http://improvec.blogspot.in/ 1

Conversions of decimal to binary number

http://improvec.blogspot.in/ 2

Objective

On completion of this period, you would be On completion of this period, you would be able to know:able to know:

Conversion of a decimal number to Conversion of a decimal number to equivalent binary equivalent binary

http://improvec.blogspot.in/ 3

Recap

Various number systems used in Various number systems used in

digital computerdigital computer

http://improvec.blogspot.in/ 4

Conversions from one Number System to other

http://improvec.blogspot.in/ 5

Conversion from decimal to binary

The integer and fractional parts of the decimal number are dealt separately.

The decimal number is divided by 2 successively.

http://improvec.blogspot.in/ 6

Conversion of decimal to binary

The quotient and remainder are noted down at each stage.

The present quotient is again divided by 2 and repeat the above step.

This process is repeated until the quotient becomes 0.

http://improvec.blogspot.in/ 7

Conversion from decimal to binary

Integer part:

Divide the integer part of the given decimal number repeatedly by 2.

And write down the remainder after each division.

The remainders are then taken in reverse order (bottom to top) to form binary equivalent to the number

http://improvec.blogspot.in/ 8

Fractional part:

The fractional part of the given decimal number is multiplied repeatedly by 2, each time recording the carry (integer part).

The integers are then taken in forward order (top to bottom) to form the binary equivalent of the number.

http://improvec.blogspot.in/ 9

Fractional part (contd) :

This process is continued until the fraction becomes zero

(or)

until sufficient accuracy is obtained.

http://improvec.blogspot.in/ 10

Convert the decimal number 125 to binary.

1256223

7

1 0

2

15

3

divisionremainder

101

1111

Thus (125)10 = (1111101)2

222222

http://improvec.blogspot.in/ 11

Convert the decimal number 0.4375 to binary.

Multiplication Product Integral part0.4375*2 0.8750 00.8750*2 1.75 10.75*2 1.50 10.5*2 1.00 1

Taking the integers parts in the forward (top to bottom) gives the binary fraction 0.0111.

Thus (0.4375)10= (0.0111)2

http://improvec.blogspot.in/ 12

Convert the decimal number 17.35 to binary.

Division Remainders1784 210

2

2

100

0

22

22

1

http://improvec.blogspot.in/ 13

Fractional part:

Multiplication Product Integral part0.35*2 0.70 00.70*2 1.40 10.40*2 0.80 00.80*2 1.60 10.60*2 1.20 10.20*2 0.40 0

Thus (17.35)10= (10001.010110.......)2

http://improvec.blogspot.in/ 14

Summary

In this class, we have learnt about

Conversion from decimal numbering system to binary numbering system

http://improvec.blogspot.in/ 15

Frequently Asked Questions

1. Explain the procedure to convert a decimal number into binary number?

2. Convert the decimal real number 12.625 8 into equivalent binary real number?

http://improvec.blogspot.in/ 16

Quiz:

1. The base of binary system is

a. 10

b. 2

c. 8

d. 16

Answer: b

http://improvec.blogspot.in/ 17

Quiz:

2. What is the binary equivalent of 10

a. 1000

b. 1011

c. 1010

d. 1111

Answer: c

http://improvec.blogspot.in/ 18

Quiz:

3. What is the binary equivalent of 125

a. 1111101

b. 1111001

c. 1101101

d. 1111111

Answer: a