Question

Task: Left-shifting an unsigned int by 1 bit is equivalent to μltiplying the value by 2. Write a function power2 that takes two integer arguments number and pow and calculates number * 2^pow using the shift.

a) power2(number, pow) return number << pow;
b) power2(number, pow) return number >> pow;
c) power2(number, pow) return number * pow;
d) power2(number, pow) return number / pow;

Answer 1

The correct way to calculate 'number * 2^pow' using bitwise shift is by performing a left shift. The function 'power2(number, pow) return number << pow;' accurately computes this by shifting the number to the left by 'pow' bits, effectively multiplying the number by 2 raised to the power of 'pow'.

Step-by-step explanation:

The question is asking how to calculate number * 2^pow using bitwise shift operations. In programming, particularly when dealing with unsigned integers, a left bitwise shift is equivalent to multiplying by a power of 2. So, if we want to compute number * 2^pow, we need to perform a left shift on the number by pow positions.

Among the options given, the one that correctly performs this operation is a) power2(number, pow) return number << pow;. This function will take an integer number and an integer pow, and will perform a left shift of number by pow bits.

Option b) uses a right shift, which is the equivalent of dividing by a power of 2, and thus, not the correct operation for multiplication. Option c) wrongly uses the multiplication symbol instead of a shift, and option d) performs division, thus, none of these perform the desired operation correctly.