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UGC NET CSE | June 2009 | Part 2 | Question: 13

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The octal equivalent of hexadecimal $\text{(A.B)}_{16}$ is :

  1. $47.21$
  2. $12.74$
  3. $12.71$ 
  4. $17.21$
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Hexadecimal number system represents numbers using base $16$, using $0-9$ for decimal numbers $0-9$ and $A-F$ for decimal numbers from $10-15.$

Here,

$(A)_H=(10)_{10}=(1010)_2$

similarly

$(B)_H=(11)_{10}=(1011)_2$

To obtain octal equivalent for a given number first convert into binary representation and make a group of $\log_28=3$ bits.

$(A.B)_H=(\ 1010 .\ 1011)_2=(\ 001 \ 010. \ 101 \ 100)_2$

$\therefore (A.B)_H=(12.54)_8$

So correct answer is $(12.54)_8$

Note: none of the options are correct here.
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