Questions Engineering

What is boolean logic?

Airtract

Wafa Khan

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The world of Mathematics plays a significant role in our everyday life. Boolean is part of algebra which is comprised of three main operators which are termed as Boolean Operators. “OR,” “AND,” and “NOT” are the three types of Boolean operators.
English Mathematician George Boole developed Boolean Logic (or Algebra). Boolean Logic is an essential module for a computer. The Boolean Logic matches perfectly with the binary number system (i.e., number system comprising of 0 and 1), and hence it is well supported by the computer system. The results obtained in Boolean Logic is either True which denotes 1 or False which denotes 0.

Let us now discuss the various Boolean Operators (also known as Logic Gates).

OR Operator: 

OR operator checks the given two equations and yields TRUE if either of the given equation is true. Let us understand with an example

ABR
000
011
101
111

Here A and B are the two given relations and R is the result after OR operation. We see the result R is 1 (TRUE) if either of A or B or both are True. The result is False, i.e. 0 only when both A and B are 0.

AND Operator: 

Boolean AND operator check the given two relations and yields True only when both the given relations are true; otherwise, it yields FALSE as an output. 

ABR
000
010
100
111

Here A and B are the two given relations and R is the result obtained after AND operation. We see that R is TRUE (i.e., 1) when both the relations are the same and False in all other cases.

NOT Operator: 

Boolean NOT operator is the most primitive of all the boolean operators. This operator accepts one-bit data as an input and produces the opposite results as an output.

AB
01
10

Here A is the input and B is the Output obtained after AND Operation. We see that the output stored in B is opposite to that of the data stored in A.

Based on these three primitive logic gates, few more logic gates are developed which are as follows:
  • NAND: Combination of AND and NOT.

  • NOR: Combination of NOT and OR

  • XOR and XNOR: Known as exclusive OR and exclusive NOR gates respectively.

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