How to Convert From Binary to Decimal

By Techwalla Computers Editor

The number system we most commonly use, called decimal, is a base 10 system, meaning it uses a pattern of 10 numbers. The binary number system is a base 2 system that uses zeros and ones. Computers operate on the binary system, so learning it has many practical applications. Converting from decimal to binary is challenging, so it is best to learn to convert binary to decimal first.

Step 1

Get a piece of paper and a pen. Write the binary number down.

Step 2

Count the number of digits in the binary number. For each digit, list the powers of two from right to left in order, starting with 1 until you have one power of two for each digit. For example, for a seven-digit binary number, you would list 64, 32, 16, 8, 4, 2,1.

Step 3

Connect the binary digits with their corresponding powers of two with a straight line. In the above example, the binary digit furthest to the right would be connected to the 1.

Step 4

Draw a line under the numbers you have listed. Go through the binary numbers and if the binary number is 1, bring down the power of two and write it below the line. If the binary number is 0, put a 0 below the line.

Step 5

Convert the binary numbers to decimal by adding the numbers you wrote below the line. The sum of the numbers is the decimal equivalent of the binary number.

Tips & Warnings

  • The Windows calculator will convert binary numbers of decimal. Open the calculator, choose "Scientific" from the View menu, enter the binary number and then choose "Decimal" from the list of options at the top.