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In order to detect transient faults, as well as stuck faults in logic circuits, many kinds of checkers, such as parity code checkers, duplication checkers, parity-prediction checkers, and residue code checkers, have already been applied in an adaptive manner to some functional circuits (e.g., adders, multipliers, decoding circuits, and data path circuits [SELL68]). Further the theory of self-checking circuits (e.g., totally self-checking (TSC) circuits, strongly fault-secure (SFS) circuits, and error-secure (ES) circuit) has been studied extensively [CART68, CART71b, ANDE71, WAKE74, SMIT78, NICO84, NANY88]. Some practical design methods for self-checking circuits appear in [CART77, SMIT83, NANY88]. Here we study both the general concept of the self-checking circuits and the checker concept for the self-checking checkers.
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12.1.1 General Concept Basically the logic circuits should be designed such that they indicate any malfunction during normal operation and not produce an erroneous result without an error indication. In some actual circuits any fault from a speci ed set of faults can cause a detectable erroneous output without also producing an error signal [CART68, ANDE71]. The general structure of the self-checking circuits is shown in Figure 12.1; the error indicator output Z must be designed to produce an error signal for some normal circuit input whenever a fault from a speci ed set of faults occurs within the circuit.
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Figure 12.1 Self-checking circuit.
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In the design of the circuits in Figure 12.1, the circuit G is considered to be divided into two connected circuit blocks, the functional circuit block L and the check circuit block CK. These circuit blocks are shown in Figure 12.2. First we discuss self-checking functional circuits and then extend that to self-checking functional networks. Check circuits will be covered in a subsequent section. We begin with a combinational circuit L that produces an output vector Y X; f that is a function of the input vector X and a fault f 2 F, which is a speci ed set of faults in the circuit. The absence of a fault is called a null fault and is denoted by l. If the circuit L has n inputs, then the input space x of L is the set of all 2n input vectors. Similarly, if L has r outputs, then the set of all 2r output vectors is the output space y of L. In general, logic circuits will receive only a subset of their input space during normal (i.e., fault-free) operation; this subset is called the input codespace N. Then x N is the input noncodewords. Here we consider only circuits whose outputs under normal operation are codewords, and therefore we also de ne for each circuit its output codespace S. Then
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Figure 12.2 Self-checking circuit model. Website qr code developmentwith .net
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F Y (X, f) = Y (X, ) or Y (X, f) S
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Figure 12.3 Fault-secure circuit.
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y S is the output noncodespace. For a given input X 2 N, a fault may or may not cause an error in the output. If the fault does cause an error, it may change the output, either to a noncodeword (i.e., a detectable error), or to a different codeword (i.e., an undetectable error). 1. Fault Secure and Self-testing De nition 12.1 A circuit L is fault secure (FS) for an input set N and a fault set F if for input X in N and for any fault f in F, Y X; f Y X; l , or Y X; f 62 S. & That is, the output of a fault-secure circuit is always either the correct codeword or a noncodeword but never a wrong codeword for any fault in F. This is illustrated in Figure 12.3. De nition 12.2 A circuit L is self-testing (ST) for an input set N and a fault set F if for every fault f in F there is some input X in N such that Y X; f is not in S. & Figure 12.4 illustrates this de nition. By this de nition, an input X for which Y X; f is not in S, or Y X; f 6 Y X; l , is called a test pattern for f. If each input in N occurs during the normal operations of the circuit, then self-testing guarantees that all faults in F produce detectable errors during normal operation. The properties of self-testing and fault secureness are further illustrated in Figure 12.5. Shown in the gure are also the set of all faults and its subset F, the input space y and its subset S. For example, F shows the set of single-stuck faults, or the set of unidirectional faults. The outside of F shows all possible faults excluding the faults in F. For input vectors, N shows the set of normal input codewords, and the outside of N shows the set of input noncodewords. For output vectors, S shows the set of output codewords, and outside of S shows the set of output noncodewords. In the absence of faults, inputs from N produce outputs in S, as indicated by the translation Y X; l for various X. Self-testing is demonstrated by the existence of a test Web Pages Crystal code 128c implementon visual
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