# Convert Octal to Decimal

Input a octal number like 377 in the following field and click the Convert button. |

### Octal Number System

The octal numeral system, or oct for the short form, is base 8 number system, and it uses the digits 0 to 7. Octal numerals can be made from binary numerals or binary numbers by grouping consecutive binary digits into groups of three starting from the right side.### Decimal Number System

The decimal numeral system also called base 10 or sometimes called denary, has 10 as its base, which in decimal is called base 10, as is the base in every normal numeral system. It is the numerical base most widely used by modern world.

### Base 8 to base 10

Converting octal to decimal can be done by using repeated division.

Start the decimal result at 0.

Remove the most significant octal digit from the left and add it to the result.

If you remove all octal digits, then you are done. Stop.

Otherwise, multiply all the result by 8.

The conversion can also be performed mathematical, by showing each digit place as an increasing power of 8.

125 octal = (1 * 8^{2}) + (2 * 8^{1}) + (5 * 8^{0}) = (1 * 64) + (2 * 8) + (5 * 1) = 85 decimal

The octal numeral 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 x 10^{1} + 4 x 10^{0}

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

112_{8}=1 x 8^{2} + 1 x 8^{1} + 2 x 8^{0}

Octal became widely used in computing when systems such as the UNIVAC 1050, PDP-8, ICL 1900 and IBM mainframes employed 6-bit, 12-bit, 24-bit or 36-bit words. Octal was an ideal abbreviation of binary for these machines because their word size is divisible by three (each octal digit represents three binary digits). So two, four, eight or twelve digits could concisely display an entire machine word. It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radices, and hexadecimal displays needed to display more numerals.

source: wikipedia.org

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