GATE CSE 2009 | Question: 5, ISRO2017-57

Question

$(1217)_8$ is equivalent to

• A. $(1217)_{16}$
• B. $(028F)_{16}$
• C. $(2297)_{10}$
• D. $(0B17)_{16}$

Comments

$(1217)_8$ will have 12 binary bits as there are 4 octal digits, hence its equivalent hexadecimal number will have 3 hex digits, So, options A and C are eliminated.

using last 2 octal digits 17 will be 001111 in binary hence las hex digit will be F, So option D can be further eliminated.

Answer 1

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

Answer 2

Answer is B.

Answer 3

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.

Answer 4

1217= 001 010 001 111 = 0010 1000 1111= 28F

Hence option B