1. Design of Totally Self-Checking Combinational Circuits by Use of Complementary Circuits V. Saposhnikov Vl. Saposhnikov G. Osadtchi Petersburg State Transport University A. Morozov A. Morozov M. Gössel University of Potsdam Fault Tolerant Computing Group EAST-WEST DESIGN & TEST WORKSHOP 2004 24 September, Alushta

2. Duplication and Comparison f f y y inputs error indication Must be Totally Self-Checking Must be Totally Self-Checking f - functional circuit C C C Problem: There may not be enough different inputs to test the checker Equality checker EWDTW’04

3. Error detection by use of systematic codes error indication Problem: There may not be enough different inputs to test the checker f - functional circuit Must be Totally Self-Checking Must be Totally Self-Checking C EWDTW’04

4. Error detection by use of complementary circuit The circuit is totally self-checking if: All inputs 00, 01, 10, 11 are applied to the XOR-elements All possible code words are applied to the checker f - functional circuit error indication g - complementary circuit Must be Totally Self-Checking Must be Totally Self-Checking EWDTW’04

5. Complementary Circuits for Concurrent Checking ( n )( n+k ) The checker has only ( n ) inputs instead of ( n+k ) Optimisation of the complementary circuit EWDTW’04

6. Only the outputs vectors {0000 | 0000} {1111 | 1111} will be applied Duplication and Comparison (DC) Systematic Codes (SC) All the XOR gates will not be completely tested. Only two different input words will be applied Parity Prediction (PP) DC, SC PP Circuit implementing four identical functionsEWDTW’04

7. Duplication and Comparison f Equality checker inputs 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 f Not completely tested C C EWDTW’04

8. Parity Prediction f inputs Not completely tested 0 0 P 1 1 XOR 1 2 3 C 1 f f 2 EWDTW’04

9. n-out-of-m codes duplication 4-out-of-8 code words Combinational Circuit with 4 identical functions } EWDTW’04

10. Complementary Circuit Combinational Circuit with 4 identical functions Totally self-checking circuit can be designed by use of a complementary circuit EWDTW’04

11. Formal Conditions 1. Condition Two conditions (necessary and sufficient): EWDTW’04

12. two inputs and Formal Conditions 2. Condition For every output j there exists a set of with a. b. Two conditions (necessary and sufficient): EWDTW’04

13. Design of totally self-checking circuit 1. For we put Since we have EWDTW’04

14. Design of totally self-checking circuit : Result Thus the XOR-element XOR is tested so far by 01 and 10 EWDTW’04

15. Design of totally self-checking circuit 2. Now we select for a second set of inputs with We define: ( These sets exist because of the first condition ) EWDTW’04

16. Design of totally self-checking circuits The XOR-element XOR is tested by 00 and 11 we have we conclude From and from EWDTW’04

17. Design of totally self-checking circuit For the XOR-elements are completely tested by and all the n different code vectors are actually generated. For the remaining inputs the functionscan be easily determined. EWDTW’04

18. Design of totally self-checking circuit : Result All the XOR-elements are completely tested by 00, 01, 10 and 11. All the 1-out-of-n code words are applied to the code checker. EWDTW’04

19. Example of the four identical functions 1-out-of-4 code words } EWDTW’04

20. Design What can we do for a large circuit which is given as a netlist of gates? Simulate the circuit with N pseudorandom inputs; For every output j determine: If The sets and can be easily determined and a Totally Self-Checking Circuit can be designed. EWDTW’04

21. Experimental Results For all the considered benchmarks circuits this conditions is satisfied LGSynth’89 benchmark circuits EWDTW’04