Decimal to Binary Converter

How to convert decimal to binary

Every whole number can be written as a sum of distinct powers of two, and a binary number is simply a list of which powers are present: 1 for yes, 0 for no. The repeated-division method finds that list from the bottom up. Each time you divide by 2, the remainder tells you whether the current lowest power is used, and the quotient carries the rest of the number to the next step. It is the mirror image of the binary to decimal converter, and octal and hex sit alongside both on the number system converter.

Because the first remainder belongs to the ones place, the remainders come out in reverse order. The most common mistake is writing them top to bottom; always read them from the last remainder to the first. The converter shows each division, and you can check any answer by adding up the place values of its 1 bits.

Step by step

1. Divide the decimal number by 2 and write down the remainder, which is 0 or 1.
2. Divide the quotient by 2 again and record the new remainder.
3. Repeat until the quotient reaches 0.
4. Read the remainders from the last one to the first to get the binary number.

See the place values

How do you convert decimal to binary by subtracting powers of two?

Subtract the largest power of two that fits, write a 1 in that position, and repeat with what is left; every power that does not fit gets a 0. Knowing the powers of two (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024 …) lets you build the number from the left this way. For 2,026:

• 2,026 − 1,024 = 1,002 → bit 10 is 1
• 1,002 − 512 = 490 → bit 9 is 1
• 490 − 256 = 234 → bit 8 is 1
• 234 − 128 = 106 → bit 7 is 1
• 106 − 64 = 42 → bit 6 is 1
• 42 − 32 = 10 → bit 5 is 1
• 16 does not fit into 10 → bit 4 is 0
• 10 − 8 = 2 → bit 3 is 1
• 4 does not fit into 2 → bit 2 is 0
• 2 − 2 = 0 → bit 1 is 1
• 1 does not fit into 0 → bit 0 is 0

Reading the bits from position 10 down to 0 gives 11111101010, the same answer the division method produces. This version is quicker in your head for numbers under a few thousand, while division is easier to do on paper for any size.

How do you convert a decimal fraction to binary?

To convert a decimal fraction, multiply its fractional part by 2 again and again, and collect the whole-number part of each result from top to bottom. For 0.625:

• 0.625 × 2 = 1.25 → 1
• 0.25 × 2 = 0.5 → 0
• 0.5 × 2 = 1.0 → 1

So 0.625 = 0.101₂, which is ½ + ⅛. Fractions whose denominator is a power of two end cleanly, but most others repeat forever. 0.1 in binary is 0.000110011001100…, so a computer has to round it. That is why 0.1 + 0.2 gives 0.30000000000000004 in JavaScript and Python, which use 64-bit binary floating point.

The converter on this page handles whole numbers. Binary also explains storage sizes: memory is built in powers of two, which is why the GB to TB converter distinguishes TB from TiB.

When do you need decimal to binary?

You need it whenever a value has to be set bit by bit: in code, in network settings, in electronics and in computer science exams.

• Programming: setting bit flags and permissions, reading hardware registers and writing bit masks such as 0b00101000.
• Networking: working out subnet masks and which addresses share a network; 192 is 11000000, so a /26 mask ends in .192.
• Electronics: driving LEDs, shift registers and DIP switches, where each bit maps to a physical pin or switch.
• Computer science courses: exams routinely ask for the division method with the working shown.

For shorter notation, group the bits in fours and convert to hexadecimal with the decimal to hex converter. The number system converter shows octal as well.