### Boolean Algebra

In the following circuit, a bulb is controlled by two switches.

This control mechanism is denoted as A.B - A and B - in Boolean Algebra. The state of the switch is The output is considered as 1, when it is on and 0 when it is off. The way the bulb responds is considered as the output and its state can also be described in terms of o - off -   and 1 - on.

On this basis, this animation can be summarized in the table as follows:

 A B A.B Output 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1

The following animation shows, the Boolean notation for the arrangement of the switches is A + B - A or B.

The animation and the corresponding truth table explains how it works.

 A B A + B Output 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1

The tables of this kind are called Truth Tables. A truth table describes how an arrangement of switches controls the output of a logic circuit.

E.g.

The animations and corresponding truth tables show how Boolean algebra is interpreted in real world.

 A B B A Output 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0

B means the inverse of B; If B is 1, B  is 0 and vice versa.

This is another truth table with its corresponding circuit:

 A B C A C Output 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1

Now try the following with a circuit and a truth table:

1. C.(A.B + A)
2. A.C + A.B.C + A.B
3. A.B.C.(A+B+C)
4. A.(A.B.C + B.(A+C))
5. C.(A+B).A