Decimal to Binary Conversion Process Explained

To convert a number from the decimal (base-10) system to the binary (base-2) system, a common method involves repeatedly dividing the decimal number by 2. The key is to record the remainder obtained after each division.

Understanding Successive Division

The process works as follows:

• Take the decimal number you want to convert.
• Divide this number by 2.
• Record the remainder (which will be either 0 or 1).
• Take the quotient from the division and repeat the process: divide the quotient by 2 and record the new remainder.
• Continue this cycle of dividing the quotient by 2 and recording the remainder until the quotient becomes 0.
• The binary equivalent of the decimal number is formed by reading the recorded remainders in reverse order (from the last remainder obtained to the first).

This method is used because binary is a base-2 system, meaning each place value represents a power of 2 ($2^0, 2^1, 2^2$, etc.). Dividing by 2 helps us determine how many of each power of 2 fit into the decimal number.

Example Conversion

Let's convert the decimal number 25 to binary:

Reading the remainders from bottom to top gives us 11001. Therefore, the binary equivalent of decimal 25 is $11001_2$.

The options provided represent potential divisors. Based on the standard algorithm for converting decimal to binary, the correct divisor is 2.