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:

Boolean0

 

A BA.BOutput
1 000
0100
0000
1111

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


Boolean1

 

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

A BA + BOutput
1011
0111
0000
1111

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:

Boolean4

 

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


 

 

Recommended Reading

 

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

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