Btech first year digital logic notes

Digital Logic
Short Notes

, 1 LOGIC GATE

1.1. Logic Operations
In Boolean algebra, all the algebraic functions performed is logical. The AND, OR and NOT are the basic operations that are
performed in Boolean algebra. There are some derived operations such as NAND, NOR, EX-OR, EX-NOR that are also
performed in Boolean algebra.

1.1. NOT Operation

Symbol:



Fig. 1.1.

A⎯N⎯O⎯T→A or A (Complementation law)

and A= A  Double complementation law

Truth table for NOT operation
Input Output
A Y=A

0 1
1 0


A NOT gate can be represented using switch whose circuit representation is shown in figure below.




Fig. 1.2.

, Digital Electronics

A buffer is a basic logic gate that passes its input, unchanged, to its output. Its behaviour is the opposite of a NOT
gate.
The main purpose of a buffer is to regenerate the input, usually using a strong high and a strong low. Buffers are
also used to increase the propagation delay of circuits by driving the large capacitive loads.




Input Output
0 0
1 1

1.1.2. AND Operation

Symbol:




A.A = A, A.0 = 0, A.1 = A, AA = 0
Truth table for AND operation:
Input Output
A B Y = AB
0 0 0
0 1 0
1 0 0
1 1 1

1.1.3. OR Operation


Symbol:

A + A = A, A + 0 = A, A + 1 = 1, A + A = 1
Truth table for OR operation:
Input Output
A B Y = A+B
0 0 0
0 1 1
1 0 1
1 1 1

, Digital Electronics

Example: Reduce the combinational logic circuit shown figure such that the desired output can be obtained using only one
gate.




Fig. 1.3.
Solution:




Fig. 1.4.
P = A, Q = B, R = C
S = A ·B · C

V = U = ABC
X =U+V+D
= ABC + ABC + D
=A+B+C+D




Fig. 1.5.

Enable or Disable Input:




Fig. 1.6.