# Convert HexaDecimal to Octal Numbers

## Hex System

Hex, or hexadecimal, is a number system of base 16. This number system is especially interesting because in our casually used decimal system we have only 10 digits to represent numbers. As hex system has 16 digits, the extra needed 6 digits are represented by the first 6 letters of English alphabet. Hence, hex digits are 0,1,2,3,4,5,6,7,8 and 9 A, B, C, D, E, F. This number system is the most commonly used in mathematics and information technologies. I.e. in html programming colors can be represented by a 6-digit hexadecimal number: FFFFFF represents white, 000000 represents black, and so on.

## 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 Hex Converter