For the function : f(A,B,C,D) = A\'BCD+ A\'B + ACD\'+ BC What would be the canon

Question

For the function:

f(A,B,C,D) = A'BCD+ A'B + ACD'+ BC

What would be the canonical sum of products expansion?

Question 5 options:

a)

f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + AB'CD'+ABCD'+ ABCD

b)

f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + ABC'D'

c)

f(A,B,C,D)= A'BC'D'+C'D+A'BCD'+ A'BCD + ABC'D'+ BC'D+BCD'+ CD

d)

The function is already expressed in canonical form

a)

f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + AB'CD'+ABCD'+ ABCD

b)

f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + ABC'D'

c)

f(A,B,C,D)= A'BC'D'+C'D+A'BCD'+ A'BCD + ABC'D'+ BC'D+BCD'+ CD

Explanation / Answer

f(A,B,C,D) = A'BCD+ A'B + ACD'+ BC

canonical form should contain all the variables in each term

Also we know that   x + x' = 1

f(A,B,C,D) = A'BCD+ A'B + ACD'+ BC

f(A,B,C,D) = A'BCD   + (A'B .1 .1) + (A . 1 . CD') + (1.BC . 1)

= A'BCD   + A'B .(C+C') .(D+D') + A . (B+ B') . CD' + (A+A').BC . (D+D')

= A'BCD   +    A'BCD +A'BC'D +A'BCD'+A'BC'D'     +      ABCD'+AB'CD'    +     ABCD+ABCD'+A'BCD+A'BCD'

= A'BCD + A'BC'D + A'BCD' + A'BC'D'   + ABCD' + AB'CD' + ABCD

hence the answer is A

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.