A signed binary number is a binary number with one digit used to represent positive or negative. The most significant (left most) bit will be a 1 for negative and 0 for positive.
To get a negative number from a positive number, all the bits must be switched, and then 1 has to be added. To get a positive from the negative, take away 1 then flip all the bits.
Two’s complement can be used to take away one number from another. Instead of actually subtracting, you add the negative number. No bits larger than the most significant are carried, so you are left with a number the same length.