Binary to Decimal

You have come to our binary to decimal webpage. Here you can convert any binary number to decimal using our binary converter below. In addition, we show you the convert to binary methods, and then continue with bin to dec examples. If you only want to do a quick conversion then head directly to our binary converter. If, on the other hand, you want to understand all about the bin to dec conversion the check our methods section and examples first. As you will see, the conversion is really easy.

Binary to Decimal Conversion

If you are really into computing and digital stuff then there will for sure come a time when you have to conduct a binary to decimal conversion. This is due to the fact that digital information is stored as sequences of 0s and 1s, that is in the binary system known as base 2. If you want to transform a binary value to decimal, also known as the base 10 system, then you are going to make a base 2 to decimal conversion. It is recommended studying our binary decimal conversion methods first, and once you understand how things are being done using out tool below for binary to dec operations.

Binary to Decimal Converter

In terms of the conversion many people find our site in search for a binary to decimal converter. If you only want to change a number from the base 2 system to the decimal system then use our binary decimal converter below. The binary to number converter does it all for you without the needs to dig trough examples and methods. However, we recommend that you bookmark us as binary to decimal converter online because you may need our online converter again in the future as binary numbers are very common in digital electronics.

Enter a binary number and then press the Convert button:

Unsigned Signed

Above you can find our converter. Enter a number in the binary format. The hit the convert button to get the result in decimal notation. Our number conversion calculator not only shows the result in the output field, but also the powers of two which add up to the decimal value when being summed. This can be helpful when studying the bin to decimal conversion methods below. You can always check if the manual method produces the same result as our converter.

Convert Binary to Decimal

We recommend you use the tool above to convert from binaries to decimal. Our keep on reading to learn all about converting using our methods below. If you have any questions left or believe something about converting numbers in base 2 is missing on our site then get in touch with us. We really appreciate any feedback to improve our page and / or tool. Also, if you like our content then please give us a Like or hit any of the sharing buttons. Thank you!

Binary to Decimal Conversion Method

Here we are going to show you two conversion methods. The first method we discuss is known as Positional Notation. The second conversion method is called Doubling.

Binary to Decimal Conversion Method 1

We start the first conversion method called Positional Notation by writing down the binary number in base 2 notation. We use 110001012 as example which translates to 197 in the decimal system.

1. List the powers of two from right to left, beginning with 20, which equals 1 in the decimal system. Next, we increment the exponent by one for each power of two until the amount of elements in our list is equal to the amount of digits the binary number has.
Binary to Decimal Conversion
In our example of 11000101 we have eight digits. Therefore, our list consisting of eight elements looks like this: 128, 64, 32, 16, 8, 4, 2, 1

2. We list the digits of the binary number below their powers of 2. Now, just write 10011011 below the numbers 128, 64, 32, 16, 8, 4, 2, and 1 so that each binary digit corresponds with its power of two.
Binary to Decimal Conversion Method
In our example we write 11000101 below the list of binary numbers such that each digit of the binary number corresponds with a power of two.

3. We match up the the digits of the binary number with their corresponding powers of two by drawing a line between them.
Binary to Decimal Conversion Positional Notation
It doesn’t matter if you start left or right. Just continue drawing lines until all powers of two and digits are connected.

4. We sum the powers of two. Moving trough the list we build the sum of powers of two which have a factor of 1, leaving out the elements with a factor of 0.
Binary to Decimal Conversion Positional Notation Method
In our example we sum 128 + 64 + 4 + 1.

5. We add the final values up.
Binary to Decimal Conversion Image
128 + 64 + 4 + 1 = 197. In our example 197 is the decimal equivalent of 11000101 in the binary number system.

6. We write down the result of the conversion using subscripts:
Binary to Decimal Conversion Depiction

19710 = 110001012. Note that our conversion method works for all binary numbers, regardless how many digits they have.

 

Binary to Decimal Conversion Method 2

Now, let’s have a look at our second conversion method. This approach is called Doubling and does without powers of two.

1. We start by writing down the binary number we are going to convert to decimal. We again use 110001012 as example.
Binary to Decimal Conversion Doubling

2. We double the previous total and add the current digit. The initial total shall be 0.
Binary to Decimal Conversion Doubling Method
As we are converting the binary number 11000101, the first digit on the left is 1. Our previous total is 0 because this is the first iteration. We multiply the previous total, 0, by two, and add 1, the current digit. With 0 x 2 + 1 resulting in 1, our new current total is 1.

3. We double the current total: Then we add the next leftmost digit.
Binary to Decimal Conversion Picture
Our current total is now 1 and the new current digit is 2. So, we multiply 1 by two and add 1. 1 x 2 + 1 = 3. The new current total we have now is 3.

4. We repeat the previous step.
Binary to Decimal Conversion Visualization

We double the new current total of 3, and add 0, the next leftmost digit. 2 x 3 + 0 = 6. Our new current total for the iteration is 6.

5. We repeat the previous step once more.
Binary to Decimal Conversion Figure
We multiply the current total of 6 by two and add the next digit: 0. 6 x 2 + 0 = 12. Our new total is 12 now.

6. We repeat the previous step once again.
Binary to Decimal Conversion Method Image
We double the new current total of 12 and get 24. Then we add the value of the next leftmost digit: 0. 12 x 2 + 0 = 24 in our example.

7. Again, we repeat the previous step.
Binary to Decimal Conversion Method Image 2
We double your 24, and add 1. 24 x 2 + 1 = 49.

8. We keep doubling the new current total whilst adding the next leftmost digit until there are no more digits left.
Binary to Decimal Image
Our current total is 98. We double it and add 1. 98 x 2 + 1 = 197.

9. We record the answer along with the respective base subscript.
Binary to Decimal Picture
19710 = 110001012

Binary to Decimal Conversion Examples

Finally, here are couple of bin to dec conversion examples for you.
12 = 110
102 = 210
112 = 310
1002 = 410
1012 = 510
1102 = 610
1112 = 710
10002 = 810
10012 = 910
10102 = 1010

You can verify that the examples are correct by adding the powers of two.
Below you can find some more binary to decimal conversion examples.

101002 = 2010
1100102 = 5010
11001002 = 10010
11111010002 = 100010
100111000100002 = 1000010

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