The Binary to Decimal Converter allows you to convert Binary numbers to decimal quickly and easily.
Read (or watch) our tutorial on How to Convert Binary to Decimal to learn more about the process of converting binary numbers to decimal.
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How to use the Binary to Decimal Converter
- Enter a Binary Number in the first field.
- Press the Convert button.
- The Decimal Number output will appear in the second field.
- Optionally, you can Copy the output to clipboard, or Save it as a file on your device.
Try the Decimal to Binary Converter too!
|🔟 Binary Input length:||Up to 25 digits|
|⚡ Conversion Speed:||Instant!|
|➡️ Decimal Output:||Display, Copy, Save|
|🎯 Conversion Accuracy:||100%|
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.
Table of the First hundred Binary numbers in Decimal
For your convenience, the following table shows the binary numbers from 0 to 1100100 along with their Decimal representation.
Questions and Answers about Binary to Decimal conversion
The Binary to Decimal Converter at ConvertBinary.com is really easy to use.
Just follow these steps: enter your binary number in the first field, then push the “Convert” button.
The decimal representation for your binary number will immediately appear in the field below.
To convert binary numbers to their decimal equivalent, you have two options: you can either use an online converter (like the one provided for free by ConvertBinary.com), or you can do it manually.
If you want to learn how to convert binary to decimal manually, you can read this guide, or watch the associated tutorial.
It uses a scripting function that parses the input (the binary number in our case) and returns an integer.
The function call specifies that the binary system should be used.
The process is automatic and so quick that it feels like it’s instant, even for very large numbers.
Of course! If you want to convert any decimal number to binary, you can use the Decimal to Binary Converter at ConvertBinary.com.
The binary number 1000 (one-zero-zero-zero) is 8 (eight) in Decimal.
You can find a table of the binary representations of decimal numbers from 0 to 100 at ConvertBinary.com.