Question

Describe an algorithm for finding the difference of two binary expansions.

Short answer

Determining the difference of two binary expansions works similar to determining the difference of two integers

Step-by-step solution

Step 1:

The input of the algorithm is two integers in binary expansion $x=x_1{x}_2\dots x_n$and $y=y_1{y}_2\dots \dots y_n$with n a positive integer. We

assume that $x>y$If one of the two integers contains less digits , then add additional zeros at the front of the integer.

We subtract corresponding digits from right to left , thus we first subtract $x_n$and $y_n$I , then $x_{n-1}$and $y_{n-1}$and so on until we subtract $x_1$and $y_1$

if $x_i\ge y_i$then $x_i-y_i$is corresponding ith digit in the difference of the two integers ,

If $x_i<y_i$, then we borrow a 1 from the nearest digit to the right of a $x_i$in $x$a that is nonzero ( similar to the regular difference between two integers ) and $\left(x_i+2\right)-y_i$, is then corresponding th digit in the difference of the two integers ,