Consider the problem of adding two $n-$bit binary integers a and $b,$

stored in two $n-$element arrays $A[0$:$n-1]$ and $B[0$:$n-1],$ where each

element is either $0$ or $1,a={\displaystyle \underset{i=0}{\overset{n-1}{}}}A[i]*2^i,$ and $b={\displaystyle \underset{i=0}{\overset{n-1}{}}}B[i]*2^i.$ The

sum $c=a+b$ of the two integers should be stored in binary form in an

$(n+1)-$element array $C[0$:$n],$ where $c={\displaystyle \underset{i=0}{\overset{n}{}}}C[i]*2^i.$ Write a procedure

ADD$-$BINARY$-$INTEGERS that takes as input arrays A and $B,$ along

with the length $n,$ and returns array $C$ holding the sum.