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.

Logic Circuit or Logic Network

Logic Circuit


Q=A AND NOT B



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