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

Question

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

a) 26.78125

b) 194.03125

c) 298.796875

d) 16.1240234375

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Answer

a) 26.78125= 11010.11001

26 =0 * 27 + 0 * 26 + 0 * 25 + 1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 0 *20

     =  so left side solution is 00011010,

0.78125 * 2 = 1.5625  ,  1 

0.5625  * 2  = 1.125.  ,   1

0.125 *  2    = 0.25.    ,   0

0.25. * 2      = 0.5.     ,    0

0.5. * 2.       = 1.0.    ,     1                so,  right side solution is 11001 

Final Answer:  combine both sides 26.78125 =  00011010.11001

0 0

Discussions

dulam shiva

  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

26

 

2

13

0(LSB)

2

6

1

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

0.78125X2

1.5625

1(MSB)

0.5625X2

1.125

1

0.125X2

0.250

0

0.25X2

0.50

0

0.5X2

1.0

1(LSB)
     

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

(26.78125)10 = (10010.11001)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

194

 

2

97

0(LSB)

2

48

1

2

24

0

2

12

0

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

0.03125X2

0.0625

0(MSB)

0.0625X2

0.125

0

0.125X2

0.250

0

0.25X2

0.50

0

0.5X2

1.0

1(LSB)
     

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

(194.03125)10 = (11000010.00001)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

298

 

2

149

0(LSB)

2

74

1

2

37

0

2

18

1

2

9

0

2

4

1

2

2

0
 

1(MSB)

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

Fractional  value

  

Integer value

0.796875X2

1.59375

1(MSB)

0.59375X2

1.1875

1

0.1875X2

0.375

0

0.375X2

0.75

0

0.75X2

1.50

1

0.5X2

1.0

1(LSB)

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

(298.76875)10 = (100101010.110011)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

16

 

2

8

0(LSB)

2

4

0

2

2

0
 

1

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

Fractional  value

  

Integer value

0.1240234375X2

0.248046875

0(MSB)

0. 248046875X2

0.49609375

0

0. 49609375X2

0.9921875

0

0. 9921875X2

1.984375

1

0.984375X2

1.96875

1

0.96875x2

1.9375

1

0.9375x2

1.875

1

0.875x2

1.75

1

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

(16.1240234375)10 = (10000.000111)2

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

To cross check your answer here is the complete answer:

(16.1240234375)10 = (10000.0001111111) 2

Post the discussion to improve the above solution.