Binary Converter

What Is a Number Base?

A number base defines how many unique digits are available before a new place value is needed. Decimal (base 10) uses digits 0–9. Binary (base 2) uses only 0 and 1 — the language computers operate in at the hardware level, where every value is stored as a sequence of on/off electrical states.

Why Hexadecimal and Octal Exist

Binary numbers get long fast — the decimal number 255 is 11111111 in binary, eight digits for a single byte. Hexadecimal (base 16) and octal (base 8) exist as more compact, human-readable shorthand: exactly 4 binary digits map to 1 hex digit, and 3 binary digits map to 1 octal digit, which is why programmers use them constantly when working with memory addresses, colors, and byte values.

The Division-Remainder Method

Converting a decimal number to another base by hand uses repeated division: divide by the target base, record the remainder, then repeat with the quotient until it reaches zero. Reading the remainders from bottom to top gives the converted number — exactly the working shown in the step-by-step section here.

Who Uses This

• Computer science students learning number systems and binary arithmetic.
• Programmers converting between hex color codes, memory addresses, and decimal values.
• Teachers building worksheets or demonstrations on number base conversion.
• Anyone decoding a hex or binary value found in technical documentation.

Reading the Bit Visualization

Each square in the bit visualization represents one binary digit, labeled underneath with its place value — 1, 2, 4, 8, 16, and so on, doubling each time. A highlighted bit means that power of two is included in the total; adding up every highlighted place value reconstructs the original decimal number.

Nothing Is Saved or Uploaded

All conversions happen entirely in your browser using arbitrary-precision arithmetic, so even very large numbers stay accurate. Refreshing the page clears every field and the history list — nothing is sent to a server or stored anywhere.