Lecture 04 - Test Generation Combinational

Lecture 04 - Test Generation Combinational - Testing and...

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1 1 Testing and Testable Design Testing and Testable Design `x{Üwtw aÉâÜtÇ| Dept. of EE Univ. of Texas at Dallas 2 Test Generation for Combinational Circuits Session 04 Session 04
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2 3 Fault Analysis System (Review) Fault Collapsing Test Generation Fault Simulation 4 Test Generation Techniques There are two main test vector generation techniques 1. Non-Structural Analyzes the gate-level description of a circuit and implicitly enumerate all possible input combinations to find a test vector for a target fault. 2. Structural Analyzes the structure of a given circuit to generate a test vector for a given target fault, or declare it untestable.
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3 5 Non-Structural Test Generation 6 Fault Detection in Combinational Circuits A test (vector) t detects a fault f if and only if Z f (t) Z(t) (i.e., at least one of the outputs are different in N and N f ). For a single output circuit Z f (t) Z(t) is equivalent to Example: find tests to detect s-a-0 at x 4 . ( ) ( ) 1 = t Z t Z f
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4 7 Fault Detection in Combinational Circuits (cont’d) Fault-free output: Faulty output: Test vectors to detect s-a-0 at x 4 satisfy x 1 x 4 =1 that are: ( ) 4 1 1 3 2 x x x x x Z + + = ( ) 1 3 2 f x x x Z + = () [] ( ) [ ] 4 1 1 3 2 4 1 1 3 2 f x x x x x x x x x x Z Z = = + + + = ... 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 x x 0 x 4 x 3 x 2 x 1 x 4 x 3 x 2 x 1 8 Boolean Difference Consider a Boolean function f(x) where x=(x 1 ,x 2 ,…,x i ,…,x n ) is the input vector. Cofactors of f: Shannon Expansion Theorem: ( ) () = = = = = = = = 1 1 0 x x 1 1 1 x x ,..., 0 ,..., f f ,..., 1 ,..., f f i i i i x x x f x x x f i i () () + + = + = i i i i x i x i x i x i f x f x f(x) f x f x f(x)
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5 9 Boolean Difference (cont’d) Definition of Boolean difference: means s-a-0 or s-a-1 at x i cannot be observed at the output. In other words, s-a-f at x i is undetectable. If then: i i x x i f f dx df = 0 dx df i = 1 dx df i = i i i i i i x at 1 - a - s detect can that vectors test all gives 1 x dx df x at 0 - a - s detect can that vectors test all gives 1 x dx df = = Stimulate the fault Propagate the fault effect 10 Boolean Difference (cont’d) Example: So ab=01 is the only test vector that can detect s-a-0 at line p. [] [] [] 01
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This note was uploaded on 08/23/2009 for the course EE 6303 taught by Professor Mehrdadnourani during the Fall '08 term at University of Texas at Dallas, Richardson.

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Lecture 04 - Test Generation Combinational - Testing and...

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