CS302 ASSIGNMENT NO:2 Solution


ASSIGNMENT NO:2
Course: CS302
1: Write the SOP expression for the given sum.
Sol:
A
B
C
D
E
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1

A
B
C
D
E
OUTPUT
    (F)
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
FOR SOP WE FOCUS ON 1 VALUE.
A
B
C
D
E
MINTERM
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
ABCDE


SOP EXPRESSION:
SUM OF PRODUCT EXPRESSION

2: Find Prime Implicant of minterm using QuineMcculsky method.
Step-1
00010
2
00100
4
01000
8
10000
16
00110
6
01010
10
01100
12
10010
18
10100
20
11000
24
01110
14
10110
22
11010
26
11100
28
11110
30

Step-2
2,6(00-10) 2,10(0-010) 2,18(-0010)
4,12(0-100) 4,6(001-0) 4,20(-0100)
8,10(010-0) 8,24(-1000)
16,18(100-0) 16,20(10-00) 16,24(10-00)
6,14(0-110) 6,22(-0110)
10,14(01-10)10,26(-1010)
12,14(011-0) 12,28(-1100)
18,26(1-010) 18,22(10-10)
20,22(101-0) 20,22(1-100)
24,26(110-0)  24,28(11-00)
14,30(-1110) 22,30(1-110) 26,30(11-10) 28,30(111-0)
Step-3
2,6,18,22(-0-10) 2,6,10,14(  0--10)2,10,18,26(--010)2,18,6,22(-0-10)
2,18,10,26(--010)4,12,6,14(0-1-0)  4,6,12,14 (0-1-0)
4,6,20,22(-01-0)4,20,6,22(-01-0)  4,20,12,28(--100)  8,10,12,14(01--0) 8,24,10,26(-10-0) 8,24,12,28 (-1-00)
6,14,22,30 (--110) 6,22,14,30(--110) 10,14,26,30(-1-10) 10,26,14,30(-1-10) 12,14,28,30(-11-0) 12,14,28,30(-11-0)
18,26,22,30(1--10) 18,22,26,30(1--10) 20,22,28,30(1-1-0)
20,22,22,30(1-1-0) 24,26,28,30(11--0) 24,28,26,30(11--0)
Step-3
2,6,18,22(-0-10)            4,6,20,22(-01-0) 
2,18,10,22(-0-10)           4,20,6,22(-01-0)  
2,10,18,26(--010)           4,12,6,14(0-1-0)  
2,18,6,22(--010)            4,6,12,14 (0-1-0)  
4,20,12,28(--100)                   10,14,26,30(-1-10)
6,14,22,30 (--110)                  10,26,14,30(-1-10)
12,14,28,30(-11-0)                  18,26,22,30(1--10)
12,14,28,30(-11-0)                 18,22,26,30(1--10)
20,22,28,30(1-1-0)                  24,26,28,30(11--0) 
20,22,22,30(1-1-0)                  24,28,26,30(11--0) 
6,22,14,30(--110)
8,10,12,14(01--0) 
8,24,12,28 (-1-00)
8,24,10,26(-10-0)
Step-4
2,6,8,22(-0-10)                       4,6,20,22(-01-0) 
2,10,18,26(--010)           4,12,6,14(0-1-0)  
4,20,12,28(--100)                   10,14,26,30(-1-10)
12,14,28,30(-11-0)                 18,26,22,30(1--10)
20,22,28,30(1-1-0)                 24,26,28,30(11--0) 
6,22,14,30(--110)                   8,10,12,14(01--0) 
8,24,12,28 (-1-00)                  8,24,10,26(-10-0) 
These are the prime implicates


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