## V22.0002 - ASSIGNMENT 1

Write a program that performs the addition of two numbers that are expressed in any arbitrary base.

To compute the sum of two numbers, we compute the sum of each pair of digits, starting with the least significant ones, and the carry-over from the sum of the previous pair of digits.

In order to perform this operation in a program, we have to break our algorithm into three parts:

1. Isolate the individual digits of the two numbers.
2. For each pair of digits: compute the sum, the result digit and the carry-over.
3. Use the result digits to contruct the answer.
Part 1: We use integer division ("/") and the integer modulo operator ("%").

Part 2: We obtain each result digit by "mod-ing" the sum by the base. We obtain each carry-over by dividing the sum by the base.

Part 3: We multiply the second least significant result digit by 10, the third least significant digit by 100, etc. We then sum all of the values together.

Example 1:

Compute the sum of the two base-10 numbers 6592 and 7685

Part1:

 Digit 1 Digit 2 6592 % 10 => 2 7685 % 10 => 5 (6592 / 10) % 10 => 9 (7685 / 10) % 10 => 8 (6592 / 100) % 10 => 5 (7685 / 100) % 10 => 6 6592 / 1000 => 6 7685 / 1000 => 7
Part 2:
 Carry Over(from previous line) Digit 1 Digit 2 Sum Result Digit Carry Over(to next line) 0 2 5 7 7 % 10 = 7 7 / 10 = 0 0 9 8 17 17 % 10 = 7 17 / 10 = 1 1 5 6 12 12 % 10 = 2 12 / 10 = 1 1 6 7 14 14 % 10 = 4 14 / 10 = 1
Part 3:
Result : 7 + 7 * 10 + 2 * 100 + 4 * 1000 + 1 * 10000 = 14277

Note: The final term in the addition is the final carry over.

Example 2:

Compute the sum of the two base-8 numbers 6512 and 675

Part1:

 Digit 1 Digit 2 6512 % 10 => 2 675 % 10 => 5 (6512 / 10) % 10 => 1 (675 / 10) % 10 => 7 (6512 / 100) % 10 => 5 (675 / 100) % 10 => 6 6512 / 1000 => 6 675 / 1000 => 0
Part 2:
 Carry Over(from previous line) Digit 1 Digit 2 Sum Result Digit Carry Over(to next line) 0 2 5 7 7 % 8 = 7 7 / 8 = 0 0 1 7 8 8 % 8 = 0 8 / 8 = 1 1 5 6 12 12 % 8 = 4 12 / 8 = 1 1 6 0 7 7 % 8 = 7 7 / 8 = 0
Part 3:
Result : 7 + 0 * 10 + 4 * 100 + 7 * 1000 + 0 * 10000 = 7407

Note: The final term in the addition is the final carry over.

The program you have to write will read a base and two numbers of at most 4 digits in that base. The program will compute the sum of the two numbers using the above algorithm and display the result.

Example run:

```   Enter base: 8
Enter two numbers (no more than 4 digits) in base 8: 2361 6642
Result: 2361 + 6642 = 11223
```
Notes:
• You should run the program at least twice with different bases.
• You can assume all inputs are correct (numbers expressed in the right base, etc.)