introduction to digital electornics

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

IMPORTANT POINTS 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

INTRODUCTION TO CONVERSION

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

LET’S DO SOME CONVERSIONS Let us 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

ANOTHER EXAMPLE OF FIRST FORM OF CONVERSION.

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 =1Write 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

2ND FORM OF CONVERSION 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

CONSIDERING THE FRACTIONAL VALUE

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

3RD FORM OF CONVERSION

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 thenDecimal to something.

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