Binary to Decimal Converter

What is Binary to Decimal Conversion?

Binary to decimal conversion turns a base-2 number (using only 0 and 1) into its base-10 equivalent. Computers store and process data in binary, but decimal numbers are what people read and reason about, so converting between the two is a routine step when working with binary data. Curious why computers store data in base-2 in the first place? See why computers use binary.

For example, the binary number 11111111 equals decimal 255 — the maximum value of a single byte (8 bits), which is why byte values commonly range from 0 to 255. For arithmetic on binary numbers rather than conversion, see the Binary Calculator.

How Binary to Decimal Conversion Works

Each binary digit (bit) represents a power of 2. Numbering positions from right to left starting at 0, a bit of 1 contributes its position's value to the total; a bit of 0 contributes nothing. Adding up every position's contribution gives the decimal value.

Example: 1101₂

Binary:   1    1    0    1
Position: 2³   2²   2¹   2⁰
Value:    8    4    2    1

(1 × 2³) = 8
(1 × 2²) = 4
(0 × 2¹) = 0
(1 × 2⁰) = 1

8 + 4 + 0 + 1 = 13

1101₂ = 13₁₀

The converter above shows this same breakdown for whatever binary number you enter. For the reverse operation, use the Decimal to Binary Converter.

Binary place values

Binary to Decimal Conversion Table

A quick reference for common binary numbers and their decimal, hexadecimal, and octal equivalents:

An 8-bit binary number (like 11111111) can represent decimal values from 0 to 255, which is why computer memory and file sizes are commonly measured in bytes.

Where Binary to Decimal Conversion Is Used

Converting binary to decimal comes up whenever binary data needs to be read by a person rather than a machine:

• Programming and debugging: reading raw binary output, bitwise operation results, and memory dumps in a readable form.
• Networking: converting binary IP address octets to standard dotted-decimal notation, e.g. 11000000.10101000.00000001.00000001 → 192.168.1.1.
• Digital electronics: interpreting sensor readings and register values that hardware reports in binary.
• Computer science education: learning positional notation, memory addressing, and how digital systems represent numbers.
• Systems administration: reading Unix/Linux permission bits (e.g. rwxrwxrwx) and 8-bit color channel values (0–255) that are stored in binary.

Need to go the other direction with hex instead of decimal? Try the Binary to Hex Converter. For binary-to-text conversion, see the Binary Translator.

Related Converters

Frequently Asked Questions