How To Use This Converter
Type a number in any of the Number-Base Radix input fields and press Enter or Return on your keyboard or keypad.
The other Number-Base Radix fields will show the number you entered, converted to the other radixes.
TIP:Entry Errors
If the data you type into any Base field contains disallowed symbols for that field, the converter will notify you.
In that case, simply re-type valid data in the field of your choice and press Enter or Return.
TIP:Copy and Paste
You can Copy and Paste any of the fields by selecting the text in the field,
then pressing Control-C to copy, and Control-V to paste.

Radix-8

Octal or Radix-8 Number System
Octal is a Radix-8 positional notation number system. Radix-8 or Base-8 means that each Octal "digit"
represents a multiple of increasing powers of 8, from right to left, such as:
... 8^{3}, 8^{2}, 8^{1}, 8^{0}
The valid Octal symbols are:
0, 1, 2, 3, 4, 5, 6, 7
For example, the Octal number 657 represents the number 431 in the Decimal number system, like so:
(6 x 8^{2}) + (5 x 8^{1}) + (7 x 8^{0})History of the Octal Number System
The Yuki language in California and the Pamean languages in central Mexico use Octal because the speakers
count using the spaces between their fingers rather than the fingers themselves.
Octal is occassionally used in computing, for example to represent the disk file permissions in the Unix
operating system and its variants. Octal has the advantage of not requiring additional symbols beyond the digits 0 through 7.
One Octal digit perfectly represents 3-bits of Binary, and for this reason Octal was used on computers
whose word-length was a multiple of 3, such as the 24-bit and 36-bit word-length IBM computers that were
popular in the 1960's. Those word-lengths could be efficiently represented by numerical displays consisting of 8 and 12 Octal digits.
Modern computers, however, use 16-bit, 32-bit, or 64-bit words, which are not perfectly represented by Octal.
Instead, modern computers use Hexadecimal (or Hex) to represent their words for display to humans, because a
Hex digit can perfectly represent 4-bits. Consequently, modern computer words are represented perfectly with 4, 8, or 16 Hex digits.

Radix-10

Decimal or Radix-10 Number System
Decimal is a Radix-10 positional notation number system. Radix-10 or Base-10 means that each Decimal "digit"
represents a multiple of increasing powers of 10, from right to left, such as:
... 10^{3}, 10^{2}, 10^{1}, 10^{0}
The valid Decimal symbols are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
For example, the Decimal number 927 represents the following numerical expression:
(9 x 10^{2}) + (2 x 10^{1}) + (7 x 10^{0})History of the Decimal Number System
The modern Decimal number system, known as the Hindu-Arabic number system, originated in India around the 9th century CE.
The system spread to the western world during the Middle Ages (1000 to 1300 CE) as a result of trade.
Some scholars attribute the first documented use of a Decimal system to China in the 1st century BCE.