Binary to Decimal Converter

Q: Can I convert many binary numbers at once?

Yes. Put one number per line and every line is converted, with the results lined up against the input. A line that is not a valid binary number is left blank and reported by line number, so one typo does not stop the rest.

Q: How do you convert binary to decimal by hand?

Write the powers of two under the digits from the right — 1, 2, 4, 8, 16 and so on — and add up the powers that sit under a 1. For 1011 that is 8 + 2 + 1 = 11. Alternatively, go left to right: start at 0, and for each digit double your total and add the digit.

Q: Why does 11111111 sometimes mean −1?

Because computers store signed integers in two's complement, where the top bit counts as negative. In an 8-bit signed byte, 11111111 is −128 + 127 = −1. The same bits as an unsigned byte are 255. The binary does not say which; the type in your code does.

Q: What is the largest number in n bits?

2^n − 1 when unsigned: 255 for 8 bits, 65,535 for 16, 4,294,967,295 for 32. Signed, the range is −2^(n−1) to 2^(n−1) − 1, so −128 to 127 for a byte.

Convert binary to decimal instantly — any length, one number per line — with bit width and signed (two's complement) readings.

Binary

Decimal

Group digits Add 0x / 0b / 0o prefix Uppercase hex Pad to whole bytes

What It Does

This converter reads a binary number — a string of 0s and 1s — and gives its decimal value. Each binary digit is a power of two, read from the right: 1, 2, 4, 8 and so on, and the decimal value is the sum of the powers whose digit is 1. The tool also tells you how many bits the value needs and, for a whole-byte pattern starting with 1, what it means as a signed integer — the reading people most often get wrong.

When to Use It

You are reading a register dump or a protocol field written in binary and need the number.
You are checking homework or exam answers for base conversion.
A bit flag field is documented in binary and you need the decimal value to put in code.
You have a column of binary values and want them all converted at once.

Worked Examples

101010

32 + 8 + 2 = 42. Six bits, so it fits in a single byte.

11111111

255 unsigned — but if those eight bits are a signed byte, the value is −1. The tool shows both readings.

1000 0000 0000 0000

Spaces are ignored. 2^15 = 32,768 — one past the largest signed 16-bit value.

Features

Converts as you type

Bulk conversion one number per line

Exact for numbers of any size

Digit grouping and 0x/0b/0o prefixes

Swap direction in one click

Explains bit width and two's complement

How to Use

1. Type or paste a binary number — or a list, one per line. 2. The decimal value appears alongside, line for line. 3. Use the options to group digits or add a prefix, and the swap button to convert the other way.

Common Mistakes

Converting a number through a JavaScript Number. Above 9,007,199,254,740,991 it silently rounds, so the last digits come out wrong. This tool uses BigInt and stays exact at any size.
Forgetting that the same digits mean different values in different bases. 10 is ten in decimal, two in binary, eight in octal and sixteen in hex — always label which base a value is in.
Treating a minus sign as how a computer stores a negative number. Hardware uses two's complement, so a negative value's bit pattern looks nothing like its positive counterpart.

Frequently Asked Questions

Can I convert many binary numbers at once?

How do you convert binary to decimal by hand?

Why does 11111111 sometimes mean −1?

What is the largest number in n bits?

Conversion runs in your browser with exact integer arithmetic. Nothing is uploaded.