Numbers Converter
Convert numbers between binary, octal, decimal, hexadecimal, and many other bases (2–36).
Result
OCT
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Conversion Formula
1 (Base-10) → 1 (Decimal) 1 (Decimal) → 1 (Base-10)
About Number Systems
Number systems are methods of representing numeric values using different bases.
- Binary (Base-2) - Uses only 0 and 1, fundamental for computers.
- Octal (Base-8) - Digits from 0 to 7, compact for binary data representation.
- Decimal (Base-10) - Standard human-readable system using digits 0–9.
- Hexadecimal (Base-16) - Uses 0–9 and A–F, common in programming and networking.
- Bases 2–36 - Extended systems supporting digits and letters for broader conversions.
Numeral Systems and Their Uses
Number systems are the basis for all digital computation, mathematics, and data representation. They determine how numbers are represented and calculated in most scientific, engineering, and computing fields.
The most widely used systems include:
- Binary (Base-2): The fundamental system used in all digital electronics and computing. It uses just two digits — 0 and 1 — to represent values and operations.
- Octal (Base-8): It uses digits 0 through 7. Octal is sometimes used shorthand for binary in computers, because each octal digit simply represents three binary bits.
- Decimal (Base-10): It is the most familiar system of numbers to which typical humans are habituated, using digits 0 through 9. It is the most utilized and popular system on the planet.
- Hexadecimal (Base-16): Used widely in programming and computer electronics. It uses the digits 0–9, with A–F being added to represent values, with each digit equating to four binary bits.
- Other than these, generalized Base-N systems allow representing numbers in varying bases from Base-2 to Base-36. For example:
- Base-3 to Base-9: Used sometimes in theoretical math or puzzle work.
- Base-11 to Base-20: Used in specialized purposes or experimental computing.
- Base-21 to Base-36: Useful for encoding dense data, as they both utilize numeric and alphabetic digits to encode them.
These number systems are not theoretical curiosities — they are common tools that are used in encoding, digital design, cryptography, and software construction. Understanding these bases gives insight into the form and processing of information on all levels of modern technology.