Convert Binary offers a free online converter tool, that allows you to convert binary numbers to their decimal representation.
At the bottom of this page, there is a tutorial on How to Convert Binary to Decimal – read it if you want to learn more about the process of converting binary numbers to decimals.
CONVERT BINARY TO DECIMAL
ConvertBinary.com makes it easy to convert decimal numbers to binary: just enter any binary number in the form below.
You can also convert Decimal to Binary.
How to Convert Binary to Decimal
So, you need to know how to convert binary to decimal? All those ones and zeros can be intimidating. You can find a binary to decimal converter here, or you can learn to convert yourself – no computer required.
If you thought complicated formulas were necessary for binary to decimal conversion, you can breathe a sigh of relief. To convert binary to decimal, you really only need to know three things. First, remember that the ones and zeros that make up binary can be thought of as the answer to a yes or no question. One for “yes”, and zero for “no”. Next, if you have an understanding of the powers of 2, this will be a breeze. The last step is basic addition.
The (Super) Powers of 2
We can thank the powers of 2 for making this so easy. If you’re not familiar with them, having a table for reference will make your job even easier. You won’t need an extensive table unless you’re converting very large binary numbers. For example, if the binary number you want to convert is three digits long, you’ll only need the first three powers of 2 (20 , 2¹, and 2²).
Let’s look at a three-digit binary number, 101.
To convert 101 in binary to decimal, we’ll must use the first three powers of 2. The most straightforward way to visualize this is to write your binary number, and above it, fill in powers of 2. Just remember to start from 20 on the right, and work your way left until you’ve run out of binary digits.
We have 1, 0, and 1, and a power of 2 for each binary digit. Look at 20; what’s underneath it? A one. This indicates we will use 20 in the decimal output.
Now, let’s work left. What’s under 2¹? A zero. This means we will not use 2¹. And under 2²? Another one. To find out what 101 is in decimal, we’ll need 20 and 2².
The rest is simple – 20 and 2² are 1 and 4, respectively. Now just add 1 + 4. The binary number 101 is the decimal 5.
It’s incredibly easy once you can think of 1 as a “yes”, and 0 as a “no”. Bigger numbers work in the same way. Let’s throw some extra zeros into the mix and use 100001. It’s long, but the method is identical. We just need 6 powers of 2 this time; one for each digit in the binary number.
Which powers of 2 correspond to a one? Only 26 and 20. Now we add those powers of 2 together. 100001 as a decimal is 33.
Just to prove how simple converting binary to decimal is, let’s look at an even longer binary figure: 11001100. We’ll need to go all the way to 27 for this conversion.
All we need to do is add the powers of 2 we used. Remember, we only “use” them when they correspond to a one. In this case, we need to add 128, 64, 8, and 4 to find the decimal. Everything else is indicated by a zero, so we don’t need to include them! 11001100 in binary is the decimal 204.
If you want to try it out for yourself, you can use the binary to decimal calculator on this page to check your work. Practice a few times, and you’ll be speaking the language of computers with ease.