What is the easiest way to convert decimal to binary?

For small numbers, subtract the largest power of two that fits and repeat down the list, marking a 1 wherever a power fits. For any size number, divide repeatedly by 2 and read the remainders in reverse.

How do you convert 37 to binary?

Divide 37 by 2 repeatedly and record the remainders: 1, 0, 1, 0, 0, 1. Read them bottom to top to get 100101. Check it by adding 32 + 4 + 1, which equals 37.

How is conversion different for a BCD clock?

A BCD clock converts each decimal digit separately, so no value exceeds 9. To show 37 you convert 3 to 0011 and 7 to 0111, using only the weights 8, 4, 2, and 1 for each digit.

How can I check a decimal to binary conversion?

Add the position values wherever you wrote a 1. If the powers of two you switched on sum to your original number, the conversion is correct. Comparing against a live binary clock also confirms it.

How to Convert Decimal to Binary

Converting a number from decimal to binary sounds intimidating until you see how mechanical it really is. There are two dependable methods, and both come down to simple arithmetic you already know. Once you have them, you can turn any everyday number into a string of ones and zeros, and you will understand exactly why a binary clock lights up the way it does.

In this guide you will learn the repeated-division method and the subtract-the-powers method, work through several examples, and pick up tricks for checking your answers. Keep the live binary clock open as a self-marking practice tool, because every second it displays is a fresh decimal number already converted to binary for you.

What Binary Really Means

Decimal is a base-ten system: each position is worth ten times the one to its right, giving the familiar ones, tens, hundreds, and thousands. Binary is base two, so each position is worth twice the one to its right: ones, twos, fours, eights, sixteens, and so on. A binary number is written using only the digits 0 and 1, where each 1 means the value of that position is included and each 0 means it is left out.

Because of this, converting to binary is really the act of expressing a number as a sum of powers of two. The number 13, for example, is 8 + 4 + 1, so its binary form switches on the eight, four, and one positions and switches off the two, giving 1101. If the powers of two feel unfamiliar, our explainer on binary numbers explained lays out the ladder in detail.

Method 1: Repeated Division by 2

The most reliable method for any size of number is to divide by two over and over, writing down each remainder. The remainders, read in reverse, are your binary digits.

Worked Example: Converting 37

37 divided by 2 is 18 remainder 1. Write down 1.
18 divided by 2 is 9 remainder 0. Write down 0.
9 divided by 2 is 4 remainder 1. Write down 1.
4 divided by 2 is 2 remainder 0. Write down 0.
2 divided by 2 is 1 remainder 0. Write down 0.
1 divided by 2 is 0 remainder 1. Write down 1.

Now read the remainders from bottom to top: 100101. So 37 in binary is 100101. You can check this by adding the position values that are switched on: 32 + 4 + 1 = 37. The method works for any whole number, however large, and never requires you to guess.

Method 2: Subtract the Powers of Two

The second method is faster for small numbers and mirrors exactly how you read a binary clock. You list the powers of two, then subtract the largest one that fits, working downward.

Worked Example: Converting 52

The relevant powers of two are 32, 16, 8, 4, 2, and 1. Walk down the list:

Does 32 fit into 52? Yes. Set that bit to 1 and subtract, leaving 20.
Does 16 fit into 20? Yes. Set that bit to 1 and subtract, leaving 4.
Does 8 fit into 4? No. Set that bit to 0.
Does 4 fit into 4? Yes. Set that bit to 1 and subtract, leaving 0.
Does 2 fit into 0? No. Set that bit to 0.
Does 1 fit into 0? No. Set that bit to 0.

The bits from 32 down to 1 read 110100, so 52 in binary is 110100. This is exactly the pattern a true binary clock would show for 52 seconds, which is why this method feels so natural once you start reading real lights. The distinction between that and a per-digit display is covered in binary clock vs BCD clock.

Converting for a BCD Clock

Most binary clocks use binary-coded decimal, so they never convert the whole number at once. Instead they convert each decimal digit on its own, and every digit only needs the four weights 8, 4, 2, and 1. This makes conversion delightfully small. To show 37 on a BCD clock, you convert the 3 and the 7 separately: 3 is 0011 and 7 is 0111. You never handle a number larger than 9. The full logic of this per-digit approach lives in what is binary-coded decimal.

A Quick Digit Table

Because BCD digits only run from 0 to 9, it helps to memorise the ten patterns. They are 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, and 1001 for the digits 0 through 9. Once these ten are in your head, reading or writing any BCD time becomes instant.

Converting Larger Numbers

Both methods scale to any size, but a little organisation keeps big conversions tidy. When converting a number in the hundreds, write the powers of two in a row first, 128, 64, 32, 16, 8, 4, 2, 1, then walk down them with the subtract method, ticking off each one that fits. This visual scaffold prevents the most common slip, skipping a position and shifting every later bit out of place. For example, 200 becomes 128 + 64 + 8, which switches on those three positions and leaves the rest off, giving 11001000. Laying the powers out in advance turns even a three-digit conversion into a calm, mechanical walk rather than a juggling act, and it makes checking your answer afterwards much simpler.

Checking Your Work

Every conversion can be verified in seconds, so there is never any need to trust a shaky answer.

Add the position values. Sum the powers of two wherever you wrote a 1. If the total matches your original number, the conversion is correct.
Count the digits. A number under 8 needs at most three bits, under 16 needs four, under 32 needs five. A wildly long answer is a warning sign.
Compare with a clock. Read the current second from the live binary clock, convert it yourself, and confirm the lamps agree.

Practising Without Getting Bored

Conversion is a skill that rewards short, frequent practice far more than a single long session. A live clock turns practice into a game, since a new number appears every second and marks your answer instantly.

Race the seconds. Try to convert each second to binary before the next one arrives.
Work backwards too. Read a binary pattern and convert it back to decimal to build both directions.
Compare formats. Glance at a digital clock to confirm your decimal reading, then translate.
Mix it up. Once the seconds feel easy, try the minutes and hours, or watch an analog clock and convert the numbers it points to.

If you are helping a younger learner, turning conversion into this kind of timed game works wonders, an approach we expand on in teaching kids binary with a clock.

Conclusion

Converting decimal to binary is nothing more than expressing a number as a sum of powers of two, and you now have two reliable ways to do it: divide by two and collect the remainders, or subtract the powers from largest to smallest. Both are quick, both are checkable, and both are exactly what a binary clock does every second of the day. Put your new skill to the test on the live binary clock, then explore more binary guides on the binclock.com homepage.

How to Convert Decimal to Binary (Step by Step)