DIGITAL LOGIC Kmap DOUBT

Question

by solving K-MAP , i am not getting any of the A or B, ithink there is an extra term ACD in a option and ACD' in b option but given ans. is C. someone confirm this.

Comments

i am not getting how to use this ORANge gate?

from the switching func ,i am getting otuput as A'B'C' +BCD' +AC + AB'D

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same, i used KMAP and got same function as yours. do not know how they have given ans. as c?

Answer 1

ABCD	00	01	11	10
00	1	1	0	0
01	0	0	0	1
11	0	0	1	1
10	0	1	1	1

Given Above is K-Map of the function f(A,B,C,D)=$\sum m(0,1,6,9,10,11,14,15)$

Minimized Expression we get is

$AC+BC\widetilde{D}+\widetilde{A}\widetilde{B}\widetilde{C}+\widetilde{B}\widetilde{C}D$

Simplifying option A)

A'B'C'+B'C'D+ABC+BCD'+ACB'+ACD

AC(B'+B)+BCD'+A'B'C'+B'C'D+ACD

AC+ACD+BCD'+A'B'C+B'C'D

AC(1+D)+BCD'+A'B'C+B'C'D ...............(1+D=1)

AC+BCD'+A'B'C+B'C'D which is equal to minimize expression

SImilary

Simplifying option B)

AC+ACD+'BCD'+A'B'C+B'C'D

AC(1+D')+BCD'+A'B'C+B'C'D ..............(1+D'=1)

AC+BCD'+A'B'C+B'C'D which is also equal to minimized exression

Hence Both A & B are correct Ans C