This all-in-one online Binary Number Converter transforms any given hexadecimal, decimal, binary or octal number to all the other number representations. Enter a number in the respective field of the converter and click the “Calculate” button to get the number represented in the other numeral systems.
Positional number systems
A positional numeral system with base \(b\) (where \(b\) is a natural number greater than 1, known also as the radix) is the way to represent any number using \(b\) basic symbols (or digits) corresponding to the first \(b\) natural numbers including zero. The position of a symbol in the number determines its value, hence the system is called positional. The symbol in the last position has its own value, and as it moves to the left its value is multiplied by the power of \(b\). So any number can be represented in the following form:
$${ a }_{ n }{ b }^{ n }+{ a }_{ n-1 }{ b }^{ n-1 }+…+{ a }_{ 0 }{ b }^{ 0 }$$
where the digits \({ a }_{ n }, { a }_{ n-1 } … { a }_{ 0 }\) are natural numbers less than \(b\).
The most commonly used numeral systems are: decimal, binary, octal, and hexadecimal.
• Decimal (base 10) is the common way to represent numbers by human beings. Decimal is abbreviated as Dec.
• Binary (base 2) is the way most digital circuits and devices represent and manipulate numbers. Binary is abbreviated as Bin.
• Octal (base 8) was previously a popular format for representing numbers in digital devices in a form that is more compact than binary. Octal is abbreviated as Oct.
• Hexadecimal (base 16) is currently the most popular format for representing numbers in digital devices in a form that is more compact than binary. Hexadecimal is abbreviated as Hex.
In many situations it’s important to be able to convert a number from one numeral system to another. And here our Binary Number Converter can provide invaluable help. It is actually a set of converters, like decimal to binary converter (or binary to decimal converter), decimal to hexadecimal converter (or hexadecimal to decimal converter), binary to hexadecimal converter (or hexadecimal to binary converter) and so on.
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