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Binary to Decimal Converter

Enter a binary number and get its decimal value, with every bit and its place value shown. You can also read it as a signed number.

Working

Convert a list

Quick reference

The method

Each binary digit is worth a power of 2, starting from 1 on the right: 1, 2, 4, 8, 16 and so on. Add up the values of the places that hold a 1.

1101
8 + 4 + 0 + 1 = 13

So binary 1101 is 13 in decimal. The working table shows every bit, its position, its place value and its contribution.

Signed numbers

Computers store negative numbers in two's complement. In that form the top bit has a negative weight. Choose a width, such as 8 bits, and the tool reads your bits as a signed value:

  • 01111111 is 127, the largest 8-bit value.
  • 10000000 is -128, the smallest.
  • 11111111 is -1.

The same bits mean different numbers when read as signed or unsigned, so 11111111 is 255 unsigned but -1 signed. If you give fewer bits than the width, zeros are added on the left.

Useful numbers

An 8-bit unsigned value reaches 255, a 16-bit value reaches 65535, and a 32-bit value reaches 4294967295. Each extra bit doubles the range.

Batch conversion

Paste one binary number per line in the list box to convert many at once. Spaces and underscores in the digits are ignored.

Going the other way? Use decimal to binary. To get hex, use binary to hex. The guide covers two's complement in more detail.

Frequently asked questions

How do I convert binary to decimal?

Add the powers of 2 for each position that contains a 1, counting from 1 on the right.

What is 11111111 in decimal?

255 when read as unsigned, or -1 when read as an 8-bit signed number.

What is two's complement?

The way computers store negative numbers. The top bit carries a negative weight, so 10000000 is -128 in 8 bits.

How large a binary number can I convert?

Very large. The tool uses arbitrary-size integers, up to 3000 digits.