Answer
$0 0 0 0 0 0 1 1 1 0 1 1$
Work Step by Step
$$\text{Solution}$$
Here $A = 100010011001 , B = 100001011110.$
Find $A - B = ?$ using 1's complement
$\rightarrow$ First, find 1's complement of $B = 100001011110$
$\rightarrow $ Write out the numbers as if you were subtracting decimals.
$$-\begin{array}{r|r}
100010011001\\
100001011110\\
\hline
\end{array}$$
$\rightarrow $ Let's use the 1's Complement Method
$\rightarrow $ 1's complement of a number is obtained by subtracting all bits from $111111111111$
$\rightarrow $ $\text{1's complement of 100001011110 is}$
$$-\begin{array}{r|r}
111111111111 \\
100001011110\\
\hline
0 1 1 1 1 0 1 0 0 0 0 1
\end{array}$$
$\rightarrow $ Now Add this 1's complement of B to A
Note $\rightarrow$ Addition Rules
$0 + 0 = 0$
$0 + 1 = 1$
$1 + 0 = 1$
$1 + 1 = 10$ ("$0$" in the column, carry $1$ to the next bit)
So,
$$+\begin{array}{r|r}
1 0 0 0 1 0 0 1 1 0 0 1\\
0 1 1 1 1 0 1 0 0 0 0 1\\
\hline
1 0 0 0 0 0 0 1 1 1 0 1 0
\end{array}$$
$\rightarrow$ left most bit of the above result is called carry and add it to the rest part of the result $000000111010$.
$$+\begin{array}{r|r}
0 0 0 0 0 0 1 1 1 0 1 0 \\
1 \\
\hline
0 0 0 0 0 0 1 1 1 0 1 1
\end{array}$$
so the Answer is $0 0 0 0 0 0 1 1 1 0 1 1$.
