EAST-WEST DESIGN & TEST WORKSHOP
2004
Design of Totally Self-Checking
Combinational Circuits by Use of
Complementary Circuits
V. Saposhnikov
Vl. Saposhnikov
G. Osadtchi
A. Morozov
M. Gössel
Petersburg State
Transport University
University of Potsdam
Fault Tolerant Computing
Group
24 September, Alushta
Duplication and Comparison
functional circuit
inputs
y
f
C
y
f
C
error indication
Must be Totally Self-Checking
Equality checker
f C
Problem:
There may not be enough different inputs to test the checker
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Error detection by use of systematic codes
functional circuit
Must be Totally Self-Checking
error indication
f C
Problem:
There may not be enough different inputs to test the checker
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Error detection by use of complementary circuit
functional circuit
Must be Totally Self-Checking
error indication
f -
g -
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
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Complementary Circuits for Concurrent Checking
The checker has only ( n ) inputs instead of ( n+k )
Optimisation of the complementary circuit
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Circuit implementing four identical functions
DC, SC
DC, SC
PP
Parity
Prediction (PP)
All the XOR gates
will not be
completely
tested.
Duplication and
Comparison (DC)
Only the outputs
vectors
{0000 | 0000}
{1111 | 1111}
will be applied
Systematic
Codes (SC)
Only two different
input words will be
applied
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inputs
f
C
fC
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
Equality checker
Duplication and Comparison
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Parity Prediction
f
1
inputs
f
f2
C
1 0
1 0
XOR
XOR
XOR
1
2
3
P
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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
Totally self-checking circuit can be designed
by use of a complementary circuit
Combinational Circuit with 4 identical functions
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Formal Conditions
Two conditions (necessary and sufficient):
1.
Condition
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Formal Conditions
Two conditions (necessary and sufficient):
2.
Condition
For every output j there exists a set
two inputs
and
of
with
a.
b.
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Design of totally self-checking circuit
1. For
we put
Since
we have
Since
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
(
These sets exist because of the first condition
)
We define:
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Design of totally self-checking circuits
From
we have
and from
we conclude
The XOR-element XOR
is tested by 00 and 11
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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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