Decimal to Binary

Decimal to Binary conversions are a breeze with our free online tool. Forget complex calculations or manual conversions – this is the fastest and most user-friendly solution around. Simply enter your decimal value and get the corresponding binary equivalent in seconds. Our tool is perfect for students, programmers, or anyone who needs to work with both decimal and binary systems. Say goodbye to conversion headaches and hello to effortless accuracy!

Decimal to Binary Converter

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How to Convert Decimal to Binary?

There are two main methods for converting decimal numbers to binary:

Method 1: Repeated Division by 2

This method is a straightforward approach that relies on repeated division by 2. Here’s how it works:

  1. Start with your decimal value.
  2. Divide the decimal by 2.
    • Write down the remainder (0 or 1) as the least significant bit (LSB) of the binary equivalent.

Note the quotient (whole number result of the division).

  1. Repeat step 2:

Divide the quotient obtained in the previous step by 2 again.

Write down the remainder as the next bit in the binary representation (moving left from LSB).

Keep note of the new quotient.

  1. Continue dividing by 2 until the quotient becomes 0.
  2. The binary equivalent of your decimal number is the sequence of remainders written in reverse order, starting from the LSB (the last remainder) to the MSB (most significant bit, which will be the last quotient).

Example: Convert 13 (decimal) to binary.

Divide 13 by 2: 13 / 2 = 6 (quotient) with a remainder of 1 (LSB).

Divide 6 by 2: 6 / 2 = 3 (quotient) with a remainder of 0.

Divide 3 by 2: 3 / 2 = 1 (quotient) with a remainder of 1.

Divide 1 by 2: 1 / 2 = 0 (quotient) with a remainder of 1.

Reverse the order of remainders: 1 1 0 1 (binary representation of 13).

Method 2: Using Exponents of 2

This method utilizes the concept that any binary number can be represented as a sum of powers of 2. Here’s the breakdown:

  1. Express the decimal number as the sum of the largest possible power of 2 that is less than or equal to the number and the remaining value.
  2. If the remaining value is still greater than 0, repeat step 1 with the remaining value.
  3. The binary equivalent is formed by representing each power of 2 used in step 1 with a 1 and all unused powers of 2 with a 0.

Example: Convert 13 (decimal) to binary.

The largest power of 2 less than or equal to 13 is 23 (8).

13 – 8 = 5 (remaining value).

The largest power of 2 less than or equal to 5 is 22 (4).

5 – 4 = 1 (remaining value).

Binary representation: 1 (for 23) + 0 (for 22, not used) + 1 (for 21) + 0 (for 20, not used) = 1101 (the binary equivalent of 13).

Both methods achieve the same result. The first method (repeated division) is often considered simpler and more intuitive, while the second method (using exponents) might be more suitable for larger numbers.

How Decimal to Binary is Different from Text to Binary?

Decimal to binary and text to binary deal with converting different types of data into the language of computers: binary (sequences of 0s and 1s). Here’s a breakdown of the key differences:

Data Represented:

  • Decimal to Binary: Converts numerical values represented in the decimal system (base 10) to their equivalent binary representation (base 2).
  • Text to Binary: Converts text characters (letters, symbols, punctuation) into their binary representation using a character encoding scheme like ASCII (American Standard Code for Information Interchange).

Conversion Method:

  • Decimal to Binary: Uses mathematical techniques like repeated division by 2 or identifying the highest power of 2 that fits within the decimal value.
  • Text to Binary: Relies on a predefined mapping table (like ASCII) where each character is assigned a unique binary code.


  • Decimal to Binary: Converting the decimal number 10 (base 10) to binary would result in 1010 (base 2).
  • Text to Binary: Converting the letter “A” using ASCII would result in 01000001 (base 2).


  • Decimal to Binary: Used in computer science and digital systems to represent numerical data for calculations and storage.
  • Text to Binary: Enables computers to process and store text data, allowing us to display characters on screens and communicate electronically.

In essence:

  • Decimal to binary focuses on converting numeric values, while text to binary deals with converting individual characters.
  • Decimal to binary uses mathematical calculations, while text to binary relies on a pre-defined mapping system.



Mukhopadhyay, S. (1990). An optical conversion system: From binary to decimal and decimal to binary. Optics Communications, 76, 309-312.

Schmookler, M. (1968). High-Speed Binary-to-Decimal Conversion. IEEE Transactions on Computers, C-17, 506-508.

Rhyne, V. (1970). Serial Binary-to-Decimal and Decimal-to-Binary Conversion. IEEE Transactions on Computers, C-19, 808-812.

Cao, Z. (2013). On Two Conversion Methods of Decimal-to-Binary. ArXiv, abs/1308.0555

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