Data Representation

Computer number systems use different formats for different types of numbers.

• Integers and Whole Numbers are numbers without fractional parts. They are typically represented using simple binary or 2's complement formats.
  
• Boolean Values are `true` or `false`, represented by a single bit (1 or 0).
  
• Real Numbers are numbers that can have a fractional part (e.g., 3.14159, -0.0025). To represent these numbers, especially over a wide range of magnitudes, computers use a system called floating-point representation.
  

Step 1: Convert the integer part from decimal to binary:
Thus, .

Step 2: Convert the fractional part from decimal to binary:
Thus, .

Step 3: Combine the results:
Thus, the correct answer is (a) .

The given binary number is . We will convert this into decimal by handling the integer and fractional parts separately.

1. Integer part: 2. Fractional part: Thus, the decimal value is: The equivalent decimal value is .

Step 1: Convert the decimal number to binary.
The decimal number 265 can be converted to binary as follows: Thus, the binary representation of 265 is .

Step 2: Convert the binary number to hexadecimal.
Group the binary digits into sets of four starting from the right: So, the hexadecimal representation is .

Step 3: Conclusion.
Thus, the correct hexadecimal representation of the decimal number 265 is , and the correct answer is (d).

To toggle bits starting from position , we need to create a mask that has bits set to 1, starting at position . This is achieved using the following logic:
1. shifts 1 left by positions, creating a number with the first bits as 1.

2. Subtracting 1 from this number (i.e., ) creates a number with the first bits set to 1 and the rest set to 0.

3. Shifting this mask by positions, i.e., , ensures that the mask starts at position .

4. Finally, XORing with this mask (using the `^` operator) will toggle the bits at the specified positions.

Thus, the correct expression is option (a).