Ordinal types

1. 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)

2. 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

3. 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.

4. 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.

5. 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

6. 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’

7. 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

8. 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

9. 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’);

10. Turbo Pascal Topic: Debugging

11. 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

12. 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

13. 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

14. Midterm topics • Variables • types • integers • reals • boolean • character • strings • rules for naming • garbage values

15. Midterm topics (con’t) • Arithmetic operators • integers • reals • precedence • formatting output - all types • reading data • buffer • all types

16. Midterm topics (con’t) • Units • compiler • loops • FOR TO • FOR DOWNTO • nested • ordinal types - all topics

17. Midterm topics (con’t) • Programming • any topic covered in • class • homework • chapters 1-5 • functions