Developer Tools
Binary to Decimal Converter
Paste a binary number and get the decimal value instantly. Includes a positional breakdown so you can see exactly how the conversion works.
Convert binary to decimal in three steps
No software to install. Works in any browser, on any device.
Enter a binary number
Type or paste any string of 0s and 1s.
See the decimal value
The decimal equivalent appears instantly as you type.
Copy the result
Click to copy the decimal number to your clipboard.
Binary input
Instant conversion
Results update on every keystroke. No button needed.
Validates input
Flags any non-binary characters immediately.
Shows the working
See the positional value breakdown so you can follow the math.
About Binary to Decimal Conversion
Binary is base-2 — every digit is either 0 or 1, and each position represents a power of 2. Decimal is base-10, the number system you use every day. Converting between them is a core skill in computer science, digital electronics, and low-level programming.
To convert by hand: read the binary number right to left, multiply each bit by 2 raised to its position (starting at 0), then sum the results. For 1101: 1×8 + 1×4 + 0×2 + 1×1 = 13. This tool does that work instantly and shows you the breakdown.
Understanding binary matters beyond exams. IP addresses, file permissions in Unix/Linux (chmod 755 uses binary logic), colour channels in hex codes, and data storage all rely on the binary system.
The positional breakdown this tool shows is what examiners expect you to produce by hand. It is also the clearest way to understand why a binary number equals what it does — you can see exactly which powers of 2 are “switched on.”
Need the reverse? Decimal to Binary → · Other tools: Base64 Encoder/Decoder · JSON Formatter
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Use itFrequently Asked Questions
How do you convert binary to decimal?
Assign each bit a positional value based on powers of 2, right to left: 1, 2, 4, 8, 16, 32… Multiply each digit by its positional value and sum. For 1011: (1×8)+(0×4)+(1×2)+(1×1) = 11.
What is 11111111 in decimal?
255. Eight 1s = 128+64+32+16+8+4+2+1 = 255. This is the maximum value of an 8-bit (one byte) unsigned integer.
What is the largest number a 32-bit binary can hold?
A 32-bit unsigned integer holds 0 to 4,294,967,295. A signed 32-bit integer ranges from −2,147,483,648 to 2,147,483,647.
Why does computing use binary?
Binary maps directly to electronic states — a transistor is either on (1) or off (0). Two states is the simplest and most reliable way to store data in hardware.