This document introduces basic concepts of digital electronics. It discusses that digital electronics deals with binary numbers (0 and 1). It also covers number systems like binary, octal, decimal, and hexadecimal. Finally, it demonstrates different methods of number conversion between these systems - such as decimal to binary, binary to decimal, and converting between different bases like hexadecimal to octal. Conversions are performed by dividing or multiplying by the base and writing the remainders in reverse order.

1. HELLO FRIENDS, IN THIS PRESENTATION I
WOULD TRY TO INTRODUCE YOU WITH
SOME BASIC CONCEPTS OF DIGITAL
ELECTRONICS, THAT HELP YOU LEARN IT
VERY EASILY..

2.  We always deal with 0 and 1 in digital. Where o
means false(off) and 1 means true (on)
 We have to be very clear with 2’s power that
2^0=1 ,2^1=2,2^2=4 ,2^3=8 and so on…
 Next thing to remember is if we have n inputs
then we can have 2^n combinations.
say we have 2 inputs say A and B
then we will have 2^2=4 combinations
A B
0 0
0 1
1 0
1 1

3.  Number system is generally of 4 kind:
• Binary(base 2) : It can represent only two distinct values ie 0
and 1.
• Octal (base 8): It can represent 8 distinct values from 0-7
• Decimal (base 10): It can represent 10 distinct values from 0
-9
• Hexadecimal (base 16) : it can represent 16 distinct values 0-
9 same as decimal and 10-15 as A,B,C,D,E,F
 There are three basic forms of conversions in digital
electronics:
• Decimal to something (other then decimal any number
system)
• Something to Decimal
• Something to Something

4.  Letus start with the first form of conversion i.e.
DECIMAL TO SOMETHING.
 hint to its solution is we have to Divide by base
 Say convert (56)10 = ( )2
 56%2=0
 28%2=0
 14%2=0
 7%2=1
 3%2=1
WRITE THE REMAINDER IN REVERSE ORDER =>
ANSWER IS: (11000)2

5.  Lets take a fractional value: (560.24)10 . Find its octal equivalent.
 Before decimal repeat the same steps as did in previous example:
 560%8=0
 70 %8=6
 8%8 =1
Write the remainder in reverse order
0.24*8= 1 carry.
0.92*8= 7carry.
0.36*8= 2 carry.
0.88*8= 7 carry.
Write the carry in same order
Answer is: (160.1727……)8

6.  Something to decimal
 Say convert (10101)2 into equivalend Decimal
value.
 In this form of conversion we have to multiply
each bit by base raise to the power decimal
values starting from o from extreme right.
 1*24 + 0*23 + 1*22 + 0*21 + 1*2 0
Answer is: 1*16 + 0*8 + 1*4 + 0*2 + 1* 1
=( 21)10

7.  Lets take another example of this form but
with a fractional value say (10101.1100)2
 BEFORE DECIMAL WE HAVE TO DO THE SAME WAY AS
WE DID IN PREVIOUS EXAMPLE
 1*24 + 0*23 + 1*22 + 0*21 + 1*2 0
+ 1*2 -1 + 1 *2 -2 + 0 *2 -3 + 0*2-4
Answer is: 1*16 + 0*8 + 1*4 + 0*2 + 1* 1 +1 +1
2 4
=21+0.75 = (21.75)10

8.  SOMETHING TO SOMETHING
 Here we have to convert something to
something.
 Here something means any number system
other than decimal number system
 Such conversion is done in two steps.
 First Something to decimal
then
 Decimal to something.

9.  Lets say convert (5A6)16 to its equivalent octal
form.
 First step: 5*16 2 + 10 *16 1 +6*16 0
= 5*256 + 10*16 + 6*1 = (1446)
10
so the decimal equivalent of 5A6 is 1446.
 Second step : (1446 )10 to its equivalent octal form
 1446*8=6
 180%8=4
 22%8=6
 2
 Write the remainder in reverse order (2646) 8
 ANSWER IS: (5A6)16 = (2646)8