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How to Convert Decimal to Binary

Converting a decimal number to binary is a fundamental process in computer science, revealing how numbers are represented within computers. This conversion can be achieved through a straightforward method known as the division-remainder method. Here’s a step-by-step guide to understanding and performing this conversion

Understand the Basics

  1. Binary System (Base-2): The binary system uses only two digits, 0 and 1, to represent numeric values. Each position in a binary number represents a power of 2, with the rightmost position being 2^0, the next 2^1, and so on.
  2. Decimal System (Base-10): The decimal system is what we use in everyday life, consisting of 10 digits (0-9) and based on powers of 10.

The Division-Remainder Method

The division-remainder method involves dividing the decimal number by 2 repeatedly until the quotient becomes 0, while keeping track of the remainders. These remainders represent the binary equivalent of the original decimal number.

Detailed Conversion Process

  1. Divide the Decimal Number by 2: Start with the decimal number you wish to convert and divide it by 2.
  2. Record the Remainder: After the division, record the remainder (either 0 or 1) to the side. This will be part of the binary number.
  3. Update the Quotient: Use the quotient (the result of the division) as the new number to be divided by 2 in the next step.
  4. Repeat: Continue dividing the quotient by 2 and recording the remainders until the quotient is 0.
  5. Read the Binary Number: The binary equivalent of the original decimal number is the sequence of remainders read from bottom to top (or last to first).

Example Conversion

Let’s convert the decimal number 13 to binary:

  • Divide 13 by 2: Quotient = 6, Remainder = 1
  • Divide 6 by 2: Quotient = 3, Remainder = 0
  • Divide 3 by 2: Quotient = 1, Remainder = 1
  • Divide 1 by 2: Quotient = 0, Remainder = 1
    • Reading the remainders from bottom to top, we get 1101. Therefore, the binary representation of the decimal number 13 is 1101.

Conclusion

Converting decimal numbers to binary is a critical skill in computer science, offering insights into how computers process and store numbers. Through the division-remainder method, anyone can translate decimal numbers into the binary language of computers, bridging the gap between human and machine understanding. This methodical approach ensures accuracy and provides a foundational understanding of binary arithmetic.