0195136047.pdf

302 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS

Clock

(b)

000 000

0 0

00

00 0 00 0

00 0 0

00 0 0

11

1 1

1

11

1

T 1

Q 0

Q 1

Q 2

Q 3

T 2 T 3 T 4 T 5 T 6 T 7 T 8 T (^9) Figure 6.2.74-bit ring counter using D
flip-flops.(a)Block diagram.(b)Timing
diagram.
EXAMPLE 6.2.1
A table of minterms for three variables is as follows:
A B C i Minterm mi
0000 A ̄·B ̄·C ̄
0011 A ̄·B ̄·C
0102 A ̄·B·C ̄
0113 A ̄·B·C
1004 A·B ̄·C ̄
1015 A·B ̄·C
1106 A·B·C ̄
1117 A·B·C
Implement the following Boolean functions by using one 3-to-8 decoder and three three-input
OR gates:
F 1 (A,B,C)=
∑
mi( 1 , 2 , 3 )=A ̄·B ̄·C+A ̄·B·C ̄+A ̄·B·C
F 2 (A,B,C)=
∑
mi( 2 , 4 , 6 )=A ̄·B·C ̄+A·B ̄·C ̄+A·B·C ̄
F 3 (A,B,C)=
∑
mi( 3 , 5 , 7 )=A ̄·B·C+A·B ̄·C+A·B·C
Solution
The implementation is shown in Figure E6.2.1.
F 1
F 2
F 3
A
B decoder3-to-8
C
m 0
m 1
m 2
m 3
m 4
m 5
m 6
m 7
Figure E6.2.1