##### Functionally completeness

A set of operation is said to be functionally complete or universal if and only every switching function can be expressed by means of operation in it

• The set is clearly functionally complete.
• The set also functionally complete.

Note : A set is said to be functionally complete if we can derive a set which is already functionally complete

##### Boolean algebra
• Boolean  algebra is a tool for the analysis and design of digital system
• In this Algebra, there is no fraction, no negative number, no square root, etc
• when the number of variables is less (1,2,3)
• It is preferred when output is 0 or 1

K-Map

• when number of variables 2,3,4,5(up to 5)
• It is preferred when output is 0,1 or don't care

Tabulation method:

When number of input variables are more use Tabulation method

Laws of boolean Algebra:

some axioms:

AND operation                       OR operation              Not Operation

0.0=0                                               0+0=0                            0'=1

0.1=0                                               0+1=1                            1'=0

1.0=0                                               1+0=1

1.1=1                                               1+1=1 