SHARE
SPREAD
HELP

The Tradition of Sharing

Help your friends and juniors by posting answers to the questions that you know. Also post questions that are not available.

To start with, Sr2Jr’s first step is to reduce the expenses related to education. To achieve this goal Sr2Jr organized the textbook’s question and answers. Sr2Jr is community based and need your support to fill the question and answers. The question and answers posted will be available free of cost to all.

The pleasure of all reading is doubled when one lives with another who shares the same. -Katherine Mansfield

 

#
Authors:
Linda Null ,julia Lobur
Chapter:
Data Representation In Computer Systems
Exercise:
Exercises
Question:4 | ISBN:9780763704445 | Edition: 3

Question

4. Convert the following decimal fractions to binary with a maximum of six places to the right of the binary point:

a) 25.84375

b) 57.55

c) 80.90625

d) 84.874023

TextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbookTextbook

Answer

  1. We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.
  1. Decimal part: we need to proceed with division reminder method

Divisor

Dividend

Reminder

2

25

 

2

12

1(LSB)

2

6

0

2

3

0
 

1(MSB)

1
  1. Fractional part: we need to proceed this process until the fractional part is zero
     

Fractional  value

  

Integer value

0.84375X2

1.6875

1(MSB)

0. 6875X2

1.375

1

0. 375X2

0.75

0

0. 75X2

1.5

1

0.5X2

1.0

1(LSB)

iii) Combine the Decimal and fractional result according to the LSB and MSB given

(25.84375)10 = (11001.11011)2

B)   We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.

  1. Decimal part: we need to proceed with division reminder method

Divisor

Dividend

Reminder

2

57

 

2

28

1(LSB)

2

14

0

2

7

0

2

3

1
 

1(MSB)

1
  1. Fractional part: we need to proceed this process until the fractional part is zero
     

Fractional  value

  

Integer value

0.55X2

1.10

1(MSB)

0. 1X2

0.2

0

0. 2X2

0.4

0

0. 4X2

0.8

0

0.8X2

1.6

1(

0.6x2

1.2

1(LSB)

iii) Combine the Decimal and fractional result according to the LSB and MSB given

(57.55)10 = (111001.100011)2

NOTE: the above answer , according to the question given the answer was restricted to 6 digits after decimal point .

  1. We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.
  1. Decimal part: we need to proceed with division reminder method

Divisor

Dividend

Reminder

2

25

 

2

12

1(LSB)

2

6

0

2

3

0
 

1(MSB)

1
  1. Fractional part: we need to proceed this process until the fractional part is zero
     

Fractional  value

  

Integer value

0.84375X2

1.6875

1(MSB)

0. 6875X2

1.375

1

0. 375X2

0.75

0

0. 75X2

1.5

1

0.5X2

1.0

1(LSB)

iii) Combine the Decimal and fractional result according to the LSB and MSB given

(25.84375)10 = (11001.11011)2

  1. We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.
  1. Decimal part: we need to proceed with division reminder method

Divisor

Dividend

Reminder

2

80

 

2

40

0(LSB)

2

20

0

2

10

0

2

5

0

2

2

1
 

1(MSB)

0
  1. Fractional part: we need to proceed this process until the fractional part is zero

Fractional  value

  

Integer value

0.90625X2

1.8125

1(MSB)

0. 8125X2

1.625

1

0. 625X2

1.25

1

0.25X2

0.5

0

0.5X2

1.0

1(LSB)

iii) Combine the Decimal and fractional result according to the LSB and MSB given

(80.90625)10 = (1010000.11101)2

  1. We have to perform division reminder method for the decimal value and for the fractional part we have to perform multiplication method.
  1. Decimal part: we need to proceed with division reminder method

Divisor

Dividend

Reminder

2

84

 

2

42

0(LSB)

2

21

0

2

10

1

2

5

0

2

2

1
 

1(MSB)

0
  1. Fractional part: we need to proceed this process until the fractional part is zero

 

 

     

Fractional  value

  

Integer value

0.874023X2

1.748046

1(MSB)

0. 748046X2

1.496092

1

0. 496092X2

0.992184

0

0. 992184X2

1.984368

1

0. 984368X2

1.968736

1

0.968736x2

1.937472

1(LSB)

iii) Combine the Decimal and fractional result according to the LSB and MSB given

(84.874023)10 = (1010100.110111)2

NOTE: the above answer , according to the question given the answer was restricted to 6 digits after decimal point .

0 0

Discussions

Post the discussion to improve the above solution.