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# Residue Generator of Binary Numbers in 2's Complement Form

IP.com Disclosure Number: IPCOM000094204D
Original Publication Date: 1966-Jul-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 3 page(s) / 41K

IBM

## Related People

Liu, LY: AUTHOR [+2]

## Abstract

The plurality of carry-save adders CSA is utilized to produce a final output representing the modulo-3 remainder of the binary number having positions 0... 15. A modulo-3 remainder is generated by dividing a number by the modulo base, in this example 3, and producing a signal representing the remainder. In a binary number, the binary weight of all odd-numbered bits has a modulo-3 remainder of 1. The binary weight of all even-numbered bit positions has a modulo-3 remainder of 2. Each CSA is utilized to produce outputs representing a remainder of 1, 2, or 0 based on whether or not 0, 1, 2, or 3 bit positions applied to them have a binary 1 in the number represented.

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Residue Generator of Binary Numbers in 2's Complement Form

The plurality of carry-save adders CSA is utilized to produce a final output representing the modulo-3 remainder of the binary number having positions 0...
15. A modulo-3 remainder is generated by dividing a number by the modulo base, in this example 3, and producing a signal representing the remainder. In a binary number, the binary weight of all odd-numbered bits has a modulo-3 remainder of 1. The binary weight of all even-numbered bit positions has a modulo-3 remainder of 2. Each CSA is utilized to produce outputs representing a remainder of 1, 2, or 0 based on whether or not 0, 1, 2, or 3 bit positions applied to them have a binary 1 in the number represented.

For example, CSA 10 receives as inputs the binary 1 or 0 representation from bit positions 11, 13, and 15. CSA 10 produces no output if none of these positions contain a binary 1. CSA 10 produces both outputs 1 and 2 if all input positions contain a binary 1. This is because further division by the modulo base 3 causes a zero result. An output is produced on line 1 if one or three of the positions has a binary 1. An output appears on line 2 if two inputs have binary 1's. The CSA's which sum the number of 2-weighted remainders produce no output when no inputs are present, an output when two or more inputs are present, and a 2 output when one or three inputs are present. All CSA's do this until a final output is produced representing the modulo-3 remainder for the entire binary number.

The outputs from CSA's 11 and 12 can produce two forms of a modulo-3 remainder zero ((11) or (00)) binary. This ambiguity is removed by 13 which reduces the outputs of 11 and 12 to two bits and remainder zero is 2 bits (00) binary only. This need not be done at this stage and 13 can be two more CSA. The checking circuits which rece...