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.

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

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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