Given Table n-1 * n, find the missing number


Here each row contains a bit representation of a number.These numbers come from 1..N Exactly one number is missing.Find the bit representation of the missing number.
The interviewer asked me this question.
I said: "We can find the sum of the given numbers and subtract it from the sum of first n numbers(which we know as (N*(N+1))/2)"
He said that involves changing from base 10 to base 2.
Can you give me a hint on how I can solve it without changing bases?

You can XOR together all numbers from 0..N range, then XOR the numbers from the array. The result will be the missing number.

Explanation: XORing a number with itself always results in zero. The algorithm above XORs each number exactly twice, except for the missing one. The missing number will be XOR-ed with zero exactly once, so the result is going to equal the missing number.

Note: the interviewer is wrong on needing to convert bases in order to do addition: adding binary numbers is easy and fun - in fact, computers do it all the time :-)