Question-6

Consider the following Python function:

def simple_function(Y, n, x):
    total = Y[0]
    for loop_index in range(1, n):
        total = x * total + Y[loop_index]
    return total

Let Z be an array of 10 elements with Z[i] = 1, for all i such that \(0 \leq i \leq 9\). The value returned by simple_function(Z, 10, 2) is __________.

NoteAnswer

\(1023\)

NoteSolution

Given that all values in the array Z are 1 and x = 2, the function simplifies to total = 2 * total + 1, resulting in successive left shifting of the total by one bit and adding 1 each time. This process leads to a final value of 1023.

Total in bits	Total Value
1	1
10 + 1 = 11	3
110 + 1 = 111	7
1110 + 1 = 1111	15
11110 + 1 = 11111	31
111110 + 1 = 111111	63
1111110 + 1 = 1111111	127
11111110 + 1 = 11111111	255
111111110 + 1 = 111111111	511
1111111110 + 1 = 1111111111	1023