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# Conversion of Binary to Octal, Hexadecimal

## Conversion of Binary to Octal, Hexadecimal

A binary number can be converted into octal or hexadecimal number using a shortcut method.

**The shortcut method is based on the following information—**

• An octal digit from 0 to 7 can be represented as a combination of 3 bits, since 2^{3} = 8.

• A hexadecimal digit from 0 to 15 can be represented as a combination of 4 bits, since 2^{4} = 16.

## The Steps for Binary to Octal Conversion are—

1. Partition the binary number in groups of three bits, starting from the right-most side.

2. For each group of three bits, find its octal number.

3. The result is the number formed by the combination of the octal numbers.

## The Steps for Binary to Hexadecimal Conversion are—

1. Partition the binary number in groups of four bits, starting from the right-most side.

2. For each group of four bits, find its hexadecimal number.

3. The result is the number formed by the combination of the hexadecimal numbers.

## Convert the binary number 1110101100110 to octal.

Given binary number - 1110101100110

1. Partition binary number in groups of three bits, starting from the right-most side.

1 110 101 100 110

2. For each group find its octal number.

1 110 101 100 110

1 6 5 4 6

3. The octal number is 16546.

## Convert the binary number 1110101100110 to hexadecimal

Given binary number - 1110101100110

1. Partition binary number in groups of four bits, starting from the right-most side.

1 1101 0110 0110

For each group find its hexadecimal number.

1 1101 0110 0110

1 D 6 6

3. The hexadecimal number is 1D66.