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DFCCIL Executive Electrical 2018 Official Paper

Option 3 : (5464)8

**Concept:**

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number, and the maximum numbers that can be written with the given number of digits.

**Octal numbers: **These numbers use digits from 0 to 7, total of 8 digits, and hence they are called octal number system. Octal numbers have base 8.

**Hexadecimal numbers: **The numbers which have base 16. It uses 16 different digits to represent the numbers. It is denoted as h16, where h is a hexadecimal number. It may be a combination of alphabets and numbers. Thus, it includes numbers from 0 to 9 and alphabets A to F.

**Calculation:**

**Hexadecimal to Octal Conversion:**

Given, B3416 is a hexadecimal number.

B → 1011, 3 → 0011, 4 → 0100

1011 0011 0100

Now group them from right to left, each having 3 digits.

101, 100, 110, 100

101 → 5, 100 → 4, 110 → 6, 100 → 4

Hence, **B3416 = 54648**

__Key Points__

There is grouping of 3 from right to left since octal has base of 8, and 8 = 2** ^{3},** i.e. power 3.

CT 1: Current Affairs (Government Policies and Schemes)

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