Learn Pascal in a Three Days (2nd Ed.)
(Publisher: Wordware Publishing, Inc.)
Author(s):
ISBN: 1556225679
Publication Date: 07/01/97

As mentioned earlier, you may not compare two real values for equality because of their limited precision. In the following program, the difference between the two real variables “x” and “y” is tested to see whether it is less than a specific small value “Difference,” in which case they are considered to be equal.

{ ------------------------------ figure 2-11 ----------------------------- }
{ Comparing real values }
PROGRAM Compare2(INPUT,OUTPUT);
CONST
 Difference = 0.0001;
VAR
 x, y :REAL;
 Result:BOOLEAN;
BEGIN
 WRITE('Please enter two real numbers: ');
 READLN(x, y);
 Result:= ABS(x - y) < Difference;
 WRITELN('The difference is ', ABS(x-y):2:6);
 WRITELN('The comparison is ', Result)
END.

The following is a sample run:

Please enter two real numbers: 4.5 4.50001
The difference is 0.000010
The comparison is TRUE

Compound BOOLEAN Expressions

The boolean expressions which use relational operators are called simple boolean expressions (in other languages they are called relational expressions). The compound boolean expressions are those which use the boolean operators (also called the logical operators): AND, OR, and NOT.

To understand how a compound boolean expression works, consider the example:

    (x = 4) AND (y < 50)

This expression is evaluated TRUE if both conditions “x = 4” and “y < 50” are TRUE.

Now consider the same expression using the operator OR:

    (x = 4) OR (y < 50)

This expression is evaluated as TRUE if any one of the conditions is TRUE. For example, if “x” contains the value “4,” the expression is TRUE regardless of the value of “y.”

The logical operator NOT is used to reverse the value of a boolean expression. Suppose that the boolean variable “UnderAge” means that the age is less than 18, as in the following statement:

    UnderAge:= Age < 18;

The variable “UnderAge” will contain the value TRUE if the “Age” is less than 18.

Now the expression:

    NOT(UnderAge)

is evaluated TRUE if the “Age” is 18 or above.

Turbo Pascal Operators

Turbo Pascal also contains the logical operator XOR, which is called the exclusive OR. It is used as in the following expression:

    (x = 4) XOR (x = 400)

The value of this expression is TRUE if either one of the two conditions (“x = 4” or “x = 400”) is TRUE, but the expression is evaluated as FALSE if both conditions are either TRUE or FALSE. In any implementation of Pascal you can use the operator <> as the exclusive OR. You can write the previous expression as:

    (x = 4) <> (x = 400)

Precedence of Operators

As with arithmetic expressions, the precedence of operators should be considered when building a boolean expression (relational or logical). Table 2-5 summarizes the relative precedence of all operators you have used so far.

To understand the effects of precedence, try the boolean expression:

    x = 4 OR x = 400

Because the OR has a higher precedence level than the equality, this will not compile because it will be interpreted as:

    x = (4 OR x) = 400

which is not a valid expression.

Summary

1.  In this chapter you learned the four standard data types:

•  INTEGER

•  REAL

•  CHAR

•  BOOLEAN

2.  You also learned the additional numeric types of Turbo Pascal:

I.  Integers:

•  SHORTINT

•  BYTE

•  INTEGER

•  WORD

•  LONGINT

II.  Reals

•  SINGLE

•  REAL

•  DOUBLE

•  EXTENDED

•  COMP

3.  You learned the standard arithmetic functions, classified into three groups:

Conversion:

•  ROUND

•  TRUNC

Trigonometric:

•  ARCTAN

•  COS

•  SIN

Miscellaneous:

•  ABS

•  EXP

•  LN

•  SQR

•  SQRT

4.  You also learned some additional arithmetic functions from Turbo Pascal, such as:

•  FRAC

•  INT

•  RANDOM

5.  You can now write mathematical expressions using arithmetic operators and functions.

6.  You are now familiar with four functions used to manipulate characters:

•  CHR

•  ORD

•  PRED

•  SUCC

7.  You learned some of the features of text string variables in standard Pascal, and you know that such variables are defined as PACKED ARRAYS OF CHAR. In extensions such as Turbo Pascal and UCSD Pascal, the type STRING was added to the language along with other features and functions.
You learned the STRING function:

LENGTH

which is used to measure the dynamic length of a string.

8.  Using the arithmetic, relational, and boolean operators, you learned how to build simple and compound boolean expressions and how to use the type BOOLEAN.
You know as well the boolean operators:

•  NOT

•  AND

•  OR

and you can express the exclusive OR in two ways:

•  using the relational operator {<>

•  using the Turbo Pascal operator XOR

9.  Finally, you had one last tour of Pascal operators and learned about their relative precedence.