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Design for Testability (DfT)

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OUTLINE Motivation Background and Definitions Boolean Difference and Testing of Digital Circuits Combinational Circuit Testing –Path Sensitization –D-Algorithm

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How do we know that our Design works? f(x) x=(x 0,x 1,..,x n ) q=(q 0,q 1,…q n ) Fault!!!

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System Validation Techniques Simulation –Validate a model of the system. Emulation –Build a prototype and validate. Testing –Check the correctness of actual system. Formal Verification –Mathematically show the ’Equivalence’ of the specification and the implementation.

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Definitions: Errors and Faults Error : Incorrect operation of the system. Cause of Error are Faults – Design error, fabrication error, fabrication defect, physical defects. Logical Fault: Faults which result in a change in logic value at a point in a circuit. Fault Model: The effect of a fault is represented by a model –Stuck-at-fault –Bridging fault –Stuck-open fault –Linking faults: Memories

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Fault Probabilities

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Dynamic Faults Timing Failures Components out of specification Static Faults Short-circuits Breaks Intermittent Faults (Environmental Faults) –Single-Event Upsets - SEUs ESD Particles Magnetic Fields

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Testing Techniques General Method –The behavior (Response) of the system is observed by applying a sequence of test inputs (Stimuli). Generation of Stimuli –Test various cases –Random Patterns: Random Testing –Algorithmic Test Pattern Generation Combinational Circuit Sequential Circuit Test Time –Time to generate tests and apply them to the circuit under test Fault Coverage –Percentage of all the faults detected by a set of test patterns

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Test Cost and Quality Cost of testing Quality Cost of quality Cost Cost of the fault 100% 0% Optimum test

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Design for Testability( DFT) To take into account the testing aspects during the design process so that testing is simpler and faster. –Reduce test effort –Reduce test time –Reduce cost of test equipment –Increase product quality Limitations –Hardware overhead ( 5-30%) –Performance degradation –Increase in design complexity

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Fault Models Stuck Fault Model –Stuck-at-0 (S-a-0) & Stuck-at-1 model (S-a-1) Single-Stuck Fault Model –Heuristic Model, multiple faults do occur. Model appears to be valid most of the times Other Stuck Fault Models –Variants including Stuck-at-open, Stuck-at-short

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Faults Model : Assumptions For Combinational Circuits –Logical faults only –Only those faults which can be modeled as a signal stuck-at-0 or stuck-at-1. –Single fault –Permanent fault For Sequential Circuits –State table of the faulty sequential circuit is different from the good circuit.

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Fault-oriented Test Pattern Generation Combinational circuit with n inputs –2 n possible patterns (exhaustive test) –Find minimum number of necessary input patterns Problem: Some nodes may not be testable because of circuit structure

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Fault Detection in Logic Circuits Number of possible faults Equivalent faults For an n-input AND gate, any input s-a-0 is equivalent to the output s-a-0. The same test (all 1’s) is required to test any of these faults. Gate x1 x2 x3 z x1 s-a-1 x1 s-a-0 x2 s-a-1 x2 s-a-0 x3 s-a-1 x3 s-a-0 z s-a-1 z s-a-0 N input gate may have 2(N+1) stuck at faults

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Testability Controllability –Can we control all nodes to establish whether there is a fault? Observability –Can we observe and distinguish between the behavior of a faulty node and a free node?

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Detectable Stuck-At Fault a b c d e S-a & 11 11 Good Circuit Faulty Circuit

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Fault Masking and Redundant Circuit The fault cannot be detected because the circuit has redundancy. Example: a b d e & 11 11 S-a-0 10X10X 110X110X X10X 010X010X 1 0 Good Circuit Faulty Circuit

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Undetectable faults In general, untestable faults are due to redundancy Conversely, redundant circuits are not fully testable Fan-out may also cause untestable faults

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Undetectable faults ACBACB Z D F Consider Z=AC+BC - to avoid hazard we add the term AB => Z=AC+BC+AB => Impossible to test F/0 E

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Undetectable faults’ fix ACBACB Z D F Solution: Add internal wires to propagate an internal value to a new output E Z2Z2

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Ad Hoc DFT Techniques Test Point Insertion C1C2 C1 C2 CP0 CP1 OP Demultiplexing Control Points Multiplexing Observation points DemuxDemux C CP1 CP2 CPN 1 2 m MuxMux O OP1 OP2 OPN 1 2 m

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Test Generation for Combinational Circuits Truth Table and Fault Matrix Example: x1 x2 x3 z z z z z z z Truth table approach not practical if number of inputs is large. & & & 11 x1 x2 x2 x3 x1 x3 z s-a-0 and s-a-1

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Testing Sequential Circuits Testing of sequential circuits is harder than combinational circuits Sequential Circuit Testing requires verification of the state table –Verify Reachability of all states –Verify all transitions Assumption: –Only the inputs and outputs are accessible, internal flip- flops are not accessible

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Testing Sequential Circuits Fortunately for us, ad-hoc testing techniques (like scan-chains) has made the internal flip-flops accessible, so the last assumption does not hold! In case access to internal flip-flops is too costly, standard sequential test methods still have to be applied, see Appendix.

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Testing Sequential Circuits – Scan-based Techniques Sequential Circuits have poor controllability and poor observability Comb. Part PI PO Comb. Part PI PO Scanin Scanout

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Full Scan and Partial Scan Full Scan: –Connect all the storage elements to form a long shift register (scan chain) –The storage elements can be easily tested by shifting in a pattern and observing the output –Testing of sequential circuit testing can be now treated as testing of combinational circuit –Full scan is costly and slow Partial Scan –Select a subset of storage elements to be included in the scan chain

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Random Access Scan To achieve controllability and observability of all registers –Access one register at a time Comb. Part PI PO Scan Address Scan-inScan-out Memory

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Board Level DFT: Boundary Scan Every input and output port of a chip is included in a special scan chain Main Logic Test Data In Test Clock Test Mode Test Data Out PI PO SI SO

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Boundary Scan Cell ClockDRUpdateDR MuxMux MuxMux PIPO SI SO

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JTAG Standard (IEEE ) I/O Pad Boundary-Scan cell Boundary Scan-path

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Summary of DfT Testing of complex digital systems is a hard but very important task. –Test Pattern Generation is most important in testing Testing contributes substantially to the cost and effort required to design a new product. Methods are required to reduce this cost and effort. –Design for testability –Reuse of proven designs –Formal Methods

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Test Pattern Generation - part I Built-In Self Test (BIST) Methods

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Testing a Circuit Circuit Under Test Test Pattern Generator Response Analyzer Test Equipment Pulse and Function generators Oscilloscope Logic Analyzers Computers Specialized Zigs + Test Engineer

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Self-Test a Circuit – Built-In Self Test (BIST) Circuit Under Test Test Pattern Generator Response Analyzer Test Engineer Package the test equipment along with the circuit!

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BIST: Requirements Generation of Test patterns for testing –DFT is very important –Algorithm has to be very simple and easy to implement in hardware Comparing Response –It is not possible to store the response in memory: area overhead –Related to Test Pattern Generation Compression of Test Patterns and Response is essential for BIST design

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Test Generation and Response Compression Circuit Under Test Data Compression Unit Comparator Input Test Sequence T Output Response R Signature S(R) Correct Signature Error Indicator Test Generator Unit

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General Aspects of Compression A simple hardware implementation It should not slow down normal operations Good Compression –The signatures of good and faulty circuit should be different –Small size of signature. Signature size should be log of data size. Issues: –How to generate signatures for good circuit?

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Generic Off-line BIST Architectures Classification –Centralized or Distributed BIST circuitry –Embedded or Separate BIST Key Elements of BIST –Test pattern Generator (TPG) –Output Response Analyzers (ORA) –Circuit Under Test (CUT) –A Distribution system for transmitting data from TPG to CUT and from CUT to ORAs. –A BIST Controller

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Test Pattern Generation for BISTs Exhaustive Testing Exhaustive Test Pattern Generators Pseudo-Random testing Weighted test generator Adaptive Test Generator Pseudo-Exhaustive testing Constant Weight Counter Combined LFSR and Shift Register Combined LFSR and XOR Cyclic LFSR

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Exhaustive Testing Apply all possible 2 n test patterns to a n input circuit. A binary counter can be used Or a maximum length autonomous LFSR can be used (add special circuit to generate all zeros). Normally applied when number of inputs are less than 25.

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Pseudorandom Testing Patterns are generated deterministically but have characteristics of random patterns. Pseudo-random patterns without replacement can be generated using autonomous LFSRs. Test length can be chosen to achieve the desired fault coverage. This can be determined using fault simulation. Limitation –LFSR tend to produce patterns with equal numbers of 1’s and 0’s –For some circuit it is better to bias the distribution of 0’s and 1’s of the pattern generator. For example testing of AND requires more 1’s in the test pattern.

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Weighted Test Generation Generate Test Patterns with the desired distribution of 1’s and 0’s. Such a generator can be constructed using a LFSR and a combinational circuit. Different parts of the circuit may require different distribution of 0’s and 1’s.

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Adaptive Test Generation Also employs weighted test pattern generation. Fault simulation is used to determine weights for various faults. Different distributions are used for different class of faults. A Test Pattern Generator (TPG) is designed to produce the required distributions. Advantage: Small test lengths Disadvantage: Costly TPG hardware

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Pseudo-exhaustive Testing Requires fewer tests but has the advantage of exhaustive testing. Segments the circuit into parts and each segment is exhaustively tested. Logical Segmentation –Cone Segmentation –Sensitized path segmentation Physical Segmentation

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Compression Methods for BISTs Basic Idea – Apply sequence, check signature after finishing... Simple Analyzers Ones-count Compression Transition-count Compression Signature Analyzers Single-Input Signature Response (SISR) Multi-Input Signature Response Analyser (MISR) Generic BIST architectures BILBO

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Ones-Count Compression Assume a single output circuit C. Let the response of C to a test sequence be R = r 1, r 2, , r m.In ones counting the signature 1C(R) is the number of 1s appearing in R, i.e. 1C(R) = r i where 0 1C(R) m. i & & x x x3 z R R R2 X s-a-1 f1 f2 s-a-0 X

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Ones Count Compression: Analysis CircuitCounter Clock Signatures: 1C(R0) = 1 1C(R1) = 2 1C(R2) = 0 Masking Probability The probability of an erroneous output sequence having the same number of 1’s as the correct sequence. Theorem: The masking probability for ones-count compression for a combinational network circuit asymptotically approaches ( m) -1/2. x1 x2 x3

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Transition-Count Compression The Transition Count signature is the number of 0-1 and 1-0 transitions in the output response sequence R. Let the response of C to a test sequence be R = r 1, r 2, , r m. In transition counting the signature TC(R) is TC(R) = (r i r i+1 ) i=1 & & x x x3 z R0 TC(R0)= R1 TC(R1)= R2 TC(R2)= 0 f2 s-a-0 X s-a-1 f1

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Transition Count Compression: Analysis CircuitCounter x1 x2 x3 D Transition Detector Theorem: The masking probability for transition count compression for a combinational network circuit asymptotically approaches ( m) -1/2 D Q

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Signature Analysis Period of Linear Feed back shift register depends upon –Feed back connections –Intial value of register Masking probability is inversely related to the period + S S S S S S S S 7 = S

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LFSR as a Single-Input Signature Register (SISR) + ++ CnCn C n-1 C n-2 C1C1 D Q+ + CiCi : Modulo-2 addition( an ex-or gate) : If C i =1 then there is a connection otherwise no connection This Circuit can be used to compress the response with masking probability = 2 -n.

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Multiple-Input Signature Registers Method 1: Time Multiplex the signature analyzer for each output. That is repeat the test sequence for each output.This will require long test time. Method 2: Use Multiple Input Signature Register (MISR). CnCn + C n-1 + C n-2 C1C1 + + D1D1 D2D2 D3D3 DnDn Error Masking Probability = 2 -n

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Generic BIST Architectures TPG DISTDIST CUT DISTDIST ORA BIST Controller TPG CUT ORA

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Build-In Logic Block Observer (BILBO) Motivation: It is difficult to self test a circuit which has a large number of (Inputs+Outputs+Storage Cells). –You require PRSG for inputs, MISR for outputs PRSG and MISR for storage cells. –Solution: Clustering of storage cells into registers and make these registers carry out multiple jobs. BILBO is one such scheme. –Registers can be configured for : Normal Operation As PRSG As MISR As Scan Register

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BILBO Registers B1 B2 Operation 1 1 Normal Operation 0 0 Shift Register mode 1 0 PRPG or MISR EX OR B1 B2 D Q Si So X 1 X 2 X n-1 X n

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BIST design with BILBO Registers Example: R1 C1 R2 C2 R3 To Test C1 R1 as PRPG R2 as MISR To Test C2 R2 as PRPG R3 as MISR

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Summary of BIST BIST of a system requires techniques for –Data Compression –Test Pattern Generation Linear Feedback Shift Registers are good for doing both Important concerns –Masking Probability –Fault coverage –Overhead Data Compression and Test Generation Functions can be combined in one register (BILBOs)

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Test Pattern Generation – part II Automatic Test Pattern Generation (ATPG)

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Automatic Test Pattern Generation (ATPG) With Scan-chains available, deterministic tests are preferred. Generic test method: Prepare a Fault list Repeat –Write a test –check fault cover (one test may cover more than 1 fault) –delete covered faults from list until fault cover target is reached or only un-testable faults remain.

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ATPG Example ABCDABCD Z E F To test A/0 (A stuck-at-0), set A=1. To propagate A/0, set B=1 To propagate result to Z, F must be 0 Thus, Either C=0 or D=0 or C=D=0 are solutions (3 possibilities) => (110-,11-0) The test pattern (1101/0) is good because it also covers E/1, D/0, F/1 and Z/1

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Boolean Derivatives Boolean algebra: change F(X) will change if x i changes F(X) will not change if x i changes y 0,1 , F(X) 0,1 y x y = F(x) Traditional algebra: speed xixi xkxk

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Boolean Derivatives Boolean function: Y = F(x) = F(x 1, x 2, …, x n ) Boolean partial derivative:

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Example: Functional Description Example: F( x 1, x 2,x 3 ) = x 1 x 2 + x 2 x 3 + x 3 x 1 Fault: x 1 stuck-at-1 = x 2 x 3 The function F will have different output, when x 2 x 3 = 1, that is x 2 =0 and x 3 =1 OR x 2 = 1 and x 3 = 0

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Boolean Difference: Test pattern generation For a point X i s-a-1 The solution of the equation Gives all the tests for X i stuck-at-1 For a point X i s-a-0 The solution of the equation Gives all the tests for Xi s-a-0

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Boolean derivatives Useful properties of Boolean derivatives: if F(x) is independent of x i if F(x) depends always on x i Test generation algorithm: Solve the differential equation

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Boolean derivatives Useful properties of Boolean derivatives These properties allow to simplify the Boolean differential equation to be solved for generating test pattern for a fault at x i If F(x) is independent of x i

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Boolean derivatives Given: Calculation of the Boolean Difference w.r.t. x 5

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A Complete Test: Intermediate circuit points must also be tested Example & & & & ABBCCAABBCCA F h s-a-1 Test for h s-a-1 ABC = 1 A = 1; B= 1; C= 0.

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Example: Complete Test using Boolean Derivatives E ABCDABCD Z F

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Fault Cover Check Test PatternABCDEFZ Sa0Sa1Sa0Sa1Sa0Sa1Sa0Sa1Sa0Sa1Sa0Sa1Sa0Sa1 0000XX 0001XX 0010XX 0011X 1000 RedundantXXXX 0101 RedundantXXXX 0110 RedundantXXXX 0111X 1000XX 1001XX 1010XX 1011X 1100XXXXX 1101 EssentialXXXXXXX 1110XXXXX 1111 EssentialXXXX One of these

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Path Sensitization The method consists of two steps: –Identify a sensitized path from the fault site to output –Check for consistency of the assignments to the inputs Example Circuit G1 & X1 X2 7 G2 & X3 X4 8 G3 & X5 X6 9 G5 13 G6 14 G7 & 15 G S-a-0 1/ X 0X0X X Good value Bad value

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Path Sensitization G1 G5 G7 G4 G6 G3 G2 Node Gates

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Path Sensitization: Sensitization of multiple paths Example: Fault 6 s-a-0 11 11 11 11 11 11 11 11 X1 X2 X3 X /0 G1 G2 G3 G7 G4 G5 G6 G8 0/1 1/

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Path Sensitization: Sensitization of multiple paths Example (Continued) 11 11 11 11 11 11 11 11 X1 X2 X3 X /0 G1 G2 G3 G7 G4 G5 G6 G8 0/1 1/ /

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D-Algorithm The ideas of Path sensitization method are formalized. D-Notation The signal can take value from the set { 0,1,x,D,D } D0D1 Good Circuit Faulty Circuit

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Singular Cover Singular Cube is a compact representation of the truth table of a component. Example: 2-input AND gate Truth Table Singular Cover A B C A B C 0 x 0 x

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Primitive D-Cube Model of the component in the presence of fault. Example: 2-input NOR gate Fault Primitive D-Cube A s-a A B C A s-a D C s-a D C s-a-1 1 X X 1 11 ABAB C

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Propagation D-Cube Model of a good component in a faulty circuit. Must propagate the fault from the inputs to one of the outputs. Example: 2-input NOR gate A B C D 0 0 D D D D

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D-intersection This is a method to propagate fault from the component to the output and to make consistency check. Example G1 G2 3 5 X1 X2 X3 Z Fault Node 2 s-a-0 D010 D0 xx xx Primitive D-Cube Propagation D-Cube Cube Intersection

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D-Algorithm: Forward Drive G1 G3 & 3 X1 X2 X3 X4 G2 & G4 G5 & D1 D x00 D1G5 D x00 D 0G4 x0G Primitive D-Cube of Fault G2 0 x D Propog. D-Cube G4 0 D G5 1 D D

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D-Algorithm: Consistency Check D1D0x001 0x1G1 D1Dxx00 1x0G3 D1Dx Singular Cover G3 0 x 1 G1 1 x 0

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Re-convergent Fanout Example: Point 6 s-a-0 11 11 11 11 11 11 11 11 X1 X2 X3 X /0 G1 G2 G3 G7 G4 G5 G6 G8

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D-Algorithm: Sensitizing Multiple Paths X1 X2 X3 X G2 G5&G6 G8 G4 G7 G1 G3

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D-Algorithm: Worst Case and Time Complexity In the worst case the D-Algorithm will have to consider all combinations of path. In a circuit with N components, the number of combinations of paths from fault to output are: k2 N. Worst case time complexity of D-Algorithm: O(2 N ). Fortunately, in practice average time complexity is much smaller (N 2 ). –If size of circuit grows by 10, number of tests required grows by 100.

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Appendix

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Testing Sequential Circuits

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Testing of sequential circuits is harder than combinational circuits Sequential Circuit Testing requires verification of the state table –Verify Reachability of all states –Verify all transitions Assumption: –Only the inputs and outputs are accessible, internal flip- flops are not accessible

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Case Study Example Example 1 X S0 S1 S2 S3 S1,0 S1,0 S1,0 S0,1 S0,0 S2,0 S3,0 S0,0 State X= 0 X= 1 Pattern Detector Z S0 S1 S2 S3 1/0 0/0 1/0 0/1 0/0 (0110)

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Homing Sequence Def.: Smallest input sequence which brings the machine to a known state. Therefore ‘00’ is the homing sequence for the machine {S0,S1,S2,S3} 01 {S1,S1,S1,S3}{S0,S2,S3,S0} 0 1 {S1,S1,S1,S1}{S2,S2,S2,S0}

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Distinguishing Sequence Definition: Smallest input sequence which produces a different output for each starting state. Example 2: mod-4 counter S0 S1 S2 S3 S0,0 S1,0 S2,0 S3,0 S1,0 S2,0 S3,0 S0,1 State X= 0 X= 1 Example 1 does not have a common distinguishing sequence for all states. The common distinguishing sequence for Example 2 is ’1111’. S0 S1 S2 S3 Output = 0001 Output = 0010 Output = 0100 Output = 1000 X ZMod-4 counter

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Transfer Sequence Definition: Smallest input sequence which takes the machine from state i to state j, for all states i and j. Example 1: Example 2: i j Sequence S0 S1 0 S0 S2 01 S0 S3 001 S1 S0 110 S1 S2 1 S1 S3 11 S2 S0 10 S2 S1 0 S2 S3 1 i j Sequence S0 S1 1 S0 S2 11 S0 S3 111 S1 S0 111 S1 S2 1 S1 S3 11 S2 S0 11 S2 S1 111 S2 S3 1

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Checking Experiment: Steps Steps: 1. Go to a known starting state by using a homing sequence or a distinguishing sequence. 2. Check reachability of all the states 3. Check all transitions

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Checking Experiment: Step 1 Known Initial State Example 1 Homing Sequence: 00 Known State : S1 Example 2 Distinguishing Sequence: Final State : If output = 0001 then S0 else if output = 0010 then S1 else if output = 0100 then S2 else S3;

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Checking Experiment: Step2 Check reachability of all states Example 2: Known Intial State : say S1 Check reachability to S2 Give transfer sequence for S1 to S2, that is, 1 Distinguish S2 by distinguishing sequence 1111: Output should be 0100 and final state S2. Check reachability to S3 Give transfer sequence for S2 to S3, that is, 1 Distinguish S3 by distinguishing sequence 1111 Output should be 1000 and final state S3 Check reachability to S0

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Checking Experiment: Step3 Check various transitions Example 2: Present State = S0 Check transition ( S0,0) S0/0 Give 0 and check output to be 0 To check next state as S0 give distinguishing sequence 1111 and check output to be Check transition ( S0,1) S1/0 Give 1 and check output to be 0 To check next state as S1 give distinguishing sequence 1111 and check output to be Similarly all other transitions.

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