Change-the-following-decimal-number-into-binary-number-73-108-

Question Number 113199 by Rasheed.Sindhi last updated on 11/Sep/20

C h a n g e t h e f o l l o w i n g d e c i m a l

n u m b e r i n t o b i n a r y n u m b e r :

73.108

Commented by bemath last updated on 11/Sep/20

what is binary one sir ?

Commented by Rasheed.Sindhi last updated on 11/Sep/20

R e a d t h e q u e s t i o n n o w .

Commented by bemath last updated on 11/Sep/20

ok sir . santuyy

Commented by Rasheed.Sindhi last updated on 11/Sep/20

{W h a t}^{'} s t h e m e a n i n g o f

“ {santuyy}^{″} ?

Commented by 1549442205PVT last updated on 12/Sep/20

It is counting system of base 2 . As I

known, currently we are using

countimg system of base 10, is also

called the decimal system that uses ten

symbols : 0, 1, \dots, 9 to represent numbers

. The counting system of base 2 is also

called the binary system that uses

only two sumbols 0 and 1 to represent

numbers . It is used in computer

science and digital technology

Converts decimal to binary - odd part

1) Procedure

∙ Step 1 : We multiply the odd part by

a power of 2 (say 2^{n}, n > 1)

∙ Step 2 : get the result in step 1 (only

take whole part) and then convert to

binary

∙ Step 3 : divide the result in step 2 by 2^{n}

, we get odd part in binary form

(essentially this step is to move the

comma to the left n times)

2) For example

∙ Ex 1 : Convert 2.5625 to binary

2_{10} = 10_{2}

- Multiply : . 5625 * (2^{4}) = 9

- Convert 9 to binary : 9_{10} = 1001_{2}

- Divide : 1001_{2} / (2^{4}) = . 1001

\Rightarrow 2 . 5625_{10} = 10 . 1001_{2}

∙ Ex 2 : Convert 2.3333 to binary

2_{10} = 10_{2}

- Multiply : . 3333 * (2^{16}) = 21843.1488

- Convert 21843 to binary :

21843_{10} = 0101010101010011

- divide 0101010101010011 / 2^{16}

= . 0101010101010011

\Rightarrow 2 . 3333_{10} = 10 . 0101010101010011_{2}

∙ Ex 3 : convert 2.6973 to binary

2_{10} = 10_{2}

- Multiply : . 6973 * (2^{15}) = 22849.1264

- convert 22849 to binary :

22849_{10} = 101100101000001_{2}

- dovide 101100101000001_{2} / 2^{15}

= . 101100101000001_{2}

\Rightarrow 2 . 6973_{10} = 10 . 101100101000001_{2}

Commented by Rasheed.Sindhi last updated on 12/Sep/20

T h a n k s f o r d e t a i l l e d a n s w e r .

Commented by Rasheed.Sindhi last updated on 12/Sep/20

B y^{'} o d d {p a r t}^{'} d o y o u m e a n

You can't use 'macro parameter character #' in math mode

Commented by 1549442205PVT last updated on 12/Sep/20

Ok, is also called decimal part of a

number . Ex : 12.34567245 then its

“ odd {part}^{″} is . 34567245

Answered by Aziztisffola last updated on 11/Sep/20

73.108 = 73 + 0.108

{(73)}_{10} \Rightarrow {(x)}_{2} and {(0.108)}_{10} \Rightarrow {(0 . y)}_{2}

\Rightarrow {(73.108)}_{10} = {(x . y)}_{2}

\frac{73}{2} \Rightarrow q = 36 & r = 1

\frac{36}{2} \Rightarrow q = 18 & r = 1

\frac{18}{2} \Rightarrow q = 9 & r = 0

\frac{9}{2} \Rightarrow q = 4 & r = 1

\frac{4}{2} \Rightarrow q = 2 & r = 0

\frac{2}{2} \Rightarrow q = 1 & r = 0

{(73)}_{10} = {(1001001)}_{2} = {(x)}_{2}

0.108 \times 2 = 0.216

1 - 0.216 = 0.784

0.784 \times 2 = 1.568

0.568 \times 2 = 1.136

0.136 \times 2 = 0.272

1 - 0.272 = 0.728

0.728 \times 2 = 1.456

0.456 \times 2 = 0.912

\dots \dots .

\dots \dots .

{(0.108)}_{10} = {(0.011010 \dots)}_{2} = {(0 . y)}_{2}

then {(73.108)}_{10} = {(1001001.011010 \dots)}_{2}

Commented by Rasheed.Sindhi last updated on 12/Sep/20

T h a n k s m i s s .