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I have a boolean expression for which I have to get the truth table and standard SOP expression without using a Karnaugh map.

Here is what I got:

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I do have the final answer of the SOP expression, but what are the steps that were done to reach it?

I tried solving it but I'm not sure of my answer:

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Are the steps I took correct?

I'm really confused.

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Well you are making a mistake \$(\overline{A\overline{B}}) (C+\overline{C})\$ is not eaqual to what you just wrote. You can't just ignore the complement that is sitting right there. It would be equal to \$\overline{A\overline{B}}C + \overline{A\overline{B}}(\overline{C})\$

Anyway the easier thing to do this, if you already have truth table, look for the values of F when it's 1. As you can see there are 7 terms in your SOP expression and there are 7 true (or one) values in your F column.

Let's start with the first row as you can see it's \$ A= 0, B=0, C=0\$ and the value is true. We could write that as \$\overline{A}*\overline{B}*\overline{C} \$.

Why I wrote it this way? Well since it is AND operation the only way that expression can be true is when A B C are zero. Same goes for every row except 6th one.

Let's do one more example, 7th row, \$ A= 1, B=1, C=0\$, we could write that as \${A}{B}\overline{C} \$.

Do that for every row and you have complete SOP expression.

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  • \$\begingroup\$ Got it! Thank you! \$\endgroup\$
    – AhmadBenos
    Apr 1, 2020 at 15:19

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