Binary to Decimal Converter

Enter a binary number below to convert it to a decimal.

By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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How to Convert Binary to Decimal

The binary number system is a base 2 number system since it only uses the digits 0 and 1. On the other hand, decimal is a base 10 number system since it uses ten digits, 0 to 9.

Often you’ll need to convert a binary number to its decimal value since most people use the decimal system. Binary numbers are often used in computing applications.

To convert a binary number to a decimal, you can use the positional notation method. To use this method, multiply each digit in the binary number from the rightmost number to the left by 2 to the power of n, where n is the distance from the right.

So, reading the binary number from right to left, the furthest digit to the right is equal to the digit times 2⁰. The digit that is one position from the right is equal to the digit times 2¹.

Binary to Decimal Formula

Thus, the binary to decimal formula is:

decimal number₁₀ = (d₀ × 2⁰) + (d₁ × 2¹) + … + (d_{n – 1} × 2^{n – 1})

In this formula, d₀ is the binary digit furthest to the right, d₁ is the digit one position from the right, and d_{n – 1} is the digit furthest to the left.

You can also use a tool like our binary calculator to convert to decimal or hex.

Binary to Decimal Conversion Video Tutorial

How to Convert Fractional Binary Numbers to Decimal

For real numbers that contain fractional values, you can use the positional notation system to convert as well. Start by using the method above to convert the whole portion of the number from binary to decimal.

Then, for the remaining fractional value, multiply each number to the right of the decimal point by 2 to the power of -1 times the distance from the decimal point plus 1. Ok, that sounds complicated but it’s easier than it sounds, let’s demonstrate.

decimal number₁₀ = (d_-1 × 2^-1) + (d_-2 × 2^-2) + … + (d_-n × 2^-n)

Binary to Decimal Conversion Table

The table below shows binary numbers and the equivalent decimal number values.