Why don't you just add the numbers? Surely it's easier than doing it in binary...

But if you MUST use binary...

I'm going to number the digits of the binary number going right to left.

The biggest power of 2 closest to 108 is . So there'll be 6 + 1 = 7 digits and the 7th column (closest to the left) will contain a 1.

.

The biggest power of 2 closest to 42 is .

So there'll be a 1 in the 5 + 1 = 6th column.

.

The biggest power of 2 closest to 10 is . So there'll be a 1 in the 3 + 1 = 4rd column (the 5th will have a 0).

The biggest power of 2 closest to 2 is . So there'll be a 1 in the 1 + 1 = 2nd column (the 3rd will have a 0).

. We don't need to go any further.

So .

Following the same procedure

The biggest power of 2 closest to 17 is . So there'll be 4 + 1 = 5 columns and a 1 in the 5th column.

.

The biggest power of 2 closest to 1 is . So there'll be a 1 in the 0 + 1 = 1st column. (Columns 2 - 4 will have 0's).

So .

Therefore

.

Easy huh? Not...