Electronic – Is it possible to derive a custom boolean function from a truth table in terms of known boolean operators

boolean-algebralogic-gates

And how would one do so?

I'm doing a programming project that requires me to propagate input signals through a circuit consisting of different types of logic gates. One of the gates I need to implement is a custom one whose truth table is:

+---------+---------+---------+--------+
| Input 1 | Input 2 | Input 3 | Output |
+---------+---------+---------+--------+
|       0 |       0 |       0 |      1 |
|       0 |       0 |       1 |      1 |
|       0 |       1 |       0 |      0 |
|       0 |       1 |       1 |      0 |
|       1 |       0 |       0 |      1 |
|       1 |       0 |       1 |      0 |
|       1 |       1 |       0 |      0 |
|       1 |       1 |       1 |      0 |
+---------+---------+---------+--------+

I'm not terribly familiar with boolean functions, digital logic, etc. so any help or insight is greatly appreciated.

Best Answer

Yes. This could be done by inspection, or by Karnaugh maps. Although there are different methods.

The most basic method is to express the output obtained from the truth table, as a sum of products or products of sums, following the rules of Boolean algebra.
Thus, the canonical expression function described by the truth table is achieved.
By Karnaugh map, you can reduce that logic function.

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