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How do you convert an integer to a binary number?

Published in Integer to Binary Conversion 2 mins read

Converting an integer to its binary equivalent is a fundamental process that reveals how numerical values are represented using only two digits: 0 and 1. This transformation is essential in computing, as computers primarily operate using binary code.

The most common and straightforward method for converting a decimal (base-10) integer to a binary (base-2) number is the division-by-2 method. This algorithm systematically breaks down the decimal number into its binary components by repeatedly dividing it by 2 and recording the remainders.

The Division-by-2 Method Explained

To convert an integer to binary, follow these steps:

  1. Start with the Integer: Begin with the decimal integer you wish to convert.
  2. Divide by 2: Divide the current integer by 2.
    • Record the quotient (the whole number result of the division).
    • Record the remainder (which will always be either 0 or 1).
  3. Continue Dividing: Take the quotient from the previous step and use it as the new integer. Repeat the division by 2, again recording the new quotient and remainder.
  4. Stop When Zero: Continue this process until the quotient eventually becomes zero.
  5. Reverse the Remainders: Once you have a quotient of zero, collect all the remainders you recorded throughout the process. The binary representation of the original integer is formed by writing these remainders in reverse order (from the last remainder calculated to the first).

This method works because each division by 2 essentially isolates the least significant bit (LSB) of the binary representation. The remainders represent the coefficients of increasing powers of 2, starting from 2^0.

Example: Converting the Integer 12 to Binary

Let's illustrate the division-by-2 method by converting the decimal integer 12 to its binary form:

Step Operation Quotient Remainder
1 12 ÷ 2 6 0
2 6 ÷ 2 3 0
3 3 ÷ 2 1 1
4 1 ÷ 2 0 1

Now, gather the remainders from bottom to top: 1, 1, 0, 0.

Therefore, the binary representation of the decimal integer 12 is 1100₂.

Understanding Binary Representation

Binary numbers are base-2 systems, meaning they use only two digits: 0 and 1. Each position in a binary number represents a power of 2, similar to how each position in a decimal number represents a power of 10.

For instance, the binary number 1100₂ can be converted back to decimal by summing the products of each digit and its corresponding power of 2:

  • 1 × 2³ = 1 × 8 = 8
  • 1 × 2² = 1 × 4 = 4
  • 0 × 2¹ = 0 × 2 = 0
  • 0 × 2⁰ = 0 × 1 = 0

Adding these values together: 8 + 4 + 0 + 0 = 12.

This systematic conversion method is crucial for understanding digital logic, data storage, and network communication, forming the bedrock of how computers process and store information. For more in-depth knowledge about number systems, you can explore resources like Wikipedia's article on Binary Numbers.