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Binary Calculator

Enter a number and select the base to convert from and to. This tool will help you convert between binary, decimal, octal, and hexadecimal formats.

Decimal to Binary Converter: The Easiest Way to Convert Numbers with Step-by-Step Explanations

When it comes to understanding how computers work, numbers play a big role. But while humans are used to working with the decimal system (base-10), computers think in binary (base-2). That means converting from decimal to binary is an essential skill for students, developers, and anyone exploring computer science.


A Clean and Simple Tool, Built for You

At the very top of this page, you’ll find the tool itself. Just type in your number in the “Decimal Input” box, hit the “Convert” button, and instantly get your Binary Output. It’s that easy.

Whether you’re solving homework, coding a project, or simply curious about number systems, this tool saves time and helps you learn along the way.

Why Use This Converter?

Manually converting decimals to binary can be slow and confusing, especially when the numbers get larger. Our tool does the hard work for you in seconds. But it doesn’t just stop at giving you the answer, it also gives you the option to see the step-by-step breakdown, so you can understand the process and actually learn how decimal to binary conversion works.

  1. Fast & Accurate: Get reliable results instantly.
  2. Educational Value: Learn the methods with clear, easy-to-follow steps.
  3. User-Friendly Design: No clutter, no distractions—just a clean input and output.
  4. Perfect for Everyone: From beginners in school to programmers working with binary data.

How to Convert Decimal to Binary (Step-by-Step Guide)

Converting decimal numbers into binary may sound complicated at first, but once you understand the process, it becomes very easy. There are two main methods to do this: the Division Method and the Subtraction Method. Let’s go through both with clear examples so you can learn step by step.

The Division by 2 Method

The most popular method for converting decimals to binary is this one. The idea is simple:

  1. Divide the decimal number by 2.
  2. Write down the remainder (either 0 or 1).
  3. To get to zero, keep dividing the quotient by two.
  4. Read the remainders from bottom to top, which gives you the binary number.

Example: Convert 224 to Binary

Here is an popular example

  1. 224 á 2 = 112, remainder 0
  2. 112 á 2 = 56, remainder 0
  3. 56 á 2 = 28, remainder 0
  4. 28 á 2 = 14, remainder 0
  5. 14 á 2 = 7, remainder 0
  6. 7 á 2 = 3, remainder 1
  7. 3 á 2 = 1, remainder 1
  8. 1 á 2 = 0, remainder 1

Now, pick the remainders from bottom to top: 11100000.

So, 224 in decimal = 11100000 in binary.

The Powers of 2 Subtraction Method

There has another way to convert decimals into binary: by using the powers of 2. The idea is to find the largest power of 2 that fits into your decimal number, subtract it, and continue with the remainder until you reach 0.

The powers of 2 go like this:

1, 2, 4, 8, 16, 32, 64, 128, 256…

Example: Convert 192 to Binary

Step 1: The largest power of 2 less than or equal to 192 is 128.

  1. 192 – 128 = 64

Step 2: The next largest power of 2 that fits into 64 is 64.

  1. 64 – 64 = 0

Now mark which powers of 2 were used: 128 and 64.

Write it in binary by placing 1 for used powers and 0 for unused ones:

  1. From 128 down to 1: 11000000

So, 192 in decimal = 11000000 in binary.

Why Learn Both Methods?

  1. The division method is easier for quick manual conversions.
  2. The subtraction method helps you understand how binary is built from powers of 2, which is useful in computer science and programming.

Interactive Learning: Step-by-Step Converter

With our tool, you don’t have to choose between methods. Enter a decimal number, press convert, and click “Show Me the Steps”. You’ll see both methods explained in detail for your exact number. This way, you don’t just get the answer, you actually learn the process.

Understanding Number Systems: Decimal vs. Binary

It’s important to understand the actual number systems. Humans and computers use different systems to represent numbers, and knowing the difference helps you see why conversions like decimal to binary or binary to decimal converter are so useful.

Decimal (Base-10) Numbers

Decimal is the system we use every day. It uses ten digits: 0 to 9. That's why it's called base-10. Each digit’s position has a value that is a power of 10. For example:

345 in decimal means:

  1. (3 × 100) + (4 × 10) + (5 × 1).

It’s very easy for humans, making base-10 a natural choice, because we have ten fingers.

Binary (Base-2) Numbers

On the other hand, computers use binary, or base-2. Binary numbers use two digits only: 0 and 1. Each digit (bit) represents a power of 2 instead of 10. For example:

1011 in binary means:

  1. (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1) = 11 in decimal.

Other Important Conversions & Related Tools

Decimal and binary aren’t the only systems you’ll encounter. In Because hexadecimal (base-16) is a concise way to represent binary, it is also employed in computing systems. Let’s look at some common conversions.

Binary to Decimal Conversion

Sometimes, you’ll need to switch back from binary to decimal. The process is the reverse of what we’ve seen: multiply each bit by its corresponding power of 2 and add them together.

Example: Binary 1101 = (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 13 in decimal.

Hexadecimal (often shortened to hex) uses 16 digits: 0–9 and A–F, where A = 10, B = 11, … F = 15. It’s a shorthand for binary because each hex digit equals exactly 4 binary bits.

  1. Hex 2F = Binary 0010 1111 = Decimal 47.

Why These Conversions Matter

  1. Students need them for math and computer science exams.

  3. Developers use them in programming, networking, and debugging.

  5. Tech enthusiasts can better understand how computers store and process information.

Decimal to Binary Conversion Table

Decimal Number

Binary Equivalent

0

0

1

1

2

10

3

11

4

100

5

101

6

110

7

111

8

1000

9

1001

10

1010

11

1011

12

1100

13

1101

14

1110

15

1111

16

10000

17

10001

18

10010

19

10011

20

10100

21

10101

22

10110

23

10111

24

11000

25

11001

26

11010

27

11011

28

11100

29

11101

30

11110

31

11111

32

100000

33

100001

34

100010

35

100011

36

100100

37

100101

38

100110

39

100111

40

101000

41

101001

42

101010

43

101011

44

101100

45

101101

46

101110

47

101111

48

110000

49

110001

50

110010

Common Questions About Decimal to Binary Conversion

How do you convert decimals to binary?

To convert a decimal number into binary, you can use the division by 2 method:

  1. Divide the number by 2.
  2. Write down the remainder (0 or 1).
  3. Divide the quotient by 2 again.
  4. Repeat until the quotient becomes 0.
  5. Read the remainders from bottom to top.

Example: Convert 13 to binary.

  1. 13 á 2 = 6 remainder 1
  2. 6 á 2 = 3 remainder 0
  3. 3 á 2 = 1 remainder 1
  4. 1 á 2 = 0 remainder 1

Reading from bottom to top: 1101. So, 13 in decimal = 1101 in binary.

What is 224 decimal in binary?

Using the division method:

  1. 224 á 2 = 112 remainder 0
  2. 112 á 2 = 56 remainder 0
  3. 56 á 2 = 28 remainder 0
  4. 28 á 2 = 14 remainder 0
  5. 14 á 2 = 7 remainder 0
  6. 7 á 2 = 3 remainder 1
  7. 3 á 2 = 1 remainder 1
  8. 1 á 2 = 0 remainder 1

Reading bottom to top = 11100000. So, 224 in decimal = 11100000 in binary.

How to convert 12.25 to binary?

When decimals have fractions, you handle the whole number and the fractional part separately.

  1. Whole part (12): Convert 12 into binary → 1100.
  2. Fractional part (.25): Multiply by 2 until the fraction is gone:

  4. 0.25 × 2 = 0.5 → 0

  6. 0.5 × 2 = 1.0 → 1

So fractional part = 01.

Final Answer: 12.25 in decimal = 1100.01 in binary.

What is 192 decimal in binary?

Using the powers of 2 subtraction method:

  1. Largest power of 2 less than 192 = 128.
  2. 192 – 128 = 64.
  3. Next power of 2 = 64.
  4. 64 – 64 = 0.

Now mark the used powers (128 + 64). In binary: 11000000. So, 192 in decimal = 11000000 in binary.