High-level Programming Language (Pascal)

Boolean Expressions

• implementing selection and repetition structures involves Boolean expressions
• Boolean expressions may be either simple or compound
• Boolean data type
  • there are two Boolean constants, true and false
  • Boolean variables may have only these values (either true or false)
  • the type identifier Boolean is used to specify the type of a Boolean variable
  • for example,


　var Found : Boolean;

which declares that Found is a Boolean variable

• Boolean values may be displayed with write or writeln statements
• but values for Boolean variables cannot be read
• a Boolean variable may be assigned a value with an assignment statement of the form


Boolean_variable := Boolean_expression

• for example,


　Female := true;

which assigns the Boolean constant true to the Boolean variable Femal

• Boolean expressions can contain a combination of arithmetic, relational and Boolean operators
• the precedence of operator determines its order of evaluation
• the table below shows the precedence of operators in Pascal
  
  

  Pascal Operator (Arithmetic, Relational, Boolean)	Order of Precedence
  ( ) (parentheses)	1 highest (performed first)
  - (unary operator) , not	2
  * , / , div , mod , and	3
  + , - , or	4
  = , <> , > , >= , < , <=	5 lowest (performed last)

  
  

Simple Boolean Expression

• describes a relationship between two quantities and it has the form

  <expression_1> <relational operator> <expression_2>

  • where <expression_1> and <expression_2> must be compatible, that is, numeric data must match with numeric data, and alphanumeric data with alphanumeric data which can either be a character or a string
  • the relational operator may be any of the following :
    
    

Mathematical Relational Operator	Pascal Relational Operator	Meaning
=	=	equal to
≠	<>	not equal to
>	>	greater than
≧	>=	greater than or equal to
<	<	less than
≦	<=	less than or equal to



• relational operators can be used with numeric constant, numeric variable, arithmetic expression, character and string
• within the computer, the characters are ordered in a sequence according to a certain coding scheme
• a commonly used scheme is the American Standard Code for Information Interchange (ASCII)
  
  
• for example, the Boolean expressions in the table below are evaluated assuming the following variables values :
  
  

Score	PassMark
49	50




Boolean Expression	Meaning	Result	Reason
5 > 1	5 is greater than 1	true	5 is greater 1 is true
'A' < 'F'	character 'A' is less than character 'F'	true	the ASCII code of 'A' (65) which is less than the ASCII code of F (70)
'12345' > '200'	character '12345' is greater than character '200'	false	the ASCII code of the first character of '12345' is not greater than the ASCII code of the first character of '200'
12345 > 200	12345 is greater than 200	true
'4A' > '4'	character '4A' is greater than character '4'	true
3*2 > 1+7	3 times 2 is greater than 1 plus 7	false	3 times 2 (i.e. 6) is not greater than 1 plus 7 (i.e. 8)
Score < PassMark	Score is less than PassMark	true	Score (49) is less than PassMark (50) is true

Compound Boolean Expressions

• are formed by combining Boolean expressions using the Boolean operators : and, or and not
  • for example, to determine whether an integer is greater than zero but less than 100, we can form a compound Boolean expression as follows :

　(Number > 0) and (Number < 100)

If the variable Number equals to 99, then the Boolean value of the Boolean expression becomes true


• Suppose A and B represent two simple Boolean expressions. The following truth table summarize all possible values for A and B and the corresponding values of the compound Boolean expressions.
  
  

A	B	A and B	A or B	not A
true	true	true	true	false
true	false	false	true	false
false	true	false	true	true
false	false	false	false	true