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

Polynomial Hardware Design

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

Circuit for division by: x3+x+1

Circuit Details - Descrambler

Circuit for multiplication by: x3+x+1

Design Your Own Circuit

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