### 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

### Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
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