How to Convert Binary to Decimal: Free Number Base Converter Guide

Computers think in binary, programmers often work in hexadecimal, and humans count in decimal. Moving between these number bases is a constant task in programming, electronics, and computer science. Our free number base converter translates between binary, decimal, octal, and hexadecimal in real time, all in your browser.

What Is a Number Base?

A number base (or radix) is the number of unique digits used to represent values. The base determines how numbers are written:

• Binary (base 2) — uses only 0 and 1. This is how computers store all data.
• Octal (base 8) — uses digits 0–7.
• Decimal (base 10) — the everyday system, using digits 0–9.
• Hexadecimal (base 16) — uses 0–9 plus A–F, where A=10 through F=15.

The same value can be written in any base. For example, decimal 255 is 11111111 in binary, 377 in octal, and FF in hexadecimal.

How to Convert Binary to Decimal Online

1. Type a value into any of the base fields — binary, octal, decimal, or hex.
2. All other bases update instantly to show the equivalent value.
3. Copy any representation with one click.

Because the conversion is live, you can experiment freely and see how a number looks across every base at once.

How Binary to Decimal Conversion Works

In binary, each digit represents a power of two, starting from the right. To convert 1011 to decimal:

1011 = (1×8) + (0×4) + (1×2) + (1×1)
     = 8 + 0 + 2 + 1
     = 11

The converter does this automatically, but understanding the math helps you reason about binary values directly.

Why Hexadecimal Matters in Programming

Hexadecimal is popular among programmers because it maps neatly to binary — each hex digit represents exactly four binary digits. This makes long binary numbers far more compact and readable. Hex appears constantly in:

• Color codes — #FF5733 is a hexadecimal RGB color.
• Memory addresses — debuggers and low-level tools display addresses in hex.
• Byte values — each byte is conveniently written as two hex digits (00–FF).

Frequently Asked Questions

Is the number base converter free? Yes — it is free, requires no sign-up, and runs entirely in your browser.

Which bases can I convert between? Binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) — all at the same time.

What is 255 in binary? 255 in decimal is 11111111 in binary and FF in hexadecimal — the maximum value of a single byte.

Does it convert in real time? Yes. Type into any base field and every other base updates instantly.

Working with binary or hex? Type a number and see it in every base at once.