We propose an approach to design of an algebraic signature analyzer that can be used for mixed-signal systems testing. The analyzer does not contain carry propagating circuitry, which improves its performance as well as fault tolerance. The common design technique of a signature analyzer for mixed-signal systems is based on the rules of an arithmetic finite field. The application of this technique to the systems with an arbitrary radix is a challenging task and the devices designed possess high hardware complexity. The proposed technique is simple and applicable to systems of any size and radix. The hardware complexity is low. The technique can also be used in arithmetic/algebraic coding and cryptography. 1. Introduction Signature analysis has been widely used for digital and mixed-signal systems testing [1–12]. Mixed-signal systems consist of both digital and analog circuits; however the signature analysis method is only applicable to the subset of these systems that have digital outputs (such as analog-to-digital converters, measurement instruments, etc.). Signature analysis can be employed as an external test solution or can be embedded into the system under test. In the built-in implementation, a circuit under test (CUT) of digital or mixed-signal nature is fed by test stimuli, while the output responses are compacted by a signature analyzer (SA), as illustrated in Figure 1. The actual signature is compared against the fault-free circuit’s signature and a pass/fail decision is made. A signature of a fault-free circuit is referred to as a reference signature. If the CUT is of a digital nature, the SA essentially constitutes a circuit that computes an algebraic remainder. The reference signature has only one, punctual value, and the decision making circuit consists of a simple digital comparator. If the CUT is of a mixed-signal nature, the SA computes an arithmetic residue. In this case, the reference signature becomes an interval value and the decision making circuit uses a window comparator. Figure 1: Built-in signature analysis of a circuit under test. Design methods for an algebraic signature analyzer have been well developed in error-control coding [13]. A remainder calculating circuit for an arbitrary base (binary or nonbinary) can be readily designed for a digital CUT of any size. In contrast, it is much harder to design a residue calculating circuit, specifically for a nonbinary base [14]. Furthermore, due to the presence of carry propagating circuitry, the implementation complexity and error vulnerability of the residue calculating circuit
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