Digital Logic Converter

Understanding Number Base Conversion

Binary, octal, decimal, and hexadecimal are different ways to write the same underlying value. Decimal uses powers of ten, binary uses powers of two, octal uses powers of eight, and hexadecimal uses powers of sixteen. Converting between them is useful when studying digital logic, programming, memory addresses, color values, and low-level data.

Choose the base that matches the value you already have and enter only valid digits for that system. The result table shows the equivalent forms together, which makes it easier to check place values and recognize patterns such as four binary bits represented by one hexadecimal digit. Very large values should be checked with a tool that supports arbitrary-precision integers.

What is a number base?

A number base determines how many symbols are available and how place values increase. For example, decimal is base 10, binary is base 2, octal is base 8, and hexadecimal is base 16.

Why is hexadecimal useful in computing?

Each hexadecimal digit represents four binary bits, so long binary values can be written more compactly while still being easy to translate back to binary.

How do I know whether my input is valid?

Binary accepts 0 and 1, octal accepts 0 through 7, decimal accepts ordinary digits, and hexadecimal accepts 0 through 9 plus A through F. The selected base determines which characters are allowed.

Can this converter handle very large numbers?

It is intended for common educational and programming values. JavaScript number precision becomes limited beyond the safe integer range, so verify unusually large values with an arbitrary-precision calculator.