Question

Find out the values of X. Y and Z in the following
(82.875)10 = (X)2 = (Y)8 = (Z)16

Answer 1

Given :   (82.875)₁₀  = X₂ =  Y₈  = Z₁₆

To Find : Values of X , Y , Z

Solution:

(82.875)₁₀

         82

 2       41      0

 2       20     1

 2       10      0

  2        5     0

   2        2     1

   2       1       0

   2        0      1

(82)₁₀  =  (1010010)₂

0.875  * 2  =     1.75          1

0.75    * 2   =     1.5             1

0.5      * 2    =     1                1

(0.875)₁₀ = (0.111)₂

Hence  (82.875)₁₀ = ( 1010010.111)₂

          82

   8     10        2

   8       1        2

   8       0        1

(82)₁₀  =  (122)₈

0.875  * 8  =    7          1

 (82.875)₁₀ = ( 122.7)₈

            82

   16      5        2

    16      0       5

0.875  * 16  =    14    = E

 (82.875)₁₀ = ( 52.E)₁₆

X = 1010010.111

Y  =  122.7

Z =  52.E

Learn More:

convert 97.188(10) to binary​ - Brainly.in

https://brainly.in/question/10878945

convert 97.188(10) to binary​ - Brainly.in

brainly.in/question/10878945

1.Convert the following decimal number into binary number of ...

brainly.in/question/11130869

(11011)^2 =(______)^10 then number in the blank space is

brainly.in/question/11048735

Answer 2

SOLUTION

TO DETERMINE

The value of X, Y, Z when

$\sf{(82.875)_{10} = (X)_2 = ( Y)_8 = (Z)_{16}}$

EVALUATION

Here the given decimal number is

$\sf{(82.875)_{10} }$

Now

$\sf{(82.875)_{10} = (82)_{10} + (0.875)_{10}}$

CONVERT TO BINARY

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:82 \:\:} \: \: \: \: \: }}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:41 \:\:} \boxed{0}} \\\underline{\sf{2}}&\underline{\sf{\:\:20\:\:} \boxed{1}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:10 \:\:} \boxed{0}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:5 \: \: \:} \boxed{0}}\\\underline{\sf{2}}& \underline{\sf{\:\:2\:\:} \boxed{1}} \\ \underline{\sf{}}&{\sf{\:\:1 \:\:} \boxed{0}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

We write down the Remainders in the boxes

Therefore

$\sf{(82)_{10} = (1010010)_{2} }$

Again

$\sf{0.875 \times 2 = \boxed{1}.750}$

$\sf{0.750 \times 2 = \boxed{1}.500}$

$\sf{0.500 \times 2 = \boxed{1}.000}$

Therefore

$\sf{(0.875)_{10} = (0.111)_2}$

Combining we get

$\sf{(82.875)_{10} = (1010010.111)_{2} }$

Thus we get

$\boxed{ \sf{ \: \: X = 1010010.111 \: \: } }$

CONVERT TO OCTAL

$\sf{(82.875)_{10} = (1010010.111)_{2} }$

PROCESS :

In this method we group the binary digits into three ( 3 bits form ) beginning from the right to left, writing exta zeros on the left side, if needed to make the number of bits into a multiple of 3 . Then we can directly write the equivalent decimal number for each group of binary to get the equivalent octal number.

Computation :

$\sf{ (1010010.111)_{2} }$

$\sf{ = \big( \: \boxed{ 001} \: \boxed{010} \: \boxed{010}. \boxed{111} \: \big)_{2} }$

$\sf{ = ( 122.7 )_{8} }$

This gives

$\sf{(82.875)_{10} = (122.7)_{8} }$

Thus we get

$\boxed{\sf{ \: Y = 122.7\: \: }}$

CONVERT TO HEXADECIMAL

$\sf{(82.875)_{10} = (1010010.111)_{2} }$

PROCESS :

In this method we group the binary digits into four ( 4 bits form ) beginning from the right to left, writing exta zeros on the left side, if needed to make the number of bits into a multiple of 4 . Then we can directly write the equivalent decimal number for each group of binary to get the equivalent hexadecimal number.

Computation :

$\sf{ (1010010.111)_{2} }$

$\sf{ = \big( \: \boxed{ 0101} \: \boxed{0010}. \boxed{1110} \: \big)_{2} }$

$\sf{ = \big(\: 52.E \: \big)_{16} }$

Since in hexadecimal E = 14

This gives

$\sf{(82.875)_{10} = (52.E )_{16}}$

Thus we get

$\boxed{ \: \: \sf{Z\: = 52.E } \: \: }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 11001001.1011()2=()8=()16

https://brainly.in/question/15093806

2. what is the equivalent 2s complement representation for -15 in 16 bit hexadecimal representation

https://brainly.in/question/12961284