ECE 349 Homework Assignment #8 Solutions
Show your work! You will not receive full credit for the answer alone.
1. Design a counter that counts in the sequence: 101, 100, 011, 010, 001, 000, 101, ...
Use clocked D flip-flops. Draw the circuit diagram. What will happen if your counter
starts in an invalid state?
A B C A+ B+ C+ Da Db Dc
000 101 101
001 000 000
010 001 001
011 010 010
100 011 011
101 100 100
110 XXX XXX
111 XXX XXX
Design Equations: Da =AC +A0B0C0,Db =AC 0+BC ,Dc =C0
If in state 110, NS is 011. If in state 111, NS is 110.
2. Repeat problem (1) using J-K flip-flops. You do not need to draw the circuit diagram.
A B C A+ B+ C+ Ja Ka Jb Kb Jc Kc
000 101 1X 0X 1X
001 000 0X 0X X1
010 001 0X X1 1X
011 010 0X X0 X1
100 011 X1 1X 1X
101 100 X0 0X X1
110 XXX XX XX XX
111 XXX XX XX XX
Design Equations: Ja =B0C0,K a =C0,J b =AC0,K b =C0,J c = 1, Kc = 1
If in state 110, NS is 001. If in state 111, NS is 111. It would be wise to redesign this
state machine so state 111 leads to some valid state.
