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Table Lookup Residue Adder

IP.com Disclosure Number: IPCOM000090068D
Original Publication Date: 1969-Jan-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 2 page(s) / 38K

Publishing Venue

IBM

Related People

Bliss, BE: AUTHOR

Abstract

In a residue number system, each digit has its own radix and the numerals for each radix are the sets of residues for that radix. The radices used must be relatively prime. The set of numbers having unique codes range from zero to the product of the two radices minus one. A residue number system is advantageous in that arithmetic or addition can be performed without carry propagation.

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Table Lookup Residue Adder

In a residue number system, each digit has its own radix and the numerals for each radix are the sets of residues for that radix. The radices used must be relatively prime. The set of numbers having unique codes range from zero to the product of the two radices minus one. A residue number system is advantageous in that arithmetic or addition can be performed without carry propagation.

The drawing illustrates a residue number adder based on modulo-56 and radices of 8 and 7. Three storage devices TL1...TL3 are loaded with data to provide a table lookup function. A series of registers R1...R7 is provided. In order to add a first number comprising digits M2 and M1 to the radices 8 and 7, respectively, to a second number comprising the digits D2 and D1, to the radices 8 and 7, respectively, the binary equivalents of digits M2 and D2 are loaded into registers R1 and R2. Also the binary equivalents of digits M1 and D1 are loaded into register R3 and R4, respectively. These signals are then used to address TL2 and TL1, respectively. Upon cycling these storage devices, the appropriate sums S2 and S1 are read from them into registers R5 and R6 respectively. The digits S2 and S1 provide the result in the residue number system. If desired, these signals can be further fed to TL3 so as to read from it the binary equivalent of the decimal result which signal is then placed in register R7.

The drawing also illustrates an example of the addition of dec...