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Ordinal types

• An ordinal data type is an ordered set in which every element, except the first element, has an immediate predecessor, and every element, except the last element, has an immediate successor. – all types of integers– characters– boolean– enumerated types (Enumerated types are user

defined. We will not cover them in this course)

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Ordinal types (con’t)

• Reals and strings are not ordinal types because they do not have a unique predecessor or successor.

• A FOR-DO loop’s control variable must be an ordinal type.– This is why reals cannot be control variables

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ASCII Table• ASCII (American Standard Code for

Information Exchange) table contains 128 entries relating whole numbers to characters

• Turbo Pascal extends this table with graphical characters. The total number of characters in the table for Turbo Pascal is 256 (0 to 255 or 0000 0000 to 1111 1111).

• A character’s position in this table is called it’s ordinal position.

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Distinction between integer and its character representation

• The number 6 and the character ‘6’ are not the same– The explicit representation of the character 6 in

a program is ‘6’ and its ordinal position in the ASCII table is 54.

– The explicit representation of the integer 6 in a program is 6 and its ordinal position in the integer sequence is also 6.

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Ordinal Functions

• ord(ordinal_type) This function returns the ordinal position of the value in the parenthesis.– ord (‘A’) returns 65– ord (123) returns 123– ord (TRUE) returns 1– ord (FALSE) returns 0

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Ordinal functions (con’t)

• chr(byte)– give this function an integer between 0 and 255

and it returns the character whose ordinal value is that integer.

– chr(64) returns ‘@’– chr(52) returns ‘4’ {note: this is a character}– chr(87) returns ‘W’– chr(129) returns ‘ü’

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Ordinal functions (con’t)

• succ() is the successor function. It returns the next value of the ordinal type.– succ(‘A’) returns ‘B’– succ(3) returns 4– succ(‘3’) returns ‘4’– succ(FALSE) returns TRUE– succ(TRUE) does not have a value

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Ordinal functions (con’t)

• pred() is the predecessor function. It returns the previous value of the ordinal type.– pred(‘B’) returns ‘A’– pred(3) returns 2– pred(‘3’) returns ‘2’– pred(FALSE) does not have a value– pred(TRUE) returns FALSE

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Converting numbers read as characters to integers

• Sometimes you may want to read numerical digits as characters and convert them to numerical values in your program.

Number := ord(char) - ord(‘0’);

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Turbo Pascal Topic: Debugging

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Standard Functions: arithmetic

• Sqr(x): squares x

• sqrt(x): positive square root of x

• abs(x): absolute value of x

• exp(x): raises e to x power

• ln(x): log of x to base e

• cos(x): Cosine of x

• sin(x): Sine of x

• arctan(x): Arctangent of x

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More standard functions

• Transfer functions (real to integer)– Round(x) rounds x to the closest integer– trunc (x) drops the part of x to the right of the

decimal.

• Boolean functions– odd (x) returns TRUE if x is odd or FALSE if x

is not– we will learn others later

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Turbo Pascal non-standard functions• Pi: the value of pi (note: no arguments)

• upcase(L): returns uppercase for a lowercase letter L. For any other character it returns the same character.

• Frac(x): returns part to the right of the decimal

• int(x): returns part to the left of the decimal

• random(N): returns random integer between 0 and N-1

• random: returns random real between 0 & 1

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Midterm topics

• Variables– types

• integers• reals• boolean• character• strings

– rules for naming– garbage values

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Midterm topics (con’t)

• Arithmetic operators– integers– reals– precedence

• formatting output - all types

• reading data– buffer– all types

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Midterm topics (con’t)

• Units

• compiler

• loops– FOR TO– FOR DOWNTO– nested– ordinal types - all topics

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Midterm topics (con’t)

• Programming– any topic covered in

• class

• homework

• chapters 1-5

• functions