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Does There Exist a Combinational TSC Checker

for 1/3 Code Using Only Primitive Gates?

**Wen-Feng Chang and Cheng-Wen Wu**

National Tsing Hua University

Hsinchu, Taiwan, R.O.C.

The answer is "no." For gate-level circuits and single stuck-at faults, it has been shown that all *m*/*n*-code TSC checkers can be successfully designed, except one for 1/3 code. Although many researchers believe such a checker does not exist, none has proved that this is the case, which makes the problem open. In this paper, we show that no such checker exists using only AND, OR, and NOT gates (and, therefore, NAND and NOR gates). We solve this problem by giving a strict and clear proof. We also can deduce from our proof that no such TSC checker exists for any code which has only three code words.

Keywords: concurrent error detection, digital testing, m-out-of-n code, 1-out-of-3 code, single stuck-at fault, totally self-checking checker

Received September 27, 1995; revised November 1, 1996.

Communicated by Jhing-Fa Wang.