Digital Electronics - Boolean Algebra and Logic Simplification - Discussion

When A=1, B=0, C=1, D=0 THEN ANS WILL BE ZERO.

Since B and D are not inversed their values should be 0.

A and D inversed their values should be 1.

A is negotiate the value must be 1 so that A value will be zero same like C is negotiate the value must be 1 so that C value will be zero if all the values are zero then if we add those values we will get zero.

Isnt A'=0 and b=1 and c'=0 and d=1?

Yes Sunella. You are correct. The answer is error.

A'=1 so that A=0, C'=1 and C=0 summing up the answer is zero.

As we are talking about complement so the value of a & c becomes 0 if we take them as 1. So correct answer is B.

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

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.

Sum =0 and carry generated will be 1.