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+13 votes
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$(1217)_8$ is equivalent to

  1. $(1217)_{16}$
  2. $(028F)_{16}$
  3. $(2297)_{10}$
  4. $(0B17)_{16}$

 

asked in Digital Logic by Veteran (69k points)
edited by | 1.3k views

5 Answers

+13 votes
Best answer

Answer: (b)

Here are two different ways of solving this problem.

Short Method

Given number is in base 8 thus each digit can be represented in three binary bits to get overall binary equivalent. 

$$(1217)_8 = (001\ 010\ 001\ 111)_2$$

I have written the equivalent in group of three bits for easy understanding of the conversion. We can rearrange them in group of four to get equivalent hexadecimal number (in similar manner).

$$(001 010 001 111)_2 = (0010\ 1000\ 1111)_2 = (28F)_{16}$$

Long Method

In a nut shell the long method follow the following conversion

$$OCT \rightarrow DEC \rightarrow HEX$$

This procedure is good in a sense that the given option also have a decimal equivalent, and thereby might save some time (no in this case, unfortunately).

Here is the the decimal equivalent

$$(1217)_8 = (1*8^3 + 2*8^2 + 1*8^1 + 7*8^0)_{10} = (655)_{10}$$

And we see that decimal equivalent is not in option therefore we proceed for hexadecimal conversion using division method.

$$(655)_{10} = (28F)_{16}$$

Which we can find in given options.

HTH

answered by Loyal (4.4k points)
selected by
+19 votes

(1217)_8 = ( 001\text{ }010\text{ }001\text{ }111)_8\\ \text{ Grouping by 4 bits}\\ (0010\text{ }1000\text{ }1111)_{16} = (28F)_{16}\\

Answer is B.

 

answered by Loyal (4.2k points)
+4 votes
The answer is B.

The simple way is... you can convert every option to decimal equivalent, which is easier to convert. as well as the one in question too. Compare and you'll get B.
answered by Veteran (19.8k points)
+1 vote
1217= 001 010 001 111 = 0010 1000 1111= 28F

Hence option B
answered by Active (1.8k points)
–1 vote

B) 028f16

just convert octal to hexadecimal

answered by Veteran (12.4k points)


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