On the Theory and Design of Polynomial Division Circuits

We present a theory and design techniques for polynomial division circuits with the primary focus on testing of digital and mixed-signal devices. We estimate the aliasing rate for the proposed circuits (signature analyzers) and show how to improve it. Two types of design techniques are examined for mixed-signal circuit analyzers that are arithmetical by nature. The techniques are scalable and valid for an arbitrary size and base of the number system. The proposed devices have both low hardware complexity and aliasing rate. The design techniques and devices can also be used in general arithmetic/algebraic error-control coding, cryptography, digital broadcasting and communication.