design of totally self-checking combinational circuits by use of complementary circuits v....
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Design of Totally Self-Checking Combinational Circuits by Use ofComplementary Circuits
V. Saposhnikov V. Saposhnikov Vl. SaposhnikovVl. Saposhnikov
G. OsadtchiG. Osadtchi
Petersburg State Petersburg State Transport UniversityTransport University
A. MorozovA. MorozovM. GösselM. Gössel
University of PotsdamUniversity of PotsdamFault Tolerant Computing Fault Tolerant Computing
GroupGroup
EAST-WEST DESIGN & TEST WORKSHOPEAST-WEST DESIGN & TEST WORKSHOP20042004
24 September, Alushta24 September, Alushta
Duplication and Comparison
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Must be Totally Self-CheckingMust be Totally Self-Checkingf f - - functional circuitfunctional circuitCC
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Problem:There may not be enough different inputs to test the checker
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Error detection by use of systematic codes
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Problem:There may not be enough different inputs to test the checker
f f - - functional circuitfunctional circuit Must be Totally Self-CheckingMust be Totally Self-CheckingCC
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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 f - - functional circuitfunctional circuit
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g g - - complementary circuitcomplementary circuit
Must be Totally Self-CheckingMust be Totally Self-Checking
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Complementary Circuits for Concurrent Checking
The checker has only ( n )( n ) inputs instead of ( n+k )( n+k )
Optimisation of the complementary circuit
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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
DC, SC
PP
Circuit implementing four identical functions
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Duplication and Comparison
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inputs
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Not completely testedNot completely tested
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Parity Prediction
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inputs
Not completely testedNot completely tested0
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1 XOR1
XOR2
XOR3
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n-out-of-m codes duplication
4-out-of-8 code words
Combinational Circuit with 4 identical functions }
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Complementary Circuit
Combinational Circuit with 4 identical functions
Totally self-checking circuit can be designed by use of a complementary circuit
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Formal Conditions
1. Condition
Two conditions (necessary and sufficient):
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two inputs and
Formal Conditions
2. Condition For every output j there exists a set of
with
a.
b.
Two conditions (necessary and sufficient):
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Design of totally self-checking circuit
1. For we put
Since
Since
we have
we have
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Design of totally self-checking circuit : Result
Thus the XOR-element XOR is tested so far by
01 and 10
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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 )
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Design of totally self-checking circuits
The XOR-element XOR is tested by 00 and 11
we have
we conclude
From
and from
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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 functions can be easily determined.
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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.
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Example of the four identical functions
1-out-of-4 code words
}
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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.
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Experimental Results
For all the considered benchmarks circuits this conditions is satisfied
LGSynth’89 benchmark circuits
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