Princess Nora University
College of Computer and Information Sciences
Department of Computer Sciences
CS 121- Digital Logic Design
Homework -4 (Chapter 4)
2nd Semester 1433-1434H
Model Answer
Q1: The four input function (A,B,C,D) and one output ( Y ) , the output (Y) equal ( 1 )
when ABCD is greater than 5 and the binary input value is even , otherwise the output
is equal BD .
a) Draw the truth table
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
C
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
b) Find the simplify function of ( Y ) by k-map
0
Y= AB’ + BD’+ B’D
c) Draw function gate
Best wishes
Y
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
Q2: Design a circuit that compares two 4-bit numbers, A and B, to check if they are
equal. The circuit has one output X, so that X=1 if A=B, and X=0 if A! = B.
A
0
0
1
1
B
0
1
0
1
E
1
0
0
1
E=A’B’+AB =(A xor B)’
Q3: Design a 4-to-16 line decoder with enable using five 2-to-4 line decoders with
enable.
A0
A1
A0
A2
2X4
A3
3
Decoder
A1
A0
A1
A0
A1
2X4
Decoder
EN
D0
2X4
Decoder
EN
D4
2X4
Decoder
EN
D8
2X4
Decoder
EN
D12
Best wishes
D3
D7
D11
D15
Q4:Design an 8-to-1 line multiplexer using 4-to-1 line multiplexer and one 2-to-1-line
multiplexer.
S0
4X1
S1
S2
MUX
I0
I1
I2
I3
2X1
MUX
S0
S1
I4
I5
I6
I7
Y
4X1
MUX
Q5.Priority Encoder used to resolve the ambiguity of illegal inputs, please read chapter
4 (slide 41), draw the Karnaugh maps for simplifying outputs x and y where D0 has the
highest priority and D3 lower priority and then draw the circuit.
input
D0 D1 D2 D3
0 0 0 0
1 x x x
0 1 x x
0 0 1 x
0 0 0 1
D0 D1
X
x
0
0
1
1
D2 D3
x
1
1
1
X= D0‘ D1’
D0 D1
D2 D3
x
1
1
1
1
1
Y= D0‘ D1+ D0‘ D2 ‘
Best wishes
output
Y
V
x
0
0
1
1
1
0
1
1
1
Q6: Derive the Boolean function F from Fig.
F
F=( (AB)(CD + E’))’+E
Best wishes