introduction to digital system

Spring 2020

ECET 111

Introduction to Digital System Design I

TAP 5 – Final Assessment

Analysis and Design of Sequential Circuits

Section: __f1__

Student Name	Student ID
Fatima Malaki	82696

S	Topic	Max Points	Earned Points	Feedback
1	Question 1	12
2	Question 2	23
3	Question 3	20
4	Question 4	30
5	Question 5	15
6	Question 6 (Bonus)	10
	Total	100

Question 1. Choose the correct answer for the following questions.

(12 points, 3 points each)

1. Consider a JK flip-flop with the present state Q(t)=1. The input values are J=0 and K=1. What is the value of the next state of the JK flip-flop?

a. Q(t+1) = 0

b. Q(t+1) = 1

c. Q(t+1) = x

d. Q(t+1) will have a random value

Answer:

2. Which of the following statements is correct?

a. A Latch is an edge-triggered device

b. A Latch is a level-triggered device

c. A Latch can be used only in synchronous sequential circuits

d. A Latch can be used only in combinational circuits

Answer:

3. In a T flip-flop, the next states Q(t+1) and Q’(t+1) can have the same value.

a. True

b. False

Answer:

4. For an asynchronous sequential circuit:

a. The output changes any time the clock signal goes from high to low (negative edge)

b. The output changes any time the clock signal goes from low to high (positive edge)

c. Its operation is synchronized by a clock signal

d. Its operation doesn’t depend on the clock signal

Answer:

Question 2. Answer the following questions for the given sequential circuit. (23 points)

1. Write the state equations for the following ports: (12 points)

TA = X B = XB’+X’B

A(t+1) = (X B)’A + (X B)A’

= (XB+X’B’) A + (XB’+X’B) A’

= XBA + X’B’A + XB’A’ + X’BA’

TB = X’

B(t+1) = (X’)’B +(X’)B’

= XB + X’B’

y(t) = A+B

2. Fill in the state table for the given sequential circuit. (11 points)

Present State	Input	Flip-Flop Inputs	Next State	Output
A	B	x	TA	TB	A	B	Y
0	0	0	0	1	0	1	0
0	0	1	1	0	1	0	0
0	1	0	1	1	1	0	1
0	1	1	0	0	0	1	1
1	0	0	0	1	1	1	1
1	0	1	1	0	0	0	1
1	1	0	1	1	0	0	1
1	1	1	0	0	1	1	1

Question 3. Design a sequential circuit with two JK Flip-Flops (A and B) and one input xin.

· When xin = 1, the state of the circuit remains the same.

· When xin = 0, the circuit goes through the transition from 00 to 10 to 01 to 11 back to 00 and repeats.

(20 points)

1. Fill in the state table for this sequential circuit. (8 points)

Present State	Input	Next State	A Flip-Flop	B Flip-Flop
A	B	xin	A	B	JA	KA	JB	KB
0	0	0	1	0	1	X	0	X
0	0	1	0	0	0	X	0	X
0	1	0	1	1	1	X	X	0
0	1	1	0	1	0	X	X	0
1	0	0	0	1	X	1	1	X
1	0	1	1	0	X	0	0	X
1	1	0	0	0	X	1	X	1
1	1	1	1	1	X	0	X	0

2. Write the state equation for the inputs of each Flip-Flop. (12 points, 3 points each)

a. K-Map for JA

Bxin A			B
	1	o	0	1
A	x	x	x	x
		xin

State equation for JA : Xin’

b. K-Map for KA

Bxin A			B
	x	x	x	x
A	1	0	0	1
		xin

State equation for KA : Xin’

c. K-Map for JB

Bxin A			B
	0	0	x	x
A	1	0	x	x
		xin

State equation for JB : A Xin’

d. K-Map for KB

Bxin A			B
	x	x	0	0
A	x	x	0	1
		xin

State equation for KB : A Xin’

Question 4. Consider a sequential circuit with three positive edge D Flip-Flops (A, B, C), one input (xin) and one output (y). The State diagram of this circuit is given below. The circuit to be designed by treating the unused states as don’t care conditions. (30 points)

1. Fill in the state table for this sequential circuit. (6 points)

Present State	Input	Next State	Output
A	B	C	xin	A	B	C	y
0	0	0	0	1	0	0	1
0	0	0	1	0	1	1	1
0	0	1	0	0	0	0	1
0	0	1	1	1	0	1	0
0	1	0	0	0	0	0	1
0	1	0	1	0	0	1	1
0	1	1	0	0	1	0	1
0	1	1	1	0	0	0	0
1	0	0	0	1	0	1	1
1	0	0	1	0	1	1	0
1	0	1	0	0	1	0	1
1	0	1	1	0	1	1	0
1	1	0	0	X	X	X	X
1	1	0	1	X	X	X	X
1	1	1	0	X	X	X	X
1	1	1	1	X	X	X	X

2. Answer the following questions. (24 points, 6 points each)

a. Find A flip-flop input equation.

A Flip-flop K-Map:

Cxin AB			C
	1	0	1	0
	0	0	0	0	B
A	x	x	x	0
	1	0	0	0
		xin

A flip-flop input equation: B’ C’ Xin’+ A’ B’ C Xin

b. Find B flip-flop input equation.

B Flip-flop K-Map:

Cxin AB			C
	0	1	0	0
	0	0	0	1	B
A	X	X	X	X
	0	1	1	1
		xin

B flip-flop input equation: f(A,B,C,Xin)= AC + B’ C’ Xin + B C Xin’

c. Find C flip-flop input equation.

C Flip-flop K-Map:

Cxin AB			C
	0	1	1	0
	0	1	0	0	B
A	X	X	X	X
	1	1	1	0
		xin

C flip-flop input equation: A C’ + C’ Xin + B’ Xin

d. Find the state equation for the output of this sequential circuit, y.

K-Map for the output y:

Cxin AB			C
	1	1	0	1
	1	1	0	1	B
A	X	X	X	X
	1	0	0	1
		xin

State equation for y: Xin’ + A’ C’

Question 5. Answer the following questions. (15 points, 5 points each)

1. What is a synchronous sequential circuit?

2. What is a Flip-Flop? Can a Flip-Flop be used in a combinational circuit? Explain your answer.

3. Consider a sequential circuit with two inputs (x1, x2), three D Flip-Flops (A, B, C) and one output (y). How many states does this sequential circuit have? Explain your answer.

Question 6. (Bonus) Answer the following questions. (10 points, 5 points each)

1. Fill in the state table for the JK Flip-Flop and the T Flip-Flop.

JK Flip- Flop
J	K	Q(t+1)
0	0	Same
0	1	Reset
1	0	Set
1	1	Negated

T Flip- Flop
T	Q(t+1)
0	Same
1	Negated

2. How can we use a JK Flip-Flop as a T Flip-Flop? Explain your answer.

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