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

Polynomial Hardware Design

Binary values expressed as polynomials can readily be manipulated in hardware using shift registers and exclusive-OR gates.

This online tool draws and analyzes digital circuits to perform division and multiplication by a given polynomial in GF(2).

These circuits are particularly useful in digital communications as they provide the basis for data scrambling and descrambling operations. A serial data stream fed into the divider circuit will be scrambled in the division process and can be readily recovered by passing the scrambled data through the corresponding multiplier circuit. This process is also referred to as "randomization" and "derandomization".

Data scrambling circuits may be used to ensure that frequent transitions occur in a transmitted data stream. The defining polynomials would then be part of the standard describing a communications protocol.

* Click on the circuit for full analysis

Circuit Details - Scrambler

divide by 1011
Circuit for division by: x3+x+1

Circuit Details - Descrambler

multiply by 1011
Circuit for multiplication by: x3+x+1

Design Your Own Circuit

Provide the polynomial in binary form to define new circuits.

Circuit Taps (binary):    MATLAB

Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates.

2021-04-17 05:20:18 ADT
Last Updated: 05-11-16
Richard Tervo [ tervo@unb.ca ] Back to the course homepage...