How to Represent Signed Integers?

Example: Adding the $6$-bit numbers $7_{10} = 000111_2$ and $10_{10} = 001010_2$ (the result is, as we expected, $010001_2 = 17_{10}$:)

    111   <-- carry bits
0   00111
0 + 01010
    _____
0   10001

Note that the sign bits are listed to the left side of the addition. We don't touch them because both numbers are positive (= the sign bits are $0$s,) so the result is itself positive.

Also, note that when we needed to add $1 + 1$, since there is no digit "$2$" in the binary system, we needed to 'carry' this bit over to the next bit addition, just like we carry numbers that are greater than $10$ when adding base $10$ numbers.