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# Residue Checking of Connectives AND OR EXCLUSIVE OR

IP.com Disclosure Number: IPCOM000078281D
Original Publication Date: 1972-Dec-01
Included in the Prior Art Database: 2005-Feb-25
Document File: 3 page(s) / 38K

IBM

## Related People

Levine, SR: AUTHOR

## Abstract

The logical operations of AND, OR, and EXCLUSIVE OR are residue checked, while saving much of the additional hardware that would have been needed to check these three logical functions.

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Residue Checking of Connectives AND OR EXCLUSIVE OR

The logical operations of AND, OR, and EXCLUSIVE OR are residue checked, while saving much of the additional hardware that would have been needed to check these three logical functions.

The results of any connective operation can be checked by comparing its residue to a combination of the residue of its input operands and the residue of only one of the connectives, according to the following equations in which all operations are taken to the same modulus as those of the operand residues: 1. R(AND) = R(AND DUPLICATED) 2. R(OR) = R(A) +R(B) - R(AND DUPLICATED) 3. R(EXCLUSIVE OR) = R(A) +R(B) -2.R(AND DUPLICATED) 4. R(OR) = R(OR DUPLICATED) 5. R(AND) = R(A) +R(B) - R(OR DUPLICATED)
6. R(EXCLUSIVE OR) = 2.R(OR DUPLICATED) - R(A) - R(B) 7. R(EXCLUSIVE OR) = R(EXCLUSIVE OR DUPLICATED) 8. 2-R(AND) = R(A)+ R(B) - R(EXCLUSIVE OR DUPLICATED) 9. 2.R(OR) = R(A) + R(B) + R(EXCLUSIVE OR DUPLICATED).

R(A) and R(B) are the residues of the input operands A and B of which the connective is formed. R(AND), R(OR), R(EXCLUSIVE OR) are, respectively, the residues of the AND function, OR function, EXCLUSIVE OR function. When equations 1, 2, and 3 are used, the AND function is either duplicated or formed another way. This 2nd AND function called AND DUPLICATED, is formed whenever any connective (AND, OR, EXCLUSIVE OR) operation is done. The residue of AND DUPLICATED, R(AND DUPLICATED), is compared with the residue of the AND function that is being executed (R(AND), and if the residues are not equal. there is an error. Whenever the OR operation is being executed, the residue of each of the input operands is added together and R(AND DUPLICATED) is subtracted from this sum (equa...