UNB ECE4253 Digital Communications
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada

Addition and Multiplication Tables in Galois Fields GF(2m)

* See GF(2m) calculator tool.

This page presents addition and multiplication tables for Galois fields GF(2m).


Using the Galois Field GF(23) = GF(8) based on the primitive P(x) = x3 + x + 1 = (1011) = 11 (decimal)

Addition Table

Values in GF(23) are 3-bits each, spanning the decimal range [0..7]. Addition takes place on these 3-bit binary values using bitwise XOR.

For example: 5 + 5 = (101) + (101) = (000) = 0   (highlighted below)

The choice of polynomial P(x) plays no role in the addition operation.

+ 0 1 2 3 45 6 7
001234567
110325476
223016745
332107654
445670123
554761032
667452301
776543210

Multiplication Table

Values in GF(23) are 3-bits each, spanning the decimal range [0..7]. Multiplication takes place on 3-bit binary values (with modulo 2 addition) and then the result is computed modulo P(x) = (1011) = 11 (decimal).

For example: 6 × 4 = (110) × (100) =  (11000)  = (101)  mod (1011) = 5   (highlighted below)

The specific polynomial P(x) provides the modulus for the multiplication results.

× 1 2 34 5 6 7
11234567
22463175
33657412
44376251
55142736
66715324
77521643

Select a primitive polynomial P(x)

2024-03-04 14:29:03 AST
Last Updated: 2011-02-02
Richard Tervo [ tervo@unb.ca ] Back to the course homepage...