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                                                    Chapter 3
                                            SIMPLE DATA TYPES



WHAT IS A DATA TYPE?
____________________________________________________________

A type in Pascal, and in several other popular programming
languages, defines a variable in such a way that it defines
a range of values which the variable is capable of storing,
and it also defines a set of operations that are permissible
to be performed on variables of that type.  TURBO Pascal has
5 basic data types which are predefined and can be used
anywhere in a program provided you use them properly.  This
chapter is devoted to illustrating the use of these five data
types by defining the allowable range of values that can be
assigned to them, and by illustrating the operations that can
be done to variables of these types.  The five types and a
very brief description follows;

     integer    Whole numbers from -32768 to 32767
     byte       The integers from 0 to 255
     real       Floating point numbers from 1E-38 to 1E+38
     boolean    Can only have the value TRUE or FALSE
     char       Any character in the ASCII character set

Please note that the byte type of data is not a part of the
standard Pascal definition but is included as an extension to
the TURBO Pascal compiler.

TURBO Pascal versions 4.0 and 5.x have three additional types
available of the integer class, which are not available with
version 3.0.  They are defined as follows;

     shortint   The integers from -128 to 127
     word       The integers from 0 to 65535
     longint    The integers from -2147483648 to 2147483647

In addition to the above data types TURBO Pascal version 4.0
has the following data types available but in order to use
them, you must have an 80X87 math coprocessor installed in
your system;

     single     Real type with 7 significant digits
     double     Real type with 15 significant digits
     extended   Real type with 19 significant digits
     comp       The integers from about -10E18 to 10E18

TURBO Pascal version 5.x has these four types available but
because they have a software emulator for the floating point
operations, an 80X87 math coprocessor is not required to use
these with these versions.  Of course, your resulting program

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                                            Simple Data Types

will run much faster if you have the coprocessor available for
use by the program.

A complete definition of the available types for each compiler
can be found on pages 41 and 42 of the TURBO Pascal version
3.0 reference manual, and on pages 39 through 44 of the
reference manual for version 4.0.  They are defined on pages
41 to 46 of the TURBO Pascal 5.x User's guide.  It would be
good to read these pages now for a good definition prior to
learning how to define and use them in a program.  Note that
all of these will be used in example programs in this chapter.



OUR FIRST VARIABLES
____________________________________________________________

The integers are by far the easiest to       ================
understand so we will start with a simple       INTVAR.PAS
program that uses some integers in a very    ================
simple way.  Load INTVAR.PAS into your
TURBO system and let's take a look at it.

Immediately following the program statement is another
reserved word, var.  This reserved word is used to define a
variable before it can be used anywhere in the program.  There
is an unbroken rule of Pascal that states "Nothing can be used
until it is defined."  The compiler will complain by
indicating a compilation error if you try to use a variable
without properly defining it.  It seems a bit bothersome to
have to define every variable prior to its use, but this rule
will catch many spelling errors of variables before they cause
trouble.  Some other languages will simply define a new
variable with the new name and go merrily on its way producing
some well formatted garbage for you.

Notice that there is only one var, but it is used to define
three different variables, Count, X, and Y.  Once a var is
recognized, the compiler will continue to recognize variable
definitions line after line until it finds another reserved
word.  It would be permissible to put a var on the second line
also but it is not necessary.  It would also be permissible
to put all three variables on one line but your particular
programming style will dictate where you put the three
variables.  Following the colon on each line is the word
integer which is a standard identifier, and is therefore
different from a reserved word.  A standard identifier is
predefined like a reserved word, but you can redefine it,
thereby losing its original purpose and meaning.  For now and
for a long time, don't do that.  Page 38 contains a list of
standard identifiers in TURBO Pascal 3.0.  There is no
corresponding list in the reference manual for TURBO Pascal
4.0 or for TURBO Pascal 5.x.


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                                            Simple Data Types


OUR FIRST ARITHMETIC
____________________________________________________________

Now that we have three variables defined as integer type
variables, we are free to use them in a program in any way we
desire as long as we use them properly.  If we tried to assign
a real value to X, the compiler will generate an error, and
prevent a garbage output.  Observe the start of the main body
of the program.  There are three statements assigning values
to X, Y, and Count.  A fine point of mathematics would state
that Count is only equal to the value of X+Y until one of them
was modified, therefore the equal sign used in so many other
languages is not used here.  The sign := is used, and can be
read as "is replaced by the value of," when reading a listing.
Another quicker way is to use the word "gets".  Thus X := X
+ 1 would be read, "X gets the value of X plus 1".  We will
see later that the simple equal sign is reserved for use in
a different manner.

The first three statements give X the value of 12, Y the value
of 13, and Count the value of 12 + 13 or 25.  If we have a
requirement to get those values out of the computer, we need
another extension to the Writeln statement.  The first part
of the data within the parentheses should be very familiar to
you now, but the second part is new.

Multiple outputs can be handled within one Writeln if the
fields are separated by a comma.  To output a variable, simply
write the variable's name in the output field.  The number
following the variable in each case is the number of output
columns to be used by the output data.  This number is
optional and can be omitted allowing the system to use as many
columns as it needs.  For purposes of illustration, they have
all been assigned different numbers of columns.  At this
point, you can compile and run INTVAR.PAS and examine its
output.

To illustrate the various ways to output    =================
data, load INTVAR2.PAS and observe that        INTVAR2.PAS
even though the output is identical, it is  =================
output in a completely different manner.
Observe especially that a Writeln all by
itself simply moves the cursor to the beginning of a new line
on the video monitor.  Compile and run this program and
observe its output after you are certain that the two programs
are actually identical.


NOW LET'S USE LOTS OF VARIABLES
____________________________________________________________

Load ALLVAR.PAS to observe a short program using all 5 of the
basic data types.  The variables are simply assigned values

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                                            Simple Data Types

and the values are printed.  A complete      ================
and detailed description of the options         ALLVAR.PAS
available in the Write statement is given    ================
in the TURBO reference manual version 3.0
on pages 111 through 113, and on pages 500
through 502 for version 4.0.  Pages 52 and 53 of the User's
Guide has the corresponding information for TURBO Pascal
version 5.x.  It would be to your advantage to read this
section at this time since very little explanation will be
given about Write statements from this point on.  We will
discuss the method by which we can write to disk files or
other output devices in a later chapter of this tutorial.

Back to the basic types.  Pascal does lots of cross checking
for obvious errors.  It is illegal to assign the value of any
variable with a value that is of the wrong type or outside the
allowable range of that variable.  There are routines to
convert from one system to another when that is necessary.
Suppose, for example, that you wished to use the value of an
integer in a calculation of real numbers.  That is possible
by first converting the integer into a real number of the same
value and using the new real type variable in the desired
calculations.  The new real type variable must of course be
defined in a var statement as a real type variable before it
can be used.  Details of how to do several conversions of this
kind will be given in the example program named CONVERT.PAS
later in this chapter.

Since we have some variables defined, it     ================
would be nice to use the properties of         REALMATH.PAS
computers for which they are famous,         ================
namely some arithmetic.  Two programs are
available for your observation to
illustrate the various kinds of math available, REALMATH.PAS
using real variables, and INTMATH.PAS using integer variables.
You can edit, compile, and run these on your own with no
comment from me except the comments
embedded into the source files.  Chapter 6  =================
on pages 51 to 54 of your version 3.0          INTMATH.PAS
TURBO reference manual completely defines   =================
the simple mathematics available.  The
corresponding list for version 4.0 is
found in chapter 3 on pages 46 through 49, and pages 48
through 51 of the TURBO Pascal User's Guide gives the list for
version 5.x of the compiler.

A byte type variable is used just like an integer variable but
with a much smaller allowable range.  Only one byte of
computer memory is used for each variable defined as a byte
type variable, but 2 are used for each integer type variable.





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                                            Simple Data Types

BOOLEAN VARIABLES
____________________________________________________________

Let's take a look at a boolean variable, which is only allowed
to take on two different values, TRUE or FALSE.  This variable
is used for loop controls, end of file indicators or any other
TRUE or FALSE conditions in the program.  Variables can be
compared to determine a boolean value.  A complete list of the
relational operators available with Pascal is given in the
following list.

     =     equal to
     <>    not equal to
     >     greater than
     <     less than
     >=    greater than or equal to
     <=    less than or equal to

These operators can be used to compare any   ================
of the simple types of data including          BOOLMATH.PAS
integer, char, byte, and real type           ================
variables or constants, and they can be
used to compare boolean variables.  An
illustration is the best way to learn about the boolean
variable so load BOOLMATH.PAS and observe it.

In BOOLMATH.PAS we define a few boolean variables and two
integer type variables for use in the program and begin by
assigning values to the two integer variables.  The expression
Junk = Who in line 14 is actually a boolean operation that is
not true since the value of Junk is not equal to the value of
Who.  The result is therefore FALSE and that value is assigned
to the boolean variable A.  The boolean variable B is assigned
the value of TRUE because the expression Junk = (Who - 1) is
true.  The boolean variables C and D are likewise assigned
some values in a manner that should not need any comment.
After assigning a value to the variable with the big name, the
values are all printed out.


WHERE DO WE USE THE BOOLEAN VARIABLES?
____________________________________________________________

We will find many uses for the boolean type variable when we
study the loops and conditional statements soon, but until
then we can only learn what they are.  Often, in a conditional
statement, you will want to do something if either of two
things are true, in which case you will use the reserved word
and with two boolean expressions.  If either of the two are
true, the result will be true.  Line 29 is an example of this.
If the boolean variables B, C, and D, are all true, then the
result will be true and A will be assigned the value of TRUE.
If any one of them is false, the result will be false and A
will be assigned the value of FALSE.

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                                            Simple Data Types


In Line 31, where the or operator is illustrated, if any of
the three boolean variables is true, the result will be true,
and if all three are false, the result will be false.  Another
boolean operator is the not which is illustrated in line 30.
Examine line 33 which says the result is true only if the
variable Junk is one less than Who, or if Junk is equal to
Who.

Compile and run this program, then add some additional
printout to see if the boolean variables change the way you
think they should in the last few statements.


SHORT CIRCUIT OR COMPLETE EVALUATION?
____________________________________________________________

Suppose you have several boolean expressions "and"ed together,
and when evaluation starts, the first expression results in
a FALSE.  Since the first expression is FALSE, it is
impossible for the following expressions to ever allow the
final result to be TRUE because the first FALSE will force the
answer to be FALSE.  It seems like a waste of execution time
to continue evaluating terms if the final result is already
known, but that is exactly what standard Pascal will do
because of the language definition.  This is known as complete
evaluation of a boolean expression.  If the system is smart
enough to realize that the final result is known, it could
stop evaluation as soon as the final result is known.  This
is known as short circuit evaluation of a boolean expression,
and could also be applied if a term of an "or"ed boolean
expression resulted in a TRUE, since the result would always
be TRUE.

TURBO Pascal version 3.0 always does complete evaluation of
boolean expressions but TURBO Pascal versions 4.0 and 5.x
allows you to choose between complete evaluation or short
circuit evaluation.  The default for both compilers is the
short circuit form but it can be changed through the Options
menu when you are using the integrated environment, or through
use of a compiler directive.



LET'S LOOK AT THE CHAR TYPE VARIABLE
____________________________________________________________

A char type variable is a very useful        ================
variable, but usually not when used alone.     CHARDEMO.PAS
It is very powerful when used in an array    ================
or some other user defined data structure
which is beyond the scope of this chapter.
A very simple program, CHARDEMO.PAS is included to give you
an idea of how a char type variable can be used.  Study then

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                                            Simple Data Types

compile and run CHARDEMO.PAS for a very brief idea of what the
char type variable is used for.

Examine the sample program CONVERT.PAS for  =================
several examples of converting data from       CONVERT.PAS
one simple variable to another.  The        =================
program is self explanatory.


THIS IS FOR TURBO PASCAL 4.0 OR 5.X USERS
____________________________________________________________

If you are using TURBO Pascal version 3.0, you are finished
with this chapter because the data types illustrated in the
last two programs are not available with that compiler.

If you are using TURBO Pascal 4.0 or 5.x,   =================
display the program NEWINT4.PAS for an         NEWINT4.PAS
example of using the extended integer       =================
types available with that compiler.  Four
variables are defined and values assigned
to each, then the results are displayed.  When you compile and
run the program, you will see that the variable Big_int can
indeed handle a rather large number.

It must be pointed out that the calculation in lines 13 and
21 result in a different answer even though they appear to be
calculating the same thing.  An explanation is in order.  The
quantity named MaxInt used in lines 10 and 13 is a constant
built into the system that represents the largest value that
an integer type variable can store.  On the first page of this
chapter we defined that as 32767 and when running the program
you will find that Index displays that value as it should.
The constant MaxInt has a type that is of a universal_integer
type as do all of the numeric constants in line 13.  The
result then is calculated to the number of significant digits
dictated by the left hand side of the assignment statement
which is of type longint resulting in a very large number.

When we get to line 21, however, the variable Index is of type
integer so the calculations are done as though the constants
were of type integer also which causes some of the more
significant digits to be truncated.  The truncated result is
converted to type longint and assigned to the variable Big_int
and the truncated value is displayed by line 22.

After that discussion it should be apparent to you that it is
important what types you use for your variables.  It must be
emphasized that it would not be wise to use all large type
variables because they use more storage space and slow down
calculations.  Experience will dictate the proper data types
to use for each application.



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                                            Simple Data Types

NOW FOR THE NEW REAL TYPES
____________________________________________________________

If you are using TURBO Pascal 4.0 or 5.x,    ================
display the program NEWREAL4.PAS for an        NEWREAL4.PAS
example using the new "real" types           ================
available with the newer versions of TURBO
Pascal.  Note that you must have an 80X87
math coprocessor installed to compile and run this program if
you are using TURBO Pascal version 4.0.  There is a note given
in the file to aid you in selecting it for use.

If you are using TURBO Pascal version 5.x, you can use the
80X87 math coprocessor, once again getting help from the note
embedded in the file.  If you do not have a math coprocessor,
TURBO Pascal version 5.x has an emulator mode  which can be
used as instructed on page 42 of the User's Guide.  Keep in
mind that, even though the emulator will allow you to use
these newer data types, the resulting program will execute
much slower due to the extra calculations required.

This program should be self explanatory so nothing will be
said except that when you run it you can observe the relative
accuracy of each of the variable types.  Once again, you
should keep in mind that use of the larger "real" types costs
you extra storage space and reduced run-time speed, but gives
you more accuracy.


PROGRAMMING EXERCISE
____________________________________________________________

1.   Write a program containing several variable definitions
     and do some math on them, printing out the results.





















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