Problem 4.5 SOP form
15
Problem 4.5 SOP form 1 F= + x 1 x 2 x 3 x 4 0 00 01 11 10 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 00 01 11 10 (b) =1 Primary implicants: , x 2 x 1 x 2 x 1 x 2 x 3 x 4 1 00 01 11 10 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 00 01 11 10 (b) =0
description
Problem 4.5 SOP form. Primary implicants : , x 2 x 1 x 2. x. x. x. x. 1. 2. 1. 2. x. x. x. x. 3. 4. 3. 4. 00. 01. 11. 10. 00. 01. 11. 10. 00. 0. 0. 1. 0. 00. 1. 1. 1. 1. 01. 1. 1. 1. 1. 01. 1. 1. 1. 1. 11. 0. 0. 0. 0. 11. 0. 1. 1. 0. 10. - PowerPoint PPT Presentation
Transcript of Problem 4.5 SOP form
Problem 4.5 SOP form
1
F= +
x 1 x 2 x 3 x 4
0
00 01 11 10
0 1 0
1 1 1 1
0 0 0 0
1 1 1 0
00
01
11
10
(b) =1
Primary implicants:
, x2
x1x2x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 1
1 1 1 1
0 1 1 0
0 0 0 0
00
01
11
10
(b) =0
POS form
2
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 1
1 1 1 1
0 1 1 0
0 0 0 0
00
01
11
10
(a)
F= () () ()() ()
x 1 x 2 x 3 x 4
0
00 01 11 10
0 1 0
1 1 1 1
0 0 0 0
1 1 1 0
00
01
11
10
(a)
Problem 4.6
3
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 1
0 0 0 0
1 1 0 1
1 d 0 1
00
01
11
10
(a)
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 d
1 1 0 1
d d 0 d
d 1 0 1
00
01
11
10
(b)
+ ++ +
4
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 1
0 0 0 0
1 1 0 1
1 d 0 1
00
01
11
10
(a)
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 d
1 1 0 1
d d 0 d
d 1 0 1
00
01
11
10
(b)
+ + +
Problem 4.7
5
x 1 x 2 x 3 x 4
0
00 01 11 10
d 0 d
0 1 1 0
1` 0 1 d
1 1 1 1
00
01
11
10
(a)
x 1 x 2 x 3 x 4
1
00 01 11 10
1 1 1
0 0 1 1
1 1 1 1
0 0 0 d
00
01
11
10
(b)
6
x 1 x 2 x 3 x 4
1
00 01 11 10
0 0 1
d 0 0 1
d d 1 0
1 d 0 1
00
01
11
10
(a) f
f= +
x 1 x 2 x 3 x 4
1
00 01 11 10
0 0 1
d 0 0 1
d d 1 0
1 d 0 1
00
01
11
10
(a) f
f=
Problem 4.12
7
x 1 x 2 x 3 x 4
1
00 01 11 10
1 0 0
0 0 0 1
0 1 0 d
1 1 0 d
00
01
11
10
(a) f
x 1 x 2 x 3 x 4
d
00 01 11 10
1 0 0
0 0 d 1
0 0 1 0
1 0 d 1
00
01
11
10
(a) g
f= + g= +
f= g=
f= g=
f= + g= +
Problem 4.12
8
x 1 x 2 x 3 x 4
1
00 01 11 10
1 0 0
0 0 0 1
0 1 0 d
1 1 0 d
00
01
11
10
(a) f
x 1 x 2 x 3 x 4
d
00 01 11 10
1 0 0
0 0 d 1
0 0 1 0
1 0 d 1
00
01
11
10
(a) g
f= + g= +
Problem 4.12
9
x 1 x 2 x 3 x 4
1
00 01 11 10
1 0 0
0 0 0 1
0 1 0 d
1 1 0 d
00
01
11
10
(a) f
x 1 x 2 x 3 x 4
d
00 01 11 10
1 0 0
0 0 d 1
0 0 1 0
1 0 d 1
00
01
11
10
(a) g
f= + g= +
Cost = 5AND+2OR+16ins-AND+8ins-or = 31 < (15+21)=36
Problem 4.12
10
x 1 x 2 x 3 x 4
1
00 01 11 10
1 0 0
0 0 0 1
0 1 0 d
1 1 0 d
00
01
11
10
(a) f
x 1 x 2 x 3 x 4
d
00 01 11 10
1 0 0
0 0 d 1
0 0 1 0
1 0 d 1
00
01
11
10
(a) g
f= Cost = 3AND+1OR+8ins-AND+3ins-or
=15
g= + Cost = 4AND+1OR+12ins-AND+4ins-or
=21
Problem 1 and 3
11
x 1 x 2 x 3 x 4
0
00 01 11 10
1 1 1
0 1 1 0
0 0 0 0
0 1 0 0
00
01
11
10
(a) f
g= F = ()()
x1x2x3
0 0
1 0
d d
1 1
00 01 11 10
0
1
Problem 5
12
0
00 01 11 10
0 1 1
0 1 1 0
1 1 d d
0 0 d d
00
01
11
10
(a) f
f= + f = ()()
wxyz
0
00 01 11 10
0 1 1
0 1 1 0
1 1 d d
0 0 d d
00
01
11
10
wxyz
Problem 5
13
0
00 01 11 10
1 1 0
1 0 0 1
0 0 0 0
0 1 1 0
00
01
11
10
g
g= D g= () ()(B)
ABCD
0
00 01 11 10
1 1 0
1 0 0 1
0 0 0 0
0 1 1 0
00
01
11
10
ABCD
14
x 1 x 2 x 3 x 4
0
00 01 11 10
1 d 0
0 d 1 0
0 d d 0
d 1 1 d
00
01
11
10
(a)
x 1 x 2 x 3 x 4
0
00 01 11 10
0 0 0
1 0 0 1
1 0 0 1
1 1 1 1
00
01
11
10
(b)
f= +
15
x 1 x 2 x 3 x 4
0
00 01 11 10
1 d 0
0 d 1 0
0 d d 0
d 1 1 d
00
01
11
10
(a)
x 1 x 2 x 3 x 4
0
00 01 11 10
0 0 0
1 0 0 1
1 0 0 1
1 1 1 1
00
01
11
10
(b)
f = () () ()
