1
$\begingroup$

I am trying to make a truth table from an SOP boolean algebra expression. I understand AND, OR, NOT truth tables. I just don't understand these types of tables and their outputs.

This is the expression: $$A'BD' + BCD + ABC' + AB'D = A'BD' + BCD + ABC' + AB'D + BC'D' + A'BC + ABD.$$

I can use either side whichever is easier. Just let me know which side.

Would $A'$ be a $1$ and the others be a zero? I am also not sure how they get the output?

I understand the outputs of a AND, OR truth tables.

But I can't figure out these outputs. Would this be considered an OR table since the expression is $+$?

Would I just construct $A$, $B$, and $D$ with nots = 1 or zero? Then, how do I determine the output?

 -----------------------  A  | B  | D  |  output ----------------------- | 1 | 0  | 1  |   1?    |  A'BD' ------------------------ | 0 | 0  | 0  |   0?    |  BCD ------------------------ | 0 | 0  | 1  |   1?    |  ABC' ------------------------- 

something like that.

What I am trying to achieve is how the below expression is true using theorems.

$$A'BD' + BCD + ABC' + AB'D = A'BD' + BCD + ABC' + AB'D + BC'D' + A'BC + ABD$$

4 Answers 4