Power Digit Sum

Problem Statement

2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.

What is the sum of the digits of the number 2^1000?

Approach

Since 2^1000 is a very large number that exceeds the capacity of standard integer types, we need to use arbitrary-precision arithmetic.

Method 1: Using BigInteger

• Use Java’s BigInteger class to calculate 2^1000
• Convert the result to a string
• Iterate through each character (digit)
• Sum all the digits

Method 2: Manual calculation

• Implement multiplication by 2 using an array to store digits
• Start with 1 and multiply by 2 a thousand times
• Handle carries during multiplication
• Sum all the digits in the final array

The BigInteger approach is simpler and less error-prone, making it the preferred solution for this problem.