#### introduction

In digital circuits logic gates play an important role. Mostly logic gates have two inputs and one output. There are four basic logic gates.

1)NOT gate

2)AND gate

3)OR gate

4)XOR gate

1)NOT gate

is basically an inverter it is used to invert the input value. its circuit is given below when switch is off means 0 so output is 1.

Its symbol and truth table given below for A its NOT value is A’.

2)OR gate

it is a addition process its circuit is given below

when input is 0 and 1 then output is 1 as stated earlier its addition process

3)AND gate

it is multiplication process means if any input is 0 so output is 0 its circuit is given below

its symbol and truth table is following

4)XOR gate

it is very simple gate if input entries are different then there output is 1 else 0.

Example:Draw logical circuit of A B’ + A’ B

#### Boolean algebra

Name                                AND func.          OR func.

Identity                              x.1=x                  x+0=x

Complement                     x.x’=0                  x+x’=1

Commutation                    x.y=y.x                x+y=y+x

Distribution                       x(y+z)=x+y+z      x+y.z=(x+y)(x+z)

Idempotent                       x.x=x                   x+x=x

Null                                   x.0=0                  x+1=1

deMorgan’s Law              (x+y)’=x’.y’            —–

(x.y)’=x’+y’

Examples:Simplify the following

1)F = x + x’y

= (x + x’) (x + y)

= 1.(x + y)

= x + y

2)F = x (x’ + y)

= xx’ + xy

= 0 + xy

= xy

3)F =  x’y’z + x’yz + xy’

= x’z(y’ + y) + xy’

= x’z.1 + xy’

= x’z + xy’

4)F = xy + x’z + yz.(x + x’)

= xy + x’z + xyz + x’yz

= xy(1 + z) + x’z(1 + y)

= xy + x’z

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