ISRO2013-ECE: Digital Logic

Question

Which of the following is the Boolean function for majority voting, assuming $\text{A, B, C}$ are inputs and $\text{Y}$ is output?

1. $\text{Y = AB + AC + BC}$
2. $\text{Y = A + B + C}$
3. $\text{Y =  ABC}$
4. $\text{Y= AB + BC}$

Answer 1

Majority voting means that when two or more output are in set condition Boolean function should become true. So F = ABC'+ BCA' + CAB' + ABC which simplifies to Option A) AB + AC + BC

Answer 2

For the 3 inputs $A, B, C$ majority voting is performed if the number of $1’s$ is $\geq2$.

A	B	C	Y
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1

So $Y=A’BC+AB’C+ABC’+ABC$

after solving $Y$ using kmap we get $Y=AB+BC+CA$

Option (A) is correct.