This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

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Integer division and remainder calculation
You're on a roll —
a) Differentiate between call by reference and call by value • In call by value, a copy of the argument's value is passed to the subroutine. Any changes made to the parameter inside the subroutine do not affect the original argument. • In call by reference, a reference (memory address) to the original argument is passed. Changes made to the parameter inside the subroutine directly modify the original argument.
b) Construct the trace table for the subroutine call calc(8, 37)
Given d = 8 and q = 37.
Initial values: r = 0, p = 0.
| Step | q >= d * p (37 >= 8 * p) | p | r |
| :--- | :--------------------------- | :-- | :-- |
| Initial | | 0 | 0 |
| Loop 1 | 37 >= 8 * 0 (True) | 1 | 0 |
| Loop 2 | 37 >= 8 * 1 (True) | 2 | 0 |
| Loop 3 | 37 >= 8 * 2 (True) | 3 | 0 |
| Loop 4 | 37 >= 8 * 3 (True) | 4 | 0 |
| Loop 5 | 37 >= 8 * 4 (True) | 5 | 0 |
| Loop 6 | 37 >= 8 * 5 (False, 37 < 40) | 5 | 0 |
| p = p - 1 | | 4 | 0 |
| r = q - (d * p) | | 4 | 37 - (8 * 4) = 5 |
| Print | | 4 | 5 |
The subroutine will print p = 4 and r = 5.
c) Assuming that the arguments are both positive, state the operation performed by this subroutine
This subroutine performs integer division and calculates the remainder. It finds the quotient (p) and the remainder (r) when q is divided by d.
d) Give a formula that relates p, r, q & d The relationship between the quotient (), remainder (), dividend (), and divisor () is: where .
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You're on a roll — a) Differentiate between call by reference and call by value • In call by value, a copy of the argument's value is passed to the subroutine.
This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.