Question 3 (10 marks)

As we saw in lecture, all computers have an arithmetic and logic unit (ALU) to do calculations. In this question, we will pretend that our computer cannot do complicated operations like + and *, so that we can practice writing functions.

We will pretend that the computer can only do very simple arithmetic, namely, adding or subtracting 1 from an integer. We implement these two operations using functions, as follows:

int addOneTo(int number)
{
return number+1;
}
int subOneFrom(int number)
{
return number-1;
}

These functions are defined for you in a file here. This technique is obviously not practical, but it will force us to think about "normal" arithmetic in a different way.

In the exercises below, you will be asked to implement 5 functions that do not use +,-,*,/, directly. Instead, you will use the 2 functions above, as well as any that you define yourself.

(2 marks) Define the function
int add(int a, int b)
using a loop, and any of the functions defined earlier in the question. It is not allowed to use +,*,-,/ directly. Assume for simplicity that all inputs are not negative.
(2 marks) Define the function
int subtract(int a, int b)
using a loop, and any of the functions defined earlier in the question. It is not allowed to use +,*,-,/ directly.
Assume for simplicity that all inputs are not negative.
(1 mark) Define the function
int multiply(int a, int b)
using a loop, the function add(), or any of the functions defined earlier in the question. It is not allowed to use +,*,-,/ directly. Assume for simplicity that all inputs are not negative.
(1 mark) Define the function
int quotient(int a, int b)
(the result of integer division) using a loop, the function subtract(), or any of the functions defined earlier in the question. It is not allowed to use +,*,-,/ directly. Assume for simplicity that all inputs are not negative, and that b is never zero.
(1 mark) Define the function
int remainder(int a, int b)
(the remainder of integer division) using a loop, and any of the functions defined earlier in the question. It is not allowed to use +,*,-,/,% directly.
Assume for simplicity that all inputs are not negative, and that b is never zero.
Write a program that tests all your function definitions. To test your functions, you should compare the answers they give to the answers given by the normal C++ operators +,-,*,/,%. Hand in a file that shows some of the testing you did (copy-paste from your terminal window to a text editor).

Purpose: Practice with designing functions that use other functions.

What to hand in: Your program, in a file called a6q3.cpp. Your program must include 5 functions above. Be sure to include your name, NSID, student number, lecture section and tutorial section at the top of your program file. Also submit a file called a6q3_testing.txt that shows that you tested your program (copy-paste from your terminal window to a text editor).

Evaluation:

0 mark: Nothing submitted, or files cannot be opened.
1 mark: Student information provided in the program file.
2 marks: The add() function working correctly.
2 marks: The subtract() function working correctly.
1 mark: The multiply() function working correctly.
1 mark: The quotient() function working correctly.
1 mark: The remainder() function working correctly.
2 marks: A file submitted showing some testing.