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TERMS OF BOOLEAN ALGEBRA

Q.2. Define the terms or elements of Boolean algebra.

ANS. TERMS OF BOOLEAN ALGEBRA

Following terms must be known to understand Boo lean Algebra

1. BOOLEAN CONSTANTS

Definition

Binary values 0 and I used in Boolean algebra are called Boolean constants.

2. VARIABLES

Definition

The variable used in Boolean Algebra are represented by letters such as A,B,C,x,y,z etc. Each variable can have a 1 or 0 value.

3. COMPLEMENTS

Definition

The complement is the inverse of a variable and is indicated by a bar over the variable.

Example

The Complement of the variable A is Ā.

If A = l, then Ā = 0

If A = 0, then Ā = 1

A = 0110110

Ā = 1001001

Note

The complement of the variable A is read as “Not A”

4. TRUTH TABLE

Definition

Truth table is the table that represents the condition of input and output circuit involving two or more variables.

In a binary system, there is 2 numbers of combinations where n is the number of variables being used.

Example

Each combination of values of x and y, there is a value of Z specified by the definition. These definitions may be listed in compact form with all possible combinations in the truth table.

5. LOGICAL OPERATORS

Definition

Logical operators are used for binary additions, multiplication and complement operations in Boolean algebra.

There are three types of logical operators e.g. OR. AND and NOT.

1. OR Operator

A. Boolean operator that returns a value TRUE if either (or all) of its operands are TRUE otherwise it is known FALSE.

• It is represented by a plus sign.

• It is used for logical addition.

• It is a binary operation because it uses operation on two variables A and B.

Example

A+B+C it is read as “A OR B is equal to C”.

There are two v4riable A and B, so only 4 (21 combinations of input are possible.

ii. AND Operator

A Boolean operator that returns a value TRUE if all of its operands is TRUE, otherwise it returns FALSE.

• This logical operator is represented by dot “.” or the absence of an operator.

• It is used for logical multiplication.

• It is a binary operation because it uses operation on two variables A and B.

Example

A.B = C or AB = C read as “A AND B is equal to C”

iii. NOT Operator

A Boolean operator that returns value TRUE if its operand is FALSE and FALSE if its operand is TRUE.

• This logical operator is represented by a prime (’) or bar (—) on  the variable.

• It is used for complement operation.

• It s unary or inverse operation because it is applied to a single variable A.

Example

A (read as A bar) means complement of A or NOT A

 

6. OPERATORS PRECEDENCE

Definition

It is the order of operations for boolean expressions.

1. Boolean expression is scanned from left to right.

2. Parentheses if there is any

3. NOT operation

4. AND operation

5. OR operation

 

7. BOOLEAN EXPRESSIONS

Definition

A Boolean expression is an arrangement of variables and logical operators used to express the operation to a logical circuit.

For Example

A +B = C, A+ B + C + D, A (B + CD)

 

8. BOOLEAN FUNCTIONS

Definition

A Boolean function is an expression formed with variables, binary operators OR. AND and unary operator NOT parentheses and equal sign.

For a given value of the variable, the value of the function can be either 0 or 1

For example the equation.

W = X + YZ

The variable W is a function of X. Y and Z. This can be written as.

W = F (X. Y. Z)

The Boolean functions are represented as an algebraic expression. A Boolean function may also be represented in the form of a truth table.

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