Convert Decimal to Binary!

This Decimal to Binary Converter lets you convert any Decimal number to Binary quickly and easily.




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Read (or watch) our tutorial on How to Convert Decimal to Binary to learn more about the process of converting decimal numbers to binary.

How to use the Decimal to Binary Converter

  1. Enter a Decimal Number in the first field.
  2. Press the Convert button.
  3. The Binary Number output will appear in the second field.
  4. Optionally, you can Copy the output to clipboard, or Save it as a file on your device.

Try the Binary to Decimal Converter too!

Converter features

🔢 Decimal Input length:Up to 7 digits
⚡ Conversion Speed:Instant!
➡️ Binary Output:Display, Copy, Save
🎯 Conversion Accuracy: 100%

How to Convert Decimal to Binary

If you work with computers, you may find yourself needing a basic understanding of the binary number system.  Or, maybe you just want to know binary for fun. Either way, understanding how to convert from decimal number system to binary number system can be a useful tool.

Here’s the best part: you don’t need a degree in math or a decimal to binary calculator do it.

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Ones and Zeros

You can think of binary as the language computers speak.  It is made up by a series of ones and zeros.  At first glance, it may look like madness, but there is a method to it.  We’ll start with a simple, single-digit, and explain how you can convert a decimal to binary.  Let’s use the number 7.

Decimal to binary conversion involves redefining the number you wish to convert.  7 can be represented as simply 7. Or, it can be represented as 4+3.  Rewriting the number is the first step in converting to binary. Most importantly, we want to dissect our decimal into the sum of powers of 2.

So let’s look at 7, and let’s consider the powers of 2.  What power of 2 is closest to the number 7 while being equal or less than 7?

2² gives us 4, so we’re going to use 4 to start disassembling 7.  We must add 3 to make up the rest of 7.  So now, we can consider 7=4+3.

It might be helpful to have a table of powers of 2 for reference.  We’ve included part of the table in the picture below.

Converting 7 to Binary - Step 1

Now we have 3, but there are no powers of 2 that give us 3.  We must break down 3 in the same way we did 7.  So, find the sum of powers of 2 that will give us 3.  Remember, we must begin with powers of 2 equal or less than 3.  2¹ gives us 2, and 20 gives us 1.

Converting 7 to Binary - Step 2

We used three different powers of 2 in this example.  So, the binary representation of 7 will be three digits long.  Since the highest power of 2 we needed was 2², we’re going to start by counting how many times 2² was used.  In binary, there can only be two answers to this question: it was used one, or zero times. If we did use it, we’ll indicate it with a 1.  If not, we’ll indicate it with a 0.

Using 2² means we’ll mark down a 1.  Now, we work down, counting the rest of powers of 2 we used.  We used 2¹, so we’ll indicate it with another 1. We used 20, so we’ll use 1 in the final spot.

Converting 7 to Binary - Step 3

We now have the decimal 7 converted into binary, as 111.

We can use 8 as an even easier example of how to convert decimal to binary.  What power of 2 is equal or less than 8? 2³ gives us 8 exactly, so we don’t need to deconstruct anything.

We used 2³ once.  We used 2², 2¹, and 20 zero times.  So 8 gives us 1000 in binary.  Binary is simply counting how many times you used a power of 2 to break down your decimal.

Converting 8 to Binary

Does that mean if we want to write the decimal 78 in binary, we can combine the binary equivalents in each digit?  111 and 1000?  Well, not exactly. 1111000 translates to 120!  But if we want to translate 78 to binary, it’s as easy as translating a single decimal value.

Same as before, we’ll look at which power of 2 is closest to 78.  26 gives us 64, which is the closest to 78 we can find without going over 78.  We can redefine 78 as 78 = 64 + 14.

Converting 78 to Binary - Step 1

Now we must redefine 14 as well.  We can use 2³ to give us 8, and now we need to add 6 to make 14.  Since 6 isn’t an exponent of 2 either, it needs to be deconstructed into a sum of powers of 2.

Lucky for us, 2² gives us 4, and 2¹ gives us 2.  Now, no more numbers need to be deconstructed, and we can turn it into binary.  Since we started all the way at 26 we must ask if we used that power, and each one that came before it, back to 20.

How many times did we use 26? 1

How many times did we use 25? 0

How many times did we use 24? 0

How many times did we use 2³? 1

How many times did we use 2²? 1

How many times did we use 2¹? 1

How many times did we use 20? 0

So, 78 in binary is 1001110

Converting 78 to Binary - Step 2

Not as scary as you thought, right?  The same algorithm works for three digit decimals and upwards.  The only difference is you might need a more extensive table of powers of 2 (or a calculator) in order to work through the equation.  Or, you can use a decimal to binary converter for larger numbers, like the one at the top of this page.  Bottom line; converting decimal to binary is as easy as 1, 2, 3 – or shall we say, 1, 10, 11!

Table of the First hundred Decimal numbers in Binary

For your convenience, the following table shows the decimal numbers from 0 to 100 along with their Binary representation.

DecimalBinary
00
11
210
311
4100
5101
6110
7111
81000
91001
101010
111011
121100
131101
141110
151111
1610000
1710001
1810010
1910011
2010100
2110101
2210110
2310111
2411000
2511001
2611010
2711011
2811100
2911101
3011110
3111111
32100000
33100001
34100010
35100011
36100100
37100101
38100110
39100111
40101000
41101001
42101010
43101011
44101100
45101101
46101110
47101111
48110000
49110001
50110010
51110011
52110100
53110101
54110110
55110111
56111000
57111001
58111010
59111011
60111100
61111101
62111110
63111111
641000000
651000001
661000010
671000011
681000100
691000101
701000110
711000111
721001000
731001001
741001010
751001011
761001100
771001101
781001110
791001111
801010000
811010001
821010010
831010011
841010100
851010101
861010110
871010111
881011000
891011001
901011010
911011011
921011100
931011101
941011110
951011111
961100000
971100001
981100010
991100011
1001100100

Questions and Answers about Decimal to Binary conversion

👉 How do you use the Decimal to Binary Converter?

The Decimal to Binary Converter at ConvertBinary.com is really easy to use.

Just follow these steps: enter your decimal number in the first field, then push the “Convert” button.

The binary representation for your decimal number will immediately appear in the field below.

✏️ How do you Convert Decimal to Binary?

To convert decimal numbers to their binary equivalent, you have two options: you can either use an online converter (like the one provided for free by ConvertBinary.com), or you can do it manually.

If you want to learn how to convert decimal to binary manually, you can read this guide, or watch the associated tutorial.

⚙️ How does the Decimal to Binary Converter work?

It takes the decimal number, and considers the powers of 2. It finds the power of 2 that is closest to the decimal, while being equal or less than the decimal itself.

Then it iterates the process until there’s no remainder left.

The process is automatic and so quick that it feels like it’s instant, even for large numbers.

🔟 Can I convert numbers from Binary to Decimal?

Of course! If you want to convert any number represented in binary to its decimal equivalent, you can use the Binary to Decimal Converter at ConvertBinary.com.

❓ What is the binary value of 10 (ten)?

The number 10 (Ten) is 1010 (one-zero-one-zero) in Binary.

You can find a table of the binary representations of decimal numbers from 0 to 100 at ConvertBinary.com.