Truth-Table Look-Up Processing: Number Representation, Multilevel Coding, And Logical Minimization

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Abstract
The need for ultra-high-speed computing for a variety of modern processing problems has generated new interest in using truth-table look-up techniques. Further, due to the frequently parallel nature of these processing problems, optical systems appear to be promising for these applications. The basic principles of truth-table look-up processing are reviewed in this paper. The issues of number representation, multilevel coding, and logical minimization are discussed. Example fixed-radix and residue number representations are given with and without multilevel coding. Logical reduction techniques are discussed with examples. A comparison of the number of truth-table entries needed for 16-bit full-precision addition and multiplication is given, illustrating the advantage of the multilevel coded residue number representation.

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