2002 Fall Assignment 3

Due date: Oct. 15, 2002

Reminder: 2^nd Midterm Oct. 17^th, 2002

1. Simplify the Boolean function F together with the don't-care conditions d in
products-of-sum form.

F(w,x,y,z)=(0,1,2,3,7,8,10)
d(w,x,y,z)=(5,6,11,15)

2.Design a combinational circuit with three inputs x,y,z and three outputs A,B,C.
When the binary input is 0,1,2,or 3, the binary output is one greater than the input.
When the binary input is 4,5,6, or 7, the binary output is one less than the input.

3. Design a sequential circuit with two JK flip-flops A and B and two inputs E and x.
If E=0, the circuit remains in the same state regardless of the value of x. When E=1 and x=1,
the circuit goes through the state transitions from 00 to 01 to 10 to 11 back to 00,and repeat.
When E=1 and x=0,the circuit goes through the state transitions from 00 to 11 to 10 to 01
back to 00 and repeat.
(Draw state diagram, excitation table, Kmap with outputs and final logic diagram)

4. p.48 Problem 10

5. p.49 Problem 21

6. p.49 Problem 24

7. Complete the waveform for Y and Q for the following edged-triggered JK and T flip flops shown below. (Assume that the gate propagation delay is zero.)

$\begin{figure} \centerline{\psfig{file=figures/exam2_p2a_sol.xfig.eps,width=3.5in}} % \end{figure}$

8. Consider the sequential circuit depicted below.

$\begin{figure} \centerline{\psfig{file=counter.xfig.eps,height=1.8in}}\end{figure}$

Derive the J-K flip flop input equations for all three J-K flip flops.

Derive the next state function.

Construct the state table. And the state diagram.