Digital Electronics - Boolean Algebra and Logic Simplification - Discussion

Answer is B, Because for getting sum zero A' and C' must be one, because it's compliment is zero and B, D is zero.

Anwser is B, It's Correct because for getting zero in exp of addition, all terms must be zero so A' C' must be 1 so their compliment is zero. And b and c and d are zero.

Since we have to get the sum as 0 so we have to convert all the inputs into 0 so for A bar to be 0 we have to take A as 1 and for B there is no bar means inversion so we take it as 0 only do it in the same way for the other.

Sop (sum of products)
Minterm A^=1.
A=O.

POS (product of sum)
Maxterm A^=0,
A=1.

A = 1 it will be negated to 0 C = 1 it will also be negated to 0 therefore the expression has OR operator:

A + B + C + D = 0 when,
A = 0 B = 0 C = 0 D = 0 because OR operator takes the favor of 1,
0 + 0 + 0 + 0 = 0.

Anyone, please explain this problem in detail.

A=1 and C=1 so, it's complement is going to be 0.

B and D is already zero. Therefore in sum all are zero produces the result zero.

Sum =0 and carry generated will be 1.

When you add a variable with 1 result will be equivalent to 1 as the Boolean logic A+1 = 1. Again, the result will be equivalent to variable when you'd add any variable with 0 according to Boolean 2nd logic A+0 = A (if A = 1, A + 0 = 1).

So it is proved that if we make any sum term equal to 0, value of every variable will must be 0 in that sum term. If we determine A = 0, it will be inverted into 1. But value 1 is not allowed for this term. So, the values will be A = 1, B = 0, C = 1 & D = 0.

A'+B+C'+D = 1'+0+1'+0 = 0+0+0+0 = 0.