1. Sequential logic design principles
Chapter 7
Sequential logic design principles
Memory devices : Latch and Flip-flop
Sequential logic : Pipeline and FSM
Analysis and Synthesis for FSM

2. States analyze examples
Design an “1s-counting machine :
The output Z should be 1 if the number of 1 inputs on X and Y since reset is a multiple of 4, and 0 otherwise.

3. States analyze examples
Step 1: set up enough state with different meaning ;
State name state meaning
S initial or four 1s, Z=1;
S one 1s, Z=0;
S two 1s, Z=0;
S three 1s, Z=0;

4. States analyze examples
Step 2: set up the state diagram and the state table ; S* XY Z
State
meaning 00 01 11 10 S0 S1 S2 1
Zero 1s S3
One 1s
Two 1s
Three 1s

5. States analyze examples
Step 3: get the transition table according to the state coding;

6. States analyze examples
Design a “simple state machine ”:
The output Z should be 1 if :
A had the same value at each of the two previous clock ticks or B is 1 and last Z was 1.

7. States analyze examples
Step 1: set up enough state with different meaning ;
State name state meaning
S initial state;
S A=0;
S A=1;
S A=00; Z=1;
S A=11; Z=1;
S A=01; Z=1;
S A=01; Z=0;
S A=10; Z=1;
S A=10; Z=0;

8. States analyze examples
Step 2: state / output table

9. States analyze examples
Step 3: state minimization
Equivalent state:
the current output is the same;
the transition states is the same on same inputs;
The equivalent states should be replaced by a single state !

10. States analyze examples
Step 3: state minimization
Equivalent states pairs:
S5—S4 S6—S2 S7—S3 S8—S1 S* AB Z 00 01 11 10 S0 S1 S2 S3 S4 1
The minimal
state/output table

11. States analyze examples
Step 3: state minimization
The minimal state diagram

12. States analyze examples
Step 4: state assignment
Use decomposed assignment, output is Q2;

13. States analyze examples
Step 4: transition table and minimal cost design

14. Transition list and minimization
Step 4: transition list and minimal cost design

15. Transition list and minimization
Step 4: transition list and minimal cost design