arithmetic – 2’s complement substraction

In two’s complement, we compute $a-b$ by adding $a$ and $-b$. To compute $-b$ in two’s complement, we invert all bits in $b$, and increment the result by $1$.

Let’s see how it works in your example. You haven’t specified the bit length, but it appears to be $8$. We have $50 = 00110010$, and so $-50 = 11001101+1 = 11001110$. Similarly, $48 = 00110000$, and so $-48 = 11001111+1 = 11010000$. In order to subtract $-48$ from $-50$, we first negate $-48$: $-(-48) = 00101111+1 = 00110000$. Now we add $-50$ and $-(-48)$: $11001110+00110000 = 11111110$. Since the MSB is $1$, we know that this is a negative number. To find out negative what, we invert it: $-(11111110) = 00000001+1=00000010$, which is $2$. Therefore $-50-(-48)=-2$.