Write your programs using C++

In this assignment you must not use your programming language support (nor any libraries) for arbitrary length arithmetic.

In your program you must not convert the input binary vectors representing numbers to decimals and use the built-in arithmetic operations on decimals. The operations must be performed on the binary vectors.

include a brief description of the algorithms you implemented, a list of test cases you tried and the results and compilation and execution instructions for your programs.

Problem 3. Test the performance (time in seconds) of your modular exponentiation program on integers of different sizes. Comment on how the performance of the program depends on the number of digits in the input vectors representing binary integers. Use the following test inputs: N=[1, 0, 1, n 05, n 1s, 0, 11, x=[1, 1, n 05, n 1.sl,y=[1, 0, n 05, n 1.sl, [1, 0, n 0 s, n 1 s], Where n-1,2, 4, 8, 16, 32, 64, 128 etc. Continue doubling n but stop when the time of a test exceeds 600 seconds. You may want to write a procedure that generates these vectors rather than have the user to type them in. Problem 3. Test the performance (time in seconds) of your modular exponentiation program on integers of different sizes. Comment on how the performance of the program depends on the number of digits in the input vectors representing binary integers. Use the following test inputs: N=[1, 0, 1, n 05, n 1s, 0, 11, x=[1, 1, n 05, n 1.sl,y=[1, 0, n 05, n 1.sl, [1, 0, n 0 s, n 1 s], Where n-1,2, 4, 8, 16, 32, 64, 128 etc. Continue doubling n but stop when the time of a test exceeds 600 seconds. You may want to write a procedure that generates these vectors rather than have the user to type them in