CS302 Assignment 2 solution 2019

CS302 Assignment 2 solution 2019

1.       Write  the SOP expression for the given  sum

∑_ABCDE(2,4,6,8,10,12,14,16,18,20,22,24,26,28)

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	Decimal value	Output (f)
0	0	0	0	0	0	0
0	0	0	0	1	1	0
0	0	0	1	0	2	1
0	0	0	1	1	3	0
0	0	1	0	0	4	1
0	0	1	0	1	5	0
0	0	1	1	0	6	1
0	0	1	1	1	7	0
0	1	0	0	0	8	1
0	1	0	0	1	9	0
0	1	0	1	0	10	1
0	1	0	1	1	11	0
0	1	1	0	0	12	1
0	1	1	0	1	13	0
0	1	1	1	0	14	1
0	1	1	1	1	15	0
1	0	0	0	0	16	1
1	0	0	0	1	17	0
1	0	0	1	0	18	1
1	0	0	1	1	19	0
1	0	1	0	0	20	1
1	0	1	0	1	21	0
1	0	1	1	0	22	1
1	0	1	1	1	23	0
1	1	0	0	0	24	1
1	1	0	0	1	25	0
1	1	0	1	0	26	1
1	1	0	1	1	27	0
1	1	1	0	0	28	1
1	1	1	0	1	29	0
1	1	1	1	0	30	1
1	1	1	1	1	31	0

                          

Q2

ANS:

Find the prime implicant of minterm using Quine mcculsky method

∑_ABCDE(2,4,6,8,10,12,14,16,18,20,22,24,26,28)

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)

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(1-100)

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(-01-1)           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)

These are the prime implicant.