Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

8 Solved Questions on Input string Circuit - Homework 6 | CSE 120, Study notes of Computer Science

Homework 6 Material Type: Notes; Professor: Goryll; Class: Digital Design Fundamentals; Subject: Computer Science and Engineering; University: Arizona State University - Tempe; Term: Fall 2011;

Typology: Study notes

2010/2011

Uploaded on 11/15/2011

hnquy
hnquy 🇺🇸

5

(2)

14 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Chapter 6, problem 1: For each of the following state tables, show a state diagram and complete
the timing trace as far as possible (even after the input is no longer known).
(a)
Since q1*q2* go through all possible two bit combinations, we have four states to account for in
our state diagram. Since the states do not correspond to the output values for z, we have to take
into account the input variable x in the output equation. We can come up with the following state
transition diagram (labels at the arrows denote the x/z pair):
The timing trace can be completed as follows:
x 1 0 1 1 0 0 0 1
q1 0 0 0 1 0 1 0 0 1 0 1 0
q2 0 0 1 1 1 0 0 1 1 1
z 1 0 0 0 0 1 0 0 ? 0
After the last input is known, state 11 always goes to 01 independent of the input. Then 01 goes
to either 10 or 11; thus q1 = 1. Finally, both 10 and 11 go to either 00 or 01, making q1 = 0. The
output depends upon the input in state 11, but is 0 for both values of x in state 01. Generally, we
do not worry about values once one is not known; thus the last z may be omitted.
q1*q2* z
q1 q2 x = 0 x = 1 x = 0 x = 1
0 0 0 1 0 0 0 1
0 1 1 0 1 1 0 0
1 0 0 0 0 0 1 1
1 1 0 1 0 1 1 0
S1
S0
1/1 S3
S2
0/1
1/1
0/0 0/0
1/0
0/1
1/0
pf3
pf4
pf5

Partial preview of the text

Download 8 Solved Questions on Input string Circuit - Homework 6 | CSE 120 and more Study notes Computer Science in PDF only on Docsity!

Chapter 6, problem 1 : For each of the following state tables, show a state diagram and complete the timing trace as far as possible (even after the input is no longer known).

(a)

Since q 1 q2 go through all possible two bit combinations, we have four states to account for in our state diagram. Since the states do not correspond to the output values for z , we have to take into account the input variable x in the output equation. We can come up with the following state transition diagram (labels at the arrows denote the x/z pair):

The timing trace can be completed as follows:

x 1 0 1 1 0 0 0 1 q 1 0 0 0 1 0 1 0 0 1 0 1 0 q 2 0 0 1 1 1 0 0 1 1 1 z 1 0 0 0 0 1 0 0? 0

After the last input is known, state 11 always goes to 01 independent of the input. Then 01 goes to either 10 or 11; thus q 1 = 1. Finally, both 10 and 11 go to either 00 or 01, making q 1 = 0. The output depends upon the input in state 11, but is 0 for both values of x in state 01. Generally, we do not worry about values once one is not known; thus the last z may be omitted.

*q 1 q 2 * z q 1 q 2 x = 0 x = 1 x = 0 x = 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0

1/1 S 0 S 1 S 2 S 3

Chapter 6, problem 3 : For the input shown below, show the flip flop outputs (assume negative edge triggered flip flops)

Clock D or T CLR' (b and e) CLR' PRE'

a) Assume a D flip-flop without a clear or preset

b) Assume a D flip-flop with active low clear

c) Assume a D flip-flop with active low clear and preset inputs

d) Assume a T flip-flop,and the Q is initially 0 (no clear or preset)

e) Assume a T flip-flop with active low clear

Chapter 6, problem 5 : Considering the following circuit, complete the timing diagram if the flip flop is:

a) A D flip-flop (assume Q = 0 initially)

From the circuit above, we see that IN = D = xQ' + x'Q = x ⊕ Q. When x = 0 then D = Q and when x = 1 then D = Q'. Thus the output holds its state whenever x = 0 and toggles whenever x = 1. Therefore, this circuit behaves like a T flip-flop, where x serves as the T input. This behavior allows us to complete the timing diagram:

CLK x Q Q'

b) A T flip-flop (assume Q = 0 initially)

As in part (a), IN = T = x ⊕ Q. When x = 0 and Q = 0, then T = 0 and the output holds its state at 0. When x = 0 and Q = 1, then T = 1 and the output toggles its state to 0. When x = 1 and Q = 0, then T = 1 and the output toggles its state to 1. When x = 1 and Q = 1, then T = 0 and the output holds its state at 1. So, whenever x = 0, the output goes to 0 and whenever x = 1 the output goes to 1. Thus, this circuit behaves like a D flip-flop, with x serving as the D input.

CLK x Q Q'

Chapter 6, problem 6 : We have a new type of flip flop with inputs A and B. if A = 0, then Q* = B; if A = 1, Q* = B'.

(a) Show the state diagram for this flip flop.

To determine the state diagram for this flip flop, it is advisable to set up a behavioral table first, indicating all possible input combinations and output states before and after an input transition:

The flip flop has two states S 0 and S 1 , which can be represented by a 0 or a 1 at the output. From the description and the behavioral table we see that the output transition is independent of the previous state Q. Our state diagram looks like that:

(b) Write an equation for Q* in terms of A, B and Q.

We can use a K-Map to determine the algebraic expression for Q*:

Q

AB

00^0

11^0

A B Q Q*

S 1

0 0 S 0

Q* = A'B + AB' = A + B

Chapter 6, problem 8: For the following circuit and input string: i. Construct a state table ii. Show a timing trace for the flip-flops and the output. Assume an initial value of 0 on each flip-flop.

a)

From this circuit, we can see that Q1* = X + Q2', Q2* = Q1, and Z = Q1 + Q2'. This information can be used to construct the state transition table, and the table can be used to complete the timing trace.

Q1 Q2 Q1* Q2* (X = 0) Q1* Q2* (X = 1) Z

X 0 0 1 1 0 0 1 1 0

Q1 0 1 1 1 1 0 0 1 1 0? 1?

Q2 0 0 1 1 1 1 0 0 1 1 0? 1

Z 0 0 0 0 0 1 0 0 0 1 0 0?