Boolean Operators

posted on: 26 May, 2012 | updated on: 29 Aug, 2012

A function in the form f: R^k ⇢ S, where values of ‘R’ are equals 0 or 1 and value of ‘k’ is non negative Integer is known as Boolean function.
Now we will see the Boolean operators.
There are three types of Boolean Operators which are given below:
1. AND operator, AND operator is also known as conjunction operator.
The representation of AND operator is ‘∧’
2. OR operator, OR operator is also known as disjunction operator.
The representation of or operator is ‘∨’
3. Negation of OR operation is known as NOT operator.
The representation of negation operator is ‘~’.
Now we will see the truth table of all the operators:
Truth table for AND operator is:
| R | S | R ∧S |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Now we discuss the meaning of these operators:
If both values are true then we get true in case of AND operator;
If both values of ‘R’ are true and value of ‘S’ is false then we get the result false;
If both values of ‘R’ are false and value of ‘S’ is true then we get the result false;
If both values are false then we get the result false;
Truth table for OR operator is:
| R | S | R ∨S |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |

Now we will see the truth table for negation operator:
| R | ~R |
| T | F |
| F | T |
If value of ‘R’ is true then the negation of ‘R’ is false.
If value of ‘R’ is false then the negation of ‘R’ is true.
This is all about Boolean operator.

Topics Covered in Boolean Operators

Boolean Expressions

posted on: 28 Aug, 2012 | updated on: 29 Aug, 2012

Boolean expressions are expressions whose solutions are Binary Numbers that are represented by just two digits: 0 and 1. In a Boolean expression we work according to Boolean Algebra which implements operations between 2 numbers to get a Boolean result. Uses of binary algebra can be found in many computer applications which involve solving circuits and procedures for ...Read More

Logical And Operations

posted on: 28 Aug, 2012 | updated on: 29 Aug, 2012

We can perform different logical operations such as And, Or, Not, XOR etc. Logical operations take value in binary form means 0, 1 (0 → false , 1 → true) as input. Logical AND operation represents multiplication operation. Suppose we have two values a, b and if we apply Logical And Operations on them, then there are four cases:

Case 1:- If value of a = 0, and b...Read More

Logical Or Operations

posted on: 28 Aug, 2012 | updated on: 29 Aug, 2012

Logical Or operation represents the operation of addition. Suppose we have two values a, b and if we apply Logical Or Operations on them, then we will denote this as, "a or b", a + b. There are four case of Logical Or Operations on a and b are:-

Case 1:- If value of a = 0, and b = 0, a and b both are false, then “Or” of these two values is, a Or b => a + b = > 0...Read More

Logical Not Operations

posted on: 28 Aug, 2012 | updated on: 29 Aug, 2012

Logical operators can be defined as those operators which are used to compare two conditions at a time for confirming whether a row can be selected for output or not. Logical operators are mainly used with Boolean values. There are mainly three types of logic operators used, they are AND, OR, and NOT logical operators. Other logical gates such as X-OR, NAND operat...Read More

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