Describe an efficient algorithm to implement each of the following operations on an array of n binary digits that represent a certain unsigned decimal number d$.$ For example, if d is $12,$ then the array is $[1,1,0,0]$ and n$=4.$ In each case, the time your algorithm takes must not depend on n$,$ and the array must remain an array of binary digits. An array is defined by its contents and its size. Your algorithms must take the array and its size as input. You may include other parameters in the input. Add comments before each statement to explain your reasoning.