Chapter 9

Answers to Exam Preparation Exercises

1. True. A function call is always a component of an expression, but a procedure call is always a statement in itself.

3. True. VAR parameters should generally not be used in a function.

6. Given the code segment

Sum := 0; (* Sum is of type Integer *)

WHILE NOT EOF(DataFile) DO

BEGIN

Readln(DataFile, Amount);

Sum := Sum + Round(Amount);

END;

Writeln(Sum:6);

and input data (each value on a separate line)

0.5 0.5 0.5 0.5 0.5 0.5 0.5 <EOF>

the output will be 7, even though the sum of the input values is 3.5. All of the 0.5 values are read correctly into the variable Amount, but in each case 1 is added to Sum because Round(0.5) = 1. If the function had been Trunc instead of Round, the final value of Sum would have been 0.

8. Procedure Power rewritten as a function:

FUNCTION Power (Base:

Real;

Exponent:

Integer):

Real;

VAR

Answer:

Real;

I:

Integer;

BEGIN (* Power *)

Answer := 1.0;

I := 1;

WHILE I <= Exponent DO

BEGIN

Answer := Answer * Base;

I := I + 1

END;

Power := Answer

END; (* Power *)

Function call:

M := Power(K, L, M)

9. Results of executing function Test.

a. –0.5

b. 0.5

10. Definitions. Several of these definitions are taken verbatim from the text.

recursion the action of a subprogram's calling itself.

result type the data type of the result value that is returned by a function.

representation error an arithmetic error that occurs because the precision of the true result of arithmetic operations is greater than the precision of the machine.

overflow the result of an arithmetic expression's being greater than the maximum number that can be represented on the computer.

mantissa the part of a real number that contains the representable significant digits.

exponent the part of a real number that determines where the decimal point is placed relative to the mantissa.

significant digits those digits from the first nonzero digit on the left to the last nonzero digit on the right (plus any zero digits that are exact).

11. The construct ": Boolean ;" should appear at the end of the parameter list. The "(" before the second parameter should be deleted. The data type of the second parameter should also be Boolean (although this does not cause a syntax error in Turbo Pascal, we recommend strongly against using the Boolean operators with the integer types).

Answers to Programming Warm-Up Exercises

1. Function heading:

FUNCTION Epsilon (High,

Low:

Real):

Real;

3. Function Equal (two versions):

FUNCTION Equal (Num1,

Num2,

Difference:

Real):

Boolean;

BEGIN (* Equal *)

IF Abs(Num1 - Num2) < Difference

THEN

Equal := True

ELSE

Equal := False

END; (* Equal *)

FUNCTION Equal (Num1,

Num2,

Difference:

Real):

Boolean;

BEGIN (* Equal *)

Equal := Abs(Num1 - Num2) < Difference

END; (* Equal *)

4. Function heading:

FUNCTION EOForEOLN:

Boolean;

8. Function P5 (two versions):

FUNCTION P5 (X:

Real):

Real;

BEGIN (* P5 *)

P5 := X * X * X * X * X

END; (* P5 *)

or

FUNCTION P5 (X:

Real):

Real;

BEGIN (* P5 *)

P5 := X * Sqr(Sqr(X))

END; (* P5 *)

9. Function Min (two versions):

FUNCTION Min (Number1,

Number2,

Number3:

Integer):

Integer;

VAR

Smallest:

Integer;

BEGIN (* Min *)

Smallest := Number1;

IF Number2 < Smallest

THEN

Smallest := Number2;

IF Number3 < Smallest

THEN

Smallest := Number3;

Min := Smallest

END; (* Min *)

or

FUNCTION Min (Number1,

Number2,

Number3:

Integer):

Integer;

BEGIN (* Min *)

IF Number1 < Number2

THEN

IF Number1 < Number3

THEN

Min := Number1

ELSE

Min := Number3

ELSE

IF Number2 < Number3

THEN

Min := Number2

ELSE

Min := Number3

END; (* Min *)

10. Boolean function to test whether an integer is prime.

FUNCTION TestForPrime (N: (* Number to test *)

Integer):

Boolean;

(* This function returns True if the value passed to *)

(* it is a prime number other than 1 *)

VAR

Limit, (* Greatest divisor to test *)

TrialDivisor: (* A trial divisor to test *)

Integer;

BEGIN (* TestForPrime *)

Limit := Trunc(Sqrt(N)) + 1; (* Only need to check *)

(* up to Sqrt(N) *)

TrialDivisor := 2;

TestForPrime := False; (* If N <= 1, it's not prime *)

IF N > 1

THEN (* Test divisors from 2 to Limit. If N *)

BEGIN (* = 2 or we reach Limit, N is a prime *)

WHILE (TrialDivisor <= Limit) AND

(N MOD TrialDivisor <> 0) DO

TrialDivisor := TrialDivisor + 1;

TestForPrime := (N = 2) OR (TrialDivisor = Limit)

END

END; (* TestForPrime *)

12. Recursive Function Power modified to allow zero as an exponent.

FUNCTION Power (X,

N:

Integer):

Integer;

BEGIN (* Power *)

IF N = 0

THEN

Power := 1

ELSE

Power := X * Power(X, N-1)

END; (* Power *)