Binary to Decimal Converter

How to Convert Binary to Decimal

Converting binary to decimal by hand is straightforward once you know the routine. The converter above does it instantly, but working through the steps yourself is the fastest way to understand what is actually happening to the digits.

1. Write down the binary number and number each digit by its position, starting with 0 at the rightmost digit.
2. Multiply every digit by 2 raised to the power of its position.
3. Add all the products together. The total is the decimal value.

Worked example: 10101010

Result: (10101010)² = (170)¹⁰

The Binary System

Binary is the base 2 numeral system. It uses only two symbols, 0 and 1, and each digit is called a bit. Every digital circuit ever built relies on it, because a transistor has two reliable states, on and off, which map directly onto 1 and 0. Place values double as you move left: 1, 2, 4, 8, 16, 32 and so on. Eight bits make one byte, which can hold 256 distinct values, enough for every character in the original ASCII set.

Binary uses the digits 0 and 1.

The Decimal System

Decimal is the base 10 system that almost every human culture settled on, most likely because we have ten fingers. It uses the digits 0 through 9, and each position is worth ten times the position to its right. The number 2345.67 means 2 thousands, 3 hundreds, 4 tens, 5 ones, 6 tenths, and 7 hundredths. It is the default for everything people read, which is why converting to and from decimal is the most common base conversion a programmer performs.

Decimal uses the digits 0 through 9.

Binary to Decimal Conversion Examples

Binary to Decimal Conversion Chart

A full reference table for the values 1 to 256. Use it to check a conversion quickly or to look up a common value without typing anything.

Need a different pair of bases? Browse every number converter tool including binary, octal, decimal, and hexadecimal in both directions.