Chapter 5 – Sequential Circuits

Find Flip-Flop Input and Output Equations:
Example 2 – Gray Code Assignment
• Assume D flip-flops
• Obtain K-maps for D 1 , D 2 , and Z:
D 1 D
X
2
Z
X
Y 1
0
0
0 1
1 1
0 0
Y 2
Y 1
0
0
0
0
1
1
1
1
Y 2
Y 1
0
0
0
0
X
0
0
0
1
Y 2
Chapter 5 - Part 2 27
Optimization: Example 2: Assignment 2
• Performing two-level optimization:
D 1 D
X
2
Z
X
0 0 0 1 0 0
0 1
0 0
Y
0 1
2
Y Y 2
1 1
2
0 0
Y
0 1
1
Y Y 1
0 0
1
0 1 0 1
D 1 = Y 1 Y 2 + XY 2 Gate Input Cost = 9
D 2 = X Select this state assignment to
Z = XY 1 Y 2 complete design in slide
X
Chapter 5 - Part 2 28
14