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# Conversion of Binary, Octal, Hexadecimal to Decimal

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## Conversion of Binary, Octal, Hexadecimal to Decimal

A binary, octal or hexadecimal number has two parts — integer part and fraction part. For example, a binary number could be 10011, 0.011001 or 10011.0111. The numbers 45, .362 or 245.362 are octal numbers. A hexadecimal number could be A2, .4C2 or A1.34.

The method used for the conversion of integer part and fraction part of binary, octal or hexadecimal number to decimal number is the same; multiplication operation is used for the conversion. The conversion mechanism uses the face value and position value of digits. The steps for conversion are as follows—

**Find the sum of the Face Value * (from Base) ^{position} for each digit in the number.**

1. In a non-fractional number, the rightmost digit has position 0 and the position increases as we go towards the left.

2. In a fractional number, the first digit to the left of decimal point has position 0 and the position increases as we go towards the left. The first digit to the right of the decimal point has position –1 and it decreases as we go towards the right (−2,−3, etc.)

## Example

Convert 1011 from Base 2 to Base 10.

Convert 62 from Base 8 to Base 10.

Convert C15 from Base 16 to Base 10.