Why does computing use binary?

Computer hardware is built from transistors that are naturally either on or off — two states map directly onto the two digits of binary (0 and 1).

Why is hexadecimal used alongside binary?

Each hexadecimal digit represents exactly 4 binary digits, so hex is a much more compact, human-readable way to write out binary values like memory addresses and color codes.

Binary Calculator

Convert numbers between binary, octal, decimal, and hexadecimal — the number systems used throughout computing.

ValueFromTo

Converted Value

How It Works

Positional number systems

Every number system represents a value using digits in positions worth increasing powers of its base — base 2 (binary) uses powers of 2, base 16 (hexadecimal) uses powers of 16, and so on. Converting between them means re-expressing the same value in a different base.

Hexadecimal digits

Hexadecimal needs 16 distinct digits per position, so it uses A-F to represent the values 10-15 alongside the usual 0-9.

Example

The binary number 1010 equals 10 in decimal, and 10 in decimal equals A in hexadecimal.

Common Mistakes

Entering digits that aren't valid in the source base — binary can only contain 0 and 1, octal only 0-7.
Mixing up hexadecimal's letter digits with the surrounding text — hex values are case-insensitive but must only contain 0-9 and A-F.

Frequently Asked Questions

Why does computing use binary?: Computer hardware is built from transistors that are naturally either on or off — two states map directly onto the two digits of binary (0 and 1).
Why is hexadecimal used alongside binary?: Each hexadecimal digit represents exactly 4 binary digits, so hex is a much more compact, human-readable way to write out binary values like memory addresses and color codes.