Subtracting a larger binary number from a smaller binary number
If you mean you want to do it by hand like you did in elementary school, then yes. Borrow an imaginary 2 (10b) from the imaginary column to the left of the number. For example, here's your problem:

$$
\begin{matrix}
    &amp; 0 &amp; 1 &amp; 1 &amp; 1 \\
    - &amp; 1 &amp; 0 &amp; 0 &amp; 0 \\
\end{matrix}
$$

and here's what you have after borrowing a 2 from the imaginary fifth bit (sixteen's place):

$$
\begin{matrix}
      &amp; 10 \\
      &amp; 0 &amp; 1 &amp; 1 &amp; 1 \\
    - &amp; 1 &amp; 0 &amp; 0 &amp; 0 \\
\end{matrix}
$$

10b - 1b is 1b, so the answer is 1111b, or -1 in two's complement -- exactly what you'd expect if you subtract 8 from 7.

This still works if you need to borrow from a smaller place. This:

$$
\begin{matrix}
    &amp; 0 &amp; 0 &amp; 1 &amp; 1 \\
    - &amp; 0 &amp; 1 &amp; 0 &amp; 1 \\
\end{matrix}
$$

becomes:

$$
\begin{matrix}
      &amp; 1 &amp; 10 \\
      &amp; 0 &amp; 0 &amp; 1 &amp; 1 \\
    - &amp; 0 &amp; 1 &amp; 0 &amp; 1 \\
\end{matrix}
$$

which is 1110b (-2) -- again, exactly what you'd expect if you subtract 5 from 3.