1. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Topics n State assignment. n Power optimization of sequential machines. n Design validation. n Sequential testing.

2. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf State assignment n Encoding bits in symbolic state = state assignment. n State assignment affects: –combinational logic area; –combinational logic delay; –memory element area.

3. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf State assignment in n-space 0 s1 code = 111 s2 code = 110 1 1 1

4. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf State assignment and delay output Next state

5. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Power optimization Memory elements stop glitch propagation:

6. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Sequential testing n Much harder than combinational testing— can’t set memory element values directly. n Must apply sequences to put machine in proper state for test, be able to observe value of test.

7. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Example

8. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Testing the machine n To test NAND for stuck-at-1, must set both NAND inputs to 1. n Primary input i1 can be controlled directly. n To set lower NAND input, must set state to ps0 = ps1 = 1.

9. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Example state machine State codes: s0 = 11 s1 = 10 s2 = 01 s3 = 00

10. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Controlling an FSM n Don’t know initial state of machine. n Must find a sequence which drives machine to required state independent of initial state. n State sequence for test: * -> s0 -> s1 -> s3.

11. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Time-frame expansion n A model for sequential test: unroll machine in time. n Time frame expansion illustrates how single-stuck-at fault in sequential machine appears to be multiple-SA fault.

12. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Time-frame expansion example

13. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Unreachable states n State assignment may cause some states to be unreachable. n As a result, it may not be possible to apply some required test values.

14. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Unreachable state example s0s0 s1s1 s2s2 1/ 0/ 1/ 0/ 1/

15. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Example n State codes: –s0 = 00 –s1 = 01 –s2 = 10. n This creates a fourth state which is unreachable.

16. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Implemented FSM 0001 1011 1/0/ 1/ 0/0,1/ 0/ 1/

17. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf LSSD n LSSD = level-sensitive scan design. n Way to achieve full controllability, observability of registers. n Links all registers in a scan chain.

18. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf LSSD latch

19. Modern VLSI Design 4e: Chapter 5 Copyright  2008 Wayne Wolf Partial scan n Full scan is expensive—must roll out and roll in state many times during a set of tests. n Partial scan selects some registers for scanability. n Requires analysis to choose which registers are best for scan.