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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| Veröffentlicht in: | IEEE transactions on computers Jg. C-32; H. 10; S. 961 - 968 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
IEEE
01.10.1983
Institute of Electrical and Electronics Engineers |
| Schlagworte: | |
| ISSN: | 0018-9340, 1557-9956 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Papachristou |
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| Cites_doi | 10.1364/AO.18.002812 10.1147/rd.192.0098 10.1109/TC.1980.1675478 10.1109/PROC.1978.10994 10.1109/TC.1968.226466 10.1364/AO.19.001201 10.1109/TEC.1959.5219515 10.1109/T-C.1970.223026 10.1109/TC.1982.1676036 10.1109/T-C.1971.223345 10.1007/978-3-642-96552-4 10.1109/T-C.1974.223790 10.1016/S0022-0000(70)80002-2 10.1109/TC.1978.1675105 |
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| Issue | 10 |
| Keywords | Associative storage Multiplier Implantation Adder Coding Residue |
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| References | hadley (ref25) 1962 ref15 ref14 ref2 polky (ref16) 1981 muroga (ref17) 1982 ref19 ref18 huang (ref13) 1975 birkner (ref20) 1978 (ref21) 1980 szabo (ref3) 1967 rao (ref4) 1970; c 19 kohonen (ref10) 1980 (ref23) 1982 ref28 svoboda (ref1) 1957 ref29 papachristou (ref11) 1981 ref8 ref7 mead (ref30) 1980 garfinkel (ref26) 1972 ref9 barsov (ref24) 1955 collins (ref12) 1977; 128 ref6 papachristou (ref27) 1981 ref5 (ref22) 1982 |
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| SubjectTerms | 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 |
| Title | Direct Implementation of Discrete and Residue-Based Functions Via Optimal Encoding: A Programmable Array Logic Approach |
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