Convert Binary to Decimal

Convert binary to decimal instantly — free online binary to base-10 number converter.

About

About the Binary to Decimal Converter

Every value a computer stores is really just binary underneath, so converting binary to decimal is the everyday translation step between how a machine represents a number and how a person reads it — type the bits and get the familiar base-10 number back instantly.

Each binary digit is worth double the one to its right — 1, 2, 4, 8, 16 and so on — so 1011 is 8 + 0 + 2 + 1 = 11. Adding up place values like that is easy for four bits and slow for thirty-two, which is where an instant converter earns its keep: the decimal value updates with every bit you type, for inputs up to 53 bits long.

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Guide

Using the Binary to Decimal Converter

  1. 1

    Step 1

    Binary is already selected below as the input base.

  2. 2

    Step 2

    Type or paste your binary digits (0s and 1s) into the value box.

  3. 3

    Step 3

    The result table fills in instantly — the decimal value sits alongside octal, hex and binary all at once.

  4. 4

    Step 4

    For a quick manual check, add up the powers of 2 for each position where the binary digit is 1, counting from the right starting at 2^0.

  • Converts binary to decimal live as you type — there's no Convert button to press
  • Accepts an optional 0b prefix and a leading minus sign for negative numbers
  • Rejects any digit other than 0 or 1 straight away, so a stray 2 can't give a wrong answer
  • Shows the value in binary, octal, decimal, hexadecimal and base 36 at once, plus any custom base from 2 to 36
  • Exact for whole numbers up to 9,007,199,254,740,991, and tells you when a number is too large
  • Runs entirely in your browser — free, with no sign-up and no limit

Computer science students

Students check place-value sums in binary homework and see the decimal answer instantly.

Network engineers

Network engineers read an octet like 11000000 as 192 while working through an IP address by hand.

Electronics hobbyists

Hobbyists turn a row of switch or pin states into the number a datasheet or sketch expects.

Puzzle and CTF players

Puzzle solvers decode binary clues into plain numbers without counting powers of two.

Popular base conversions

Binary Octal Binary Hexadecimal Octal Binary Octal Decimal Octal Hexadecimal Decimal Binary Decimal Octal Decimal Hexadecimal Hexadecimal Binary Hexadecimal Octal Hexadecimal Decimal

Examples

Binary to Decimal examples

4 worked examples

01

A single byte

11111111 in binary equals 255 in decimal — the largest value a single 8-bit byte can hold.

02

Classroom example

1010 in binary equals 10 in decimal: (1×8)+(0×4)+(1×2)+(0×1) = 10.

03

A longer value

1100100 in binary equals 100 in decimal.

04

With a 0b prefix

0b11111111 converts to 255, the largest value a single byte can hold.

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FAQ

Frequently asked questions

Quick answers to common questions about the Binary to Decimal Converter.

How do I convert binary to decimal?

Type your binary number above, with binary selected as the input base. The decimal value appears instantly in the results table — nothing is uploaded anywhere.

How do you convert binary to decimal by hand?

Number each binary digit's position from the right starting at 0, raise 2 to that power for every position holding a 1, then add the results: 1010 is (1×2³)+(0×2²)+(1×2¹)+(0×2⁰) = 8+0+2+0 = 10.

What is binary 1010 in decimal?

1010 in binary is 10 in decimal — it's one of the first examples used to teach positional binary notation, since 8 + 2 = 10.

Is this binary to decimal converter free?

Yes. It's free, with no sign-up and no limit on how many numbers you convert.

Can I convert decimal back to binary?

Yes — the same converter works in both directions. Select decimal as the input base instead, or use the dedicated decimal to binary converter page.

How large a binary number can I convert?

Up to 9,007,199,254,740,991 in decimal terms — beyond that the conversion won't be exact, and the tool will tell you so.

Can I paste binary with a 0b prefix or leading zeros?

Yes. A leading 0b is stripped automatically and leading zeros don't change the value, so 0b00001010, 00001010 and 1010 all give 10. Spaces between groups of bits aren't accepted, so remove them first.

Can it convert binary fractions like 101.11?

No — it converts whole numbers only, so a binary point isn't accepted. For reference, 101.11 is 5.75 in decimal: the digits after the point are worth 1/2, 1/4, 1/8 and so on.

How do I read a two's-complement number like 11111111?

The tool reads binary as an ordinary positive value, or a negative one if you type a minus sign in front, so 11111111 is shown as 255, not -1. For an 8-bit value that starts with 1, subtract 256 yourself to get the signed number.

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