Binary to Decimal Converter

1. Conversion of binary numbers to decimals
2. How to convert binary to decimal
3. Binary to decimal conversion table

    Conversion of binary numbers to decimals

Binary numbers are numbers represented in the binary positional numeral system which has a base of 2 while decimals are numbers represented in the decimal positional numeral system which has a base of 10. Binary numbers see most of their applications in the field of computer architecture and software engineering while decimals are the most widespread numbering system being used for everything from everyday calculations to scientific measurements.

In everyday life one would rarely need to convert a binary number to a decimal one, but home assignments or exam tasks involving such conversions are common if you are taking any kind of computer science or computer architecture course. No matter the case, our binary to decimal converter is here to help. If you must do the calculation manually, see the section below for step-by-step instructions on how the accomplish that.

    How to convert binary to decimal

To understand the conversion, remember that each position in a binary numeral represents a power of 2 the same way each position in a decimal number represents a power of 10. For example, the number 20 in decimal is 2 · 10¹ + 0 · 10⁰ = 20. The binary number 101 is then 1 · 2² + 0 · 2¹ + 1 · 2⁰ = 4 + 0 + 1 = 5 in decimal.

The process of binary to decimal conversion is then: first, take each position and multiply its value by 2 to the power of the position number, counting from right to left and starting at zero. If you need to calculate large exponents like 2¹⁶ you might find our exponent calculator useful.

    Binary to decimal conversion table

The table shows some key values expressed in the binary numeric system and their equivalent decimal numbers. However, conversions between the two numerical systems typically require a calculator for both speed and convenience.