# Boolean Function

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

*Example*: Boolean function F1: (abc’)

The function F1 is equal to 1 if a= 1 AND b=1 AND c’ =1, otherwise F=0.

The *Boolean function* is represented as an algebraic expression. It may also be represented in truth table.

**Problem**: Simplify the following Boolean function to minimum number of variables (literals)

F(A,B)=A+A’B

A+A’B=(A+A’)(A+B)

=1.(A+B)

=A+B

**Logic Circuit or Logic Network**: The logic circuit is an electronic circuit based on the concept of *Boolean algebra*. The logic circuit contains hierarchy of AND, NAND, OR, NOR gates etc. The simplest form of electronic logic gate id Diode. To build a complete logic system, valves or transistors logic gates are used.

The Half adders, full adder, Decoder, Encoder, Flip-flop, and Multiplexer etc are logic network to perform digital activities.

** Example** : Study the following logic circuit and display value of Q.

Q=A **AND NOT** B

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