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

See GF(2^m) calculator tool.

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

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: 6 + 5 = (110) + (101) = (011) = 3   (highlighted below)

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

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: 5 × 4 = (101) × (100) =  (10100)  = (010)  mod (1011) = 2   (highlighted below)

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

Select a primitive polynomial P(x)

Model C-162 GALOIS FIELD MATH TABLE GENERATOR P(x) = 11 : P[x] = x+1 111 : P[x] = x2+x+1 1011 : P[x] = x3+x+1 1101 : P[x] = x3+x2+1 10011 : P[x] = x4+x+1 11001 : P[x] = x4+x3+1 100101 : P[x] = x5+x2+1 101001 : P[x] = x5+x3+1 101111 : P[x] = x5+x3+x2+x+1 110111 : P[x] = x5+x4+x2+x+1 111011 : P[x] = x5+x4+x3+x+1 111101 : P[x] = x5+x4+x3+x2+1 1000011 : P[x] = x6+x+1 1011011 : P[x] = x6+x4+x3+x+1 1100001 : P[x] = x6+x5+1 1100111 : P[x] = x6+x5+x2+x+1 1101101 : P[x] = x6+x5+x3+x2+1 1110011 : P[x] = x6+x5+x4+x+1    Colors | Hex | Discussion | Addition | MATLAB