ECE4253 Digital Communications | |
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada | |
This page presents addition and multiplication tables for Galois fields GF(2m).
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: 4 + 3 = (100) + (011) = (111) = 7 (highlighted below)
The choice of polynomial P(x) plays no role in the addition operation.
+ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | 1 | 0 | 3 | 2 | 5 | 4 | 7 | 6 |
2 | 2 | 3 | 0 | 1 | 6 | 7 | 4 | 5 |
3 | 3 | 2 | 1 | 0 | 7 | 6 | 5 | 4 |
4 | 4 | 5 | 6 | 7 | 0 | 1 | 2 | 3 |
5 | 5 | 4 | 7 | 6 | 1 | 0 | 3 | 2 |
6 | 6 | 7 | 4 | 5 | 2 | 3 | 0 | 1 |
7 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
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 × 6 = (101) × (110) = (11110) = (011) mod (1011) = 3 (highlighted below)
The specific polynomial P(x) provides the modulus for the multiplication results.
× | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 2 | 4 | 6 | 3 | 1 | 7 | 5 |
3 | 3 | 6 | 5 | 7 | 4 | 1 | 2 |
4 | 4 | 3 | 7 | 6 | 2 | 5 | 1 |
5 | 5 | 1 | 4 | 2 | 7 | 3 | 6 |
6 | 6 | 7 | 1 | 5 | 3 | 2 | 4 |
7 | 7 | 5 | 2 | 1 | 6 | 4 | 3 |
Select a primitive polynomial P(x)
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2024-03-29 03:55:35 ADT
Last Updated: 2011-02-02 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |