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# Multi-Valued Logic Parity

IP.com Disclosure Number: IPCOM000035413D
Original Publication Date: 1989-Jul-01
Included in the Prior Art Database: 2005-Jan-28
Document File: 1 page(s) / 12K

IBM

## Related People

Millas, RJ: AUTHOR [+2]

## Abstract

This article describes a method on how to encode the resulting parity (odd-even) of each value in a multi-level logic word.

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Multi-Valued Logic Parity

This article describes a method on how to encode the resulting parity (odd- even) of each value in a multi-level logic word.

A popular and simple technique for detecting single bit errors in a binary system is by using parity. A single parity bit is appended to a data unit (byte, word, etc). The value of the parity bit is selected so that the number of 1's in the codeword is odd or even, where the codeword equals the data unit with parity bit.

Up to now this system has been a simple and effective way to detect single bit errors. As multi-valued logic, such as ternary logic, becomes more popular, a method to produce multi-valued parity is required.

Presented herein is a method to use parity in multi-valued logic. As mentioned above, parity in the binary system is defined as having an odd or even number of 1's. By knowing the parity of 1's, the parity of 0 is easily determined by knowing the length of the data unit. In multi-valued logic including binary boolean logic, the parity for all states except one must be known. As in binary, 0's parity will be determined later from the result of the other state(s)' parity. In multi-valued logic where the base is greater than 2, knowing the 1's parity is not enough. The parity for other states not including 0's must be known.

The following definitions are established: N = base of system (for example: N=2 for binary N=3 for ternary, etc.) Nit = multi-valued digit (in binary this is a bit) P = number...