Logic Design for Array-Based Circuits

by Donnamaie E. White

Faults and Fault Detection

Last Edit July 22, 2001

Selecting a Chain

When all the possible links have been formed, there will be one or more observable chains or sets of links. The longest chain defines the desired Test Sequence.

Figure 9.5 Minimal Test Sequence for the Function Y = X3X2 + X1X0

Minterm #	Y	X3	X2	X1	X0
5	0	0	1	0	1
29	1	1	1	0	1
9	0	1	0	0	1
27	1	1	0	1	1
10	0	1	0	1	0
30	1	1	1	1	0
6	0	0	1	1	0
23	1	0	1	1	1
5	0	0	1	0	1

Note that, for each vector, one input changes state and the observable output changes state. Each input switches from 0-1 and from 1-0 during the test sequence. If the internal nets X4 and X5 were added to the table, they would also be observed to switch. This sequence provides 100% fault coverage for the function.

There are cases when there is no longest chain. When a circuit is redundant there may be two chains or sequences of equal length and only one needs to be used for fault detection. Some faults will remain masked regardless of the sequence selected.

Disjoint functions with terms that share no variable states will have a disjoint sequence, existing as two or more chains. A stepped sequence must be generated to connect the disjoint sequences, honoring the rule that only one input may change per vector.

Advantages of the test sequence

The advantages of the Minimal Test Sequence are listed in Table 9-5.

Table 9-5 Advantages Of The Minimal Sequence

Reduction of test hazards
One observable output changes per vector allowing for straightforward identification of the existence of an error.
All variables are toggled from 0-1 or 1-0 and back
Complete coverage of all detectable single faults
Covers multiple faults
Closed sequence which allows easy repetitive application
Possible coverage of bridging faults (not yet researched)