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