The Gateway to Computer Science Excellence

First time here? Checkout the FAQ!

x

+13 votes

+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

- All categories
- General Aptitude 1.2k
- Engineering Mathematics 4.7k
- Digital Logic 1.9k
- Programming & DS 3.5k
- Algorithms 3k
- Theory of Computation 3.7k
- Compiler Design 1.5k
- Databases 2.8k
- CO & Architecture 2.5k
- Computer Networks 2.9k
- Non GATE 835
- Others 1.2k
- Admissions 263
- Exam Queries 390
- Tier 1 Placement Questions 17
- Job Queries 50
- Projects 6

33,593 questions

40,128 answers

114,021 comments

38,389 users