Hexadecimal to Octal and Vice Versa

Question

Convert Hexadecimal number to Octal - $(FD56.52A)_{16}$ to octal

My answer - $(176526.2452)_8$

Convert Octal to Hexadecimal $(37.27)_8$

My answer - $(1F.5C)_{16}$.

Correct or incorrect?

Please help.

score 1 · Answer 1 · answered Oct 27 '13 at 09:22

1

The easiest way to do that is perhaps to go trought binary

$ FD56.52A_{16}= 1111\ 1101\ 0101\ 0110.0101\ 0010\ 1010_2 $

and then to form groups of 3 digits left and right from the decimal point and padding with zeros the extremes if necessary

$ FD56.52A16_{16}= 001\ 111\ 110\ 101\ 010\ 110.010\ 100\ 101\ 010_2 =176526.2452_8$

So I think your answer is correct.

The other is the same but reversed .

answered Oct 27 '13 at 09:22

Perspectiva8

358

Can you please tell me - Why in calculator Im not able to input a Hexadecimal number with a DOT in it? – CuriousBeing Oct 27 '13 at 09:28
1

@user2923027 This is by convetion in computer science, in most programming languages libraries exist to parse integers in a variety of bases (usually from 2 to 36) but not usually for floating point numbers. – Kile Kasmir Asmussen Oct 27 '13 at 22:07

Kile Kasmir Asmussen · Accepted Answer · 2013-10-27T22:03:15.443

First of all, use $ {inline formula} $ and $$ {paragraph formula} $$ to typeset mathematics, to get proper subscripts.

One strategy is to just convert to decimal and back, but a much better strategy is to remember that in hexadecimal each digit corresponds to four binary digits ($2^4=16$) and in octal each digit is three bits ($2^3=8$).

$$ ({\rm FD56.52A})_{16} = (1111'1101'0101'0110\,.0101'0010'1010)_2 $$

Then we regroup to three digits and pad with zeros:

$$ (001'111'110'101'010'110\,.010'100'101'010)_2 = (176526.2452)_8 $$

You can use this method the other around way too.

Hexadecimal to Octal and Vice Versa

2 Answers2