Binary to Decimal Converter

This Binary to Decimal Converter lets you convert Binary numbers to decimal quickly and easily.




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Read (or watch) our tutorial on How to Convert Binary to Decimal to learn more about the process of converting binary numbers to decimal.

How to use the Binary to Decimal Converter

  1. Enter a Binary Number in the first field.
  2. Press the Convert button.
  3. The Decimal Number output will appear in the second field.
  4. Optionally, you can Copy the output to clipboard, or Save it as a file on your device.

Try the Decimal to Binary Converter too!

Converter features

🔟 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.

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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 thingsFirst, 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.

Step 1 in converting binary to decimal

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.

Converting binary to decimal step 2

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.

Converting binary to decimal step 3

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.

Converting binary to decimal step 4

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.

Converting binary to decimal 5

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.

Converting binary to decimal 6

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.

BinaryDecimal
00
11
102
113
1004
1015
1106
1117
10008
10019
101010
101111
110012
110113
111014
111115
1000016
1000117
1001018
1001119
1010020
1010121
1011022
1011123
1100024
1100125
1101026
1101127
1110028
1110129
1111030
1111131
10000032
10000133
10001034
10001135
10010036
10010137
10011038
10011139
10100040
10100141
10101042
10101143
10110044
10110145
10111046
10111147
11000048
11000149
11001050
11001151
11010052
11010153
11011054
11011155
11100056
11100157
11101058
11101159
11110060
11110161
11111062
11111163
100000064
100000165
100001066
100001167
100010068
100010169
100011070
100011171
100100072
100100173
100101074
100101175
100110076
100110177
100111078
100111179
101000080
101000181
101001082
101001183
101010084
101010185
101011086
101011187
101100088
101100189
101101090
101101191
101110092
101110193
101111094
101111195
110000096
110000197
110001098
110001199
1100100100

Questions and Answers about Binary to Decimal conversion

👉 How do you use the Binary to Decimal Converter?

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.

✏️ How do you Convert Binary to Decimal?

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.

⚙️ How does the Binary to Decimal Converter work?

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.

🔟 Can I convert numbers from Decimal to Binary?

Of course! If you want to convert any decimal number to binary, you can use the Decimal to Binary Converter at ConvertBinary.com.

❓ What is the decimal value of 1000 (one-zero-zero-zero)?

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.