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  Integer and floating point numbers
The different number types in Delphi
Delphi provides many different data types for storing numbers. Your choice depends on the data you want to handle. In general, smaller number capacities mean smaller variable sizes, and faster calculations. Ideally, you should use a type that comfortably copes with all possible values of the data it will store.
For example, a Byte type can comfortably hold the age of a person - no-one to date has lived as long as 255 years.
With decimal numbers, the smaller capacity types also have less precision. Less numbers of significant digits. Let us look at the different types:
 Type  Storage size                        Range            
 Byte       1                             0 to 255
 ShortInt   1                          -127 to 127
 Word       2                             0 to 65,535
 SmallInt   2                       -32,768 to 32,767
 LongWord   4                             0 to 4,294,967,295
 Cardinal   4*                            0 to 4,294,967,295
 LongInt    4                -2,147,483,648 to 2,147,483,647
 Integer    4*               -2,147,483,648 to 2,147,483,647
 Int64      8    -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807
 Single     4     7  significant digits, exponent   -38 to +38
 Currency   8    50+ significant digits, fixed 4 decimal places
 Double     8    15  significant digits, exponent  -308 to +308
 Extended  10    19  significant digits, exponent -4932 to +4932
 * Note : the Integer and Cardinal types are both 4 bytes in size at present (Delphi release 7), but are not guaranteed to be this size in the future. All other type sizes are guaranteed.

Assigning to and from number variables
Number variables can be assigned from constants, other numeric variables, and expressions:
   YOUNG_AGE = 23;        // Small integer constant
   MANY      = 300;       // Bigger integer constant
   RICH      = 100000.00; // Decimal number : note no thousand commas
   Age       : Byte;      // Smallest positive integer type
   Books     : SmallInt;  // Bigger signed integer
   Salary    : Currency;  // Decimal used to hold financial amounts
   Expenses  : Currency;
   TakeHome  : Currency;
   Age       := YOUNG_AGE;// Assign from a predefined constant
   Books     := MANY + 45;// Assign from a mix of constants (expression)
   Salary    := RICH;     // Assign from a predefined constant
   Expenses  := 12345.67; // Assign from a literal constant
   TakeHome  := Salary;   // Assign from another variable
   TakeHome  := TakeHome - Expenses; // Assign from an expression

 Age       is set to 23
 Books     is set to 345
 Salary    is set to 100000.00
 Expenses  is set to 12345.67
 TakeHome  is set to 87654.33

Numerical operators
Number calculations, or expressions, have a number of primitive operators available:
 +   : Add one number to another
 -   : Subtract one number from another
 *   : Multiply two numbers
 /   : Divide one decimal number by another
 div : Divide one integer number by another
 mod : Remainder from dividing one integer by another

When using these multiple operators in one expression, you should use round brackets to wrap around sub-expressions to ensure that the result is obtained. This is illustrated in the examples below:
   myInt : Integer; // Define integer and decimal variables
   myDec : Single;
   myInt := 20;          // myInt is now 20
   myInt := myInt + 10;  // myInt is now 30
   myInt := myInt - 5;   // myInt is now 25
   myInt := myInt * 4;   // myInt is now 100
   myInt := 14 div 3;    // myInt is now 4   (14 / 3 = 4 remainder 2)
   myInt := 14 mod 3;    // myInt is now 2   (14 / 3 = 4 remainder 2)
   myInt := 12 * 3 - 4;  // myInt is now 32  (* comes before -)
   myInt := 12 * (3 - 4);// myInt is now -12 (brackets come before *)
   myDec := 2.222 / 2.0; // myDec is now 1.111

Numeric functions and procedures
Delphi provides many builtin functions and procedures that can perform numeric calculations. Some examples are given below - click on any to discover more. Note that these routines are stored in Units that are shipped with Delphi, and which form part of the standard delphi Run Time Library. You will need to include a reference to the Unit in order to use it (the code example provided with each gives the unit name and shows how to refer to it).
  href='RTL.asp?Name=Abs'>Abs  Returns the absolute value of a signed number
  href='RTL.asp?Name=Max'>Max  Gives the maximum of two integer values
  href='RTL.asp?Name=Min'>Min  Gives the minimum of two integer values
  href='RTL.asp?Name=Mean'>Mean Gives the average of a set of numbers
  href='RTL.asp?Name=Sqr'>Sqr  Gives the square of a number
  href='RTL.asp?Name=Sqrt'>Sqrt Gives the square root of a number
  href='RTL.asp?Name=Exp'>Exp  Gives the exponent of a number
  href='RTL.asp?Name=Shl'>Shl  Shifts the bits in a number left
  href='RTL.asp?Name=Shr'>Shr  Shifts the bits in a number right
  href='RTL.asp?Name=Tan'>Tan  Gives the Tangent of a number
  href='RTL.asp?Name=Cos'>Cos  Gives the Cosine of a number
  href='RTL.asp?Name=Sin'>Sin  Gives the Sine of a number

Converting from numbers to strings
Delphi also provides routines that convert numbers into strings. This is often useful for display purposes.
  href='RTL.asp?Name=Str'>Str       Converts a number to a string in a simple manner
  href='RTL.asp?Name=CurrToStr'>CurrToStr Converts a Currency variable to a string
  href='RTL.asp?Name=Format'>Format    Number to string conversion with formatting
  href='RTL.asp?Name=IntToStr'>IntToStr  Converts an integer to a string
  href='RTL.asp?Name=IntToHex'>IntToHex  Converts a number into a hexadecimal string

Converting from strings to numbers
Finally, Delphi provides string to number conversion utilities. Here are some examples:
  href='RTL.asp?Name=StrToInt'>StrToInt     Converts an integer string into an integer
  href='RTL.asp?Name=StrToIntDef'>StrToIntDef  Fault tolerant version of StrToInt
  href='RTL.asp?Name=StrToFloat'>StrToFloat   Converts a decimal string to a number


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