Logic and Functions

George Boole investigated the “laws of thought” based on a simplified version of the “group” or “set” theory and developed Boolean Algebra from his findings.

The first thing to understand is that logic gates come in many shapes and sizes. Even in our personal lives, we constantly process things through various logic gates. We often fail to recognize the thought process in motion despite our minds being optimized to do so. Nevertheless, it occurs.

When sitting an exam, one might know that not answering a question will result in a negative score. As soon as you understood this concept, your mind has just processed a NOT gate! Alternatively (pseudo code): if not [question answered], then negative consequences exist.

These logic gates form the basis of much of the world’s code as well as for electronics. In spite of the fact that some logic gates are more common than others (for example, an AND or OR gate is more common than a NAND or NOR gate), all logic gates are used somehow, sooner or later, by a computer or electronic device to process data in a particular way.

We can construct workflows that are similar to or follow human thinking to an extent by using multiple logic gates.

There is another function we may write y=y (x) mean 

In boolean algebra, logic and set operations are either “TRUE” or “FALSE” but not both at the same time.

A + A = A, not 2A as it would be in normal algebra. In Boolean Algebra, the switching action of standard logic gates is represented by logical gate operations of the AND, OR, and NOT gate functions. Here, we are concerned with the AND, OR, NOT logic gates.

And Function:

In order for an output action to occur, two or more events must occur at the same time. The order in which these actions are performed is not important since it will not affect the final result. B + A = A + B. Boolean algebra’s Logic AND Function obeys the commutative law, which allows a change in either variable’s position.

In electronics, the AND function is represented by the dot symbol ( ). Thus a 2-input (A B) AND Gate has an output term represented by the Boolean expression A.B or just AB.

OR Function:

The OR logic gate is a simple gate/construct that says, “If my first input is true, my second input is true, or both inputs are true, then my output will also be true.” Note how we have two inputs and one output. Logic gates aren’t all the same. The header image shows that all logic gates have two inputs, except for the NOT logic gate, which only has one input. Each gate has one output.

XOR Function:

EOR or EXOR are other names for the XOR gate. The correct terminology for an XOR gate is Exclusive OR. If you recall our previous example, we were a little surprised that true and true would still lead to true, contrary to human reasoning.

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