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 2³ = 8.
• A hexadecimal digit from 0 to 15 can be represented as a combination of 4 bits, since 2⁴ = 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.