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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.

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