Direct Implementation of Discrete and Residue-Based Functions Via Optimal Encoding: A Programmable Array Logic Approach

This paper presents a technique for direct truth table implementation of residue-based functions by an encoding scheme that employs programmable array logic (PAL) technology. The scheme models the basic associative memory operation, i.e., the detection of matchings between input patterns and prestor...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. C-32; no. 10; pp. 961 - 968
Main Author: PAPACHRISTOU, C. A
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.1983
Institute of Electrical and Electronics Engineers
Subjects:
Addition and multiplication mod M
Applied sciences
associative memories
Circuit properties
Digital circuits
discrete functions
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
optimal residue encoding
PLA's
programmable array logic (PAL)
residue-based functions
ROM's
VLSI
Associative storage
Multiplier
Implantation
Adder
Coding
Residue
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:This paper presents a technique for direct truth table implementation of residue-based functions by an encoding scheme that employs programmable array logic (PAL) technology. The scheme models the basic associative memory operation, i.e., the detection of matchings between input patterns and prestored information in the PAL's. The complexity of this model is related to the amount of stored logic, i.e., the P-terms in the logic arrays. A linear programming approach is proposed for the encoding of the residue set with the objective of minimizing the complexity of addition and multiplication, modulo M, simultaneously. It is shown that the addition is more complex than the multiplication modulo M, with both (two-operand) operations being upper bounded by O(M2). Results produced using the optimal encoding compare favorably to corresponding results regarding the usual binary representation of residues. Practical constraints are also considered such as limitations on the number of pins, the number of P-terms, and the chip area, with the latter shown to be more efficiently utilized in the PAL scheme than in a ROM-or PLA-based implementation. The encoding technique is also applicable to the functions of discrete logic, in general.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1983.1676143