Initial Value: 11010101 (Binary) = 205 (Decimal)

Left Shift by 4 bits:

Binary: 11010101 -> 1101010100

Decimal: 205 * 2⁴ = 205 * 16 = 3280

Right Shift by 2 bits:

Binary: 1101010100 -> 0011010100

Decimal: 3280 / 2² = 3280 / 4 = 820

Discussion of Right Shift with Negative Numbers:

If the initial value were negative, the right shift operation would perform sign extension. This means the most significant bit (the sign bit) would be copied into the vacated positions on the left. For example, if the number were -1 (binary 11111111), shifting right by 2 would result in 11111111, which is -1 in decimal. However, the behavior can vary depending on the architecture and the specific implementation of the right shift operator. Some architectures use an arithmetic right shift, while others use a logical right shift. An arithmetic right shift preserves the sign, while a logical right shift fills the vacated positions with zeros. Therefore, it's crucial to understand the architecture's behavior when working with signed integers and right shift operations.

Multiplication and division by powers of 2 can be efficiently performed using bitwise shift operators. Shifting a number's bits to the left is equivalent to multiplying by 2, and shifting to the right is equivalent to dividing by 2.

Multiplication by 8: To multiply a number by 8, we need to shift the bits 3 places to the left. This is because 8 is 2³.

Division by 4: To divide a number by 4, we need to shift the bits 2 places to the right. This is because 4 is 2².

Code Example (Python):

def multiplyby8(number):

"""Multiplies a number by 8 using a left shift."""

return number > 2

# Example usage:

num = 15

multipliednum = multiplyby_8(num)

dividednum = divideby_4(num)

print(f"Original number: {num}")

print(f"Multiplied by 8: {multiplied_num}")

print(f"Divided by 4: {divided_num}")

Efficiency Comparison:

• Bitwise Shifts: These operations are extremely fast because they are directly supported by the hardware. They typically take only a few clock cycles to execute.
• Standard Multiplication/Division Operators: These operations are generally implemented using more complex algorithms (e.g., long division for division). They are slower than bitwise shifts, often requiring multiple clock cycles.

Therefore, using bit manipulation for multiplication and division by powers of 2 is significantly more efficient than using the standard multiplication and division operators. This is particularly important in embedded systems and performance-critical applications where speed is crucial.

To turn on a specific LED using bit manipulation, we need to identify the bit position corresponding to that LED. Since the register is 8-bit, each bit represents one of the LEDs (bit 0 being the least significant bit and bit 7 being the most significant bit).

1. Identify the LED's bit position: Let's say we want to turn on the 3rd LED. This corresponds to bit position 2 (remembering that bit positions are numbered from right to left, starting at 0).

2. Use the bitwise OR operator (|): The bitwise OR operator sets a bit to 1 if either of the corresponding bits in the operands is 1. We can use this to set the desired bit to 1 without affecting the other bits. We create a mask with a 1 only at the desired bit position and then perform a bitwise OR with the register.

The mask for the 3rd LED (bit 2) would be: 00000100 (binary) which is 4 (decimal).

The operation would be: register = register | 4;

This operation will set the 3rd bit of the register to 1, effectively turning on the corresponding LED. All other bits will remain unchanged.

Example: If the initial register value is 00001010 (decimal 10), after performing the operation, the register will become 00001110 (decimal 14). The 3rd bit (counting from the right) has been set to 1.

Reasoning: The bitwise OR operation ensures that the target bit is set to 1, while the other bits are unaffected. This is a non-destructive operation, meaning it doesn't clear or change any other bits in the register.