Computer Science – 4.3 Bit manipulation | e-Consult

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.