Question

simplify the following Boolean functions using four-variable maps. a. F (A, B, C, D) =∑ (4, 6, 7, 15)

Answer 1

Answer:

Pair 1 = m₄ + m₆ = A'BD'

Pair 2 = m₇ + m₁₅ = BCD

SOP = A'BD' + BCD = B(A'D' + CD)

K-map is attached in the form of image.

We can do this question by another method:

4 = 0100 = A'BC'D'

6 = 0110 = A'BCD'

7 = 0111 = A'BCD

15 = 1111 = ABCD

A'BC'D' + A'BCD' + A'BCD + ABCD

A'BD'(C' + C) + BCD(A' + A)

A'BD'.1 + BCD.1

A'BD' + BCD

B(A'D' + CD)

Answer 2

Answer:

1=4+6= ' '

2= 7+15=

= ' ' +

= ( ' '+ )

4=0100= ' ' '

6=0110= '

7=0111= '

15=1111=

' ' '+ ' + ' +

' ' ( + ') + ( ' + )

' ' (1) + (1)

' ' +

( ' ' + )

Explanation: