Question

1. For the following function: f(a, b, c, d) =>m(0, 1, 4, 8, 10, 15)d(2,5,7, 11, 13, 14) a. Complete the K-map cdlab 00 01 11 10 00 10 b. List all prime implicants c. List all essential prime implicants d. Simplify the function based on your K-map in the sum of product format

Answer 1

Q>

a>

firstly i would like to tell you about the k map layout or index to put value

cdlab 00 01 11 10 00 04 12 8 01 1 5 13 9 11 37 15 11 10 2 6 14 10

after filling sop in k map

01 1 dd di d 1

b>list of all prime implication

dlab co on 1 10 d

14 prime implication

1>A'C'(0,1,4,5)

2>AC(10,11,14,15)

3>BCD(7,15)

4>A'C'D(1,5)

5>A'C'D'(0,4)

6>A'BC'(4,5)

7>A'B'C'(0,1)

8>ABD(13,15)

9>BD(5,7,13,15)

10>ACD'(10,14)

11>AB'C(10,11)

12>ABC(14,15)

13>ACD(11,15)

14>B'D'(0,2,8,10)

c>list of all essential prime implicants

colabo 00 01 1110 01 1 a a

1>A'C'(0,1,4,5)

2>BD(5,7,13,15)

3>B'D'(0,2,8,10)

d>

Groups (0,1,4,5) AC (0,2,8,10) B.D (5,7,13,15) B.D y= A'C' + B'D' + BD

y= A'C' + B'D' + BD A Ā B È C Č D Ď A Ā B B C TDD A Ā B B C TDD

Truth Table | A | B | C | D | Y 0 0 0 0 0 1 100011 |0|0|1|0 x UTILI- 4 0 |1|0|0|1. |0|1|0|1| x |0 1 |1|0| 011|1|| |1|0|0|0|1 910010 101 0101 11 101|1| 1211000 1311 |0|1|x 14|1|1 1 |0 |0 15|1|1|1|1|1.

Y=A'C'+BD+B'D'

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