jmc

Question

Consider the following two strings of digits: 11001010100101011 and 110100011000100. First consider them to be in base 10 and sum them to get n. Then consider them to be in binary, sum them, write the answer in binary, then interpret the digits of the sum as if they were in base 10 to get m. What is n-m?

Accepted Answer

If you notice carefully, the two sequences of digits never both have a 1 in the same place. Thus, whether you add them in base 10 or binary, the resulting sequence of digits is the same. Thus whether we add them in base 10 or add them in binary and interpret the digits in base 10, we get the same result, so the difference is 0.