to the RB representation. In particular, the p-RB (packed redundant binary) number representation introduced in this work has efficiency greater than both RB and MSD (modified signed digit) representations. With p-RB numbers the algebraic sum is always permitted in constant time for any efficiency value. p-RB representations also fit in a natural way the 2's complement binary number system. Symbolic substitution truth tables for the algebraic sum and several examples of computation are also given.
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