Decimal to Binary Calculator

About Decimal to Binary Calculator

To convert decimal to binary, repeatedly divide by 2 and record the remainders.

How to use this calculator

1. Enter a decimal number such as 13 or 42 into the input box.
2. Click the convert or calculate button.
3. Read the binary result shown by the calculator.
4. If needed, check the worked example to see how the conversion was built step by step.

The formula explained

This conversion changes a number written in base 10, written as \(n_{10}\), into the equivalent number in base 2, written as \(n_2\). In binary, each digit is either 0 or 1, and each position represents a power of 2.

• \(n_{10}\) = the decimal number you start with
• \(n_2\) = the same value written in binary
• 2 = the base used in binary place value

Step by step method

1. Find the largest power of 2 that is less than or equal to the decimal number.
2. Subtract that power of 2, then repeat with the remaining amount.
3. Write 1 for each power of 2 used and 0 for each power of 2 skipped, from largest power to smallest.

Worked example

Problem. Convert 13 from decimal to binary.

1. The largest power of 2 less than or equal to 13 is 8, so write 1 in the 8s place. Remainder: 13 - 8 = 5.
2. The next power is 4, and 5 includes 4, so write 1 in the 4s place. Remainder: 5 - 4 = 1.
3. The next powers are 2 and 1. 1 does not include 2, so write 0 in the 2s place, then write 1 in the 1s place. This gives 1101.

Tips and common mistakes

• Binary digits can only be 0 or 1, so if you see a 2 or higher, the number is not written correctly in binary.
• If the number is small, check your answer by adding the place values, for example \(1101_2 = 8 + 4 + 1 = 13\).

Frequently asked questions