Binary and Decimal Conversion Challenge!

Converting binary numbers to octal and decimal forms can be a challenging but rewarding task. In the given example of (1001 1001)₂, we first translate the binary value into octal. The binary number 1001 is represented as 9 in decimal and 11 in octal. Therefore, by dividing the binary number into groups of three (1001 and 1001), we obtain the octal value of 232₁₈.

Next, to determine the decimal value of 232₁₈, we convert each digit to decimal form. The octal number 232 is calculated as (2 * 8^2) + (3 * 8^1) + (2 * 8^0), which simplifies to 2 * 64 + 3 * 8 + 2 * 1, resulting in decimal value of 1225₁₀.

On the other hand, the decimal number 334.2301₁₀ is converted to binary by representing each digit in binary form. The integer part 334 is broken down into binary digits, while the decimal portion 0.2301 is converted using the multiplication by 2 method. Combining both parts, we arrive at the binary value 101001110.0011100110011001100110₂.

It is important to note that precision in calculation plays a crucial role in accurately converting decimal numbers to binary. In this case, none of the provided options aligned perfectly with the conversion of 334.2301 to binary, highlighting the complexity and flexibility of number systems.

Understanding the fundamentals of binary conversion opens up a world of possibilities in digital systems and computing. By mastering the art of conversion between different number bases, one can navigate complex data structures and algorithms with ease.