Decimal-Binary and Binary-Decimal Converter - Online Calculator!

Easily convert between Decimal to Binary and Binary to Decimal with just a few clicks. Try it now!

To carry out the conversion, simply type the number directly into the dialog box for an automatic conversion, or click the cursor in the dialog box and select the desired number for conversion. It's easy and simple!



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How is the Conversion of a Binary number to Decimal, and Decimal to Binary done?

Binary to Decimal Conversion!

To convert a binary to decimal number, you must follow the following steps:

  1. Write the binary number and assign each digit a weight of according to your position. The rightmost digit has weight 2⁰, the next one has weight 2¹, the next one has weight 2²,  and so on.
  2. Multiply each digit by its weight and add all results.

For example:

Let's convert the binary number 1011 in decimal:

  1. We assign the weights: 1 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2⁰
  2. We do the multiplications and add the results: 8 + 0 + 2 + 1 = 11

So the binary number 1011 is equal to 11 in decimal.

Another example:

Let's convert the binary number 11010 in decimal:

  1. We assign the weights: 1 x 2⁴ + 1 x 2³ + 0 x 2² + 1 x 2¹ + 0 x 2⁰
  2. We do the multiplications and add the results: 16 + 8 + 0 + 2 + 0 = 26

So the binary number 11010 is equal to 26 in decimal.


Decimal to Binary Conversion!

To convert a number decimal to binary, you must follow the following steps:


  1. Divide the decimal number by 2 and write down the remainder of the division.
  2. Divide the result of division by 2 and write down the remainder.
  3. Repeat the process until the result of the division is 0.
  4. The binary number is formed by the remainders of the divisions, read from bottom to top.

For exemple:

Let's convert the decimal number 12 in binary:

  1. 12 divided by 2 equals 6 with remainder 0
  2. 6 divided by 2 equals 3 with remainder 0
  3. 3 divided by 2 equals 1 with remainder 1
  4. 1 divided by 2 equals 0 with remainder 1

Reading the remainders from bottom to top, we have 1100. So the decimal number 12 is equal to 1100 in binary.

Another example:

Let's convert the decimal number 25:


  1. 25 divided by 2 equals 12 with remainder 1
  2. 12 divided by 2 equals 6 with remainder 0
  3. 6 divided by 2 equals 3 with remainder 0
  4. 3 divided by 2 equals 1 with remainder 1
  5. 1 divided by 2 equals 0 with remainder 1

Reading the remainders from bottom to top, we have 11001. So the decimal number 25 is equal to 11001 in binary.


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