# Convert Decimal to Octal Numbers

## Decimal System

Decimal number system is the most commonly used and the most familiar one to the general public. It is also known as Base 10 numbering system since it is based on 10 following symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. In decimal system, every digit has its own position as well as the decimal point. I.e. the number 356.74 has 4 in the Hundredth position, 7 in the Tenths position, 6 in the Units position, 5 in the Tens position, and 3 in the Hundreds position. Decimal number system is also one of the oldest known numeral system, which is historically related to Hindu-Arabic numeral system.

## Octal System

Octalnumeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: (00)1 001 010, corresponding the octal digits 1 1 2, yielding the octal representation 112.

In the decimal system each decimal place is a power of ten. For example:

74 10 = 7 × 10 1 + 4 × 10 0 {\displaystyle \mathbf {74} _{10}=\mathbf {7} \times 10^{1}+\mathbf {4} \times 10^{0}} {\mathbf {74}}_{{10}}={\mathbf {7}}\times 10^{1}+{\mathbf {4}}\times 10^{0}

In the octal system each place is a power of eight. For example:

112 8 = 1 × 8 2 + 1 × 8 1 + 2 × 8 0 {\displaystyle \mathbf {112} _{8}=\mathbf {1} \times 8^{2}+\mathbf {1} \times 8^{1}+\mathbf {2} \times 8^{0}} {\mathbf {112}}_{8}={\mathbf {1}}\times 8^{2}+{\mathbf {1}}\times 8^{1}+{\mathbf {2}}\times 8^{0}

By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.

Related converters:
Octal To Decimal Converter