Latest Boolean Logic Class 11 Notes including Boolean Operators, D Morgans Law, Logic Circuits, Logic Gates, Truth Table, AND, OR, NOT, NAND, NOR, XOR, XNOR gates. This Class 11 Computer Science Boolean Logic Notes is designed as very concisely to help students to secure highest marks.

Contents

**Boolean algebra**

- Boolean Algebra was introduced by George Boole in 1854.
- However, it is Claude Shannon, whose work on using Boolean Algebra to design Switching Circuits in late 1930s, became the foundation of computer Logic and Design.
- As Boolean logic allows things to be mapped into bits and bytes, it has application in telephone switching circuits, electronics, computers (both hardware and software), etc.
- Boolean algebra, which is algebra of two values may be (True, False) or (Yes, No) or (0, 1), is an important tool in analyzing, designing and implementing digital circuits.

**Boolean Algebra is made up of**

- Elements – which are variables or constants with value 1 or 0.
- Operators – which are And, Or and Not.
- Axioms and Theorems

**Boolean variable**

- A Boolean variable is a symbol used to represent a logical quantity.
- It will take value from the domain {0, 1}, and Boolean constant is single digit binary value (bit) viz. 0 or 1.

**Boolean Operators** ( AND, OR, NOT )

There are three fundamental operators- AND, OR and NOT.

AND is a binary operator, to perform logical multiplication, it is represented by ‘.’

OR is also a binary operator, to perform logical addition. It is represented by ‘+’.

NOT is a unary operator, to complement the operand. Not is represented as ‘ or ¯. Complement is the inverse of a variable/ constant.

In case of boolean algebra, since the variable/constant can have value 0 or 1 so complement will be 1 or 0.

**Axioms and Theorems (Boolean Expressions)**

Axiom is a statement which is considered to be true, and theorems are to be proved.

**De Morgan’s Law**

The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection og two sets is equal to the union of their complements. These are called De Morgan’s laws.

( A + B ) ‘ = A’ . B’

and

( A . B )’ = A’ + B’

**Truth Table**

- A truth table is a chart of 1’s and 0’s, arranged to indicate the results of all possible input options.
- Number of columns in the table is decided by the number of Boolean variables in the function.
- Each variable will be n represented in a column.
- For n variables used in a Boolean expression, there will be 2
^{n}possible combinations.

**Truth table for A + B + C, A.B.C**

Three variables A,B and C,

Possible combinations 2^{3} = 8

**Truth Table for AB + C**

**Logic Circuits**

- A digital electronic circuit which is built up from certain elementary circuits called logic gates and perform logical operation on data.
- It is a logic network or structure of logic gates.
- Most electronics products such as computers, video games, rotbots, calculators etc. have some forms of logical circuits.

**Logic Gates**

- Are elementary electronic circuits that performs basic logical function (Boolean function) such as AND, OR and NOT.
- It is a block of hardware that produces a logic 0 or logic 1 output, in response to the binary signal to it as input.
- Most logic gates have two inputs and one output.

There are seven logic gates:

- AND
- OR
- NOT
- NAND
- NOR
- XOR
- XNOR

**AND Gate**

Digital circuit that performs an AND operation. It can have two or more than two logic inputs and one output.

**OR Gate**

Digital circuits that performs an OR operation. It can have two or more than two logic inputs and one output.

**NOT Gate**

Also called Logical Inverter that reverses the logic state. It can have only one logic input and one output.

**NAND Gate**

Combination of NOT with AND operation makes NAND operation. It can have two or more than two logic inputs and one output.

**NOR Gate**

Combination of NOT with OR operation becomes NOR operation. It can have two or more than two logic inputs and one output.

**XOR Gate**

XOR is abbreviation of Exclusive-OR gate. The output is ‘true’ if either, but not all, of the inputs are ‘true’. The output is ‘false’ if all of the inputs are either ‘false’ or ‘true’.