Challenge Problem - April 18 2011

[ambikasrinivas]

Hi - I understand the answer for this question, but I am having issues with the stem of the question:

1101 = (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 25

When I add this, I get 13: 8 + 4 + 0 + 1

What am I missing?

Thanks!

Question
Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^n - 1. For instance, 1101 = (1 × 2^3) + (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 25. What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?
(A) 10
(B) 11
(C) 101
(D) 1011
(E) 10001

[shoumik]

I think there is a mistake. I am pretty sure the binary of 1101 = 13. Hmm..

[jnelson0612]

I get 13 also. I agree with you both that 25 is an error.