c++ data types

Data Types

The following topics are covered in this section:

Introduction

Integer

Floating Type

Double

Character

Boolean

Data Type Ranges and determining the ranges

More on Binary Numbers

Every piece of data has to belong to some basic category. Consider a simple example in real life:

every number has to be of a particular type. The number 5 is a natural number (or it can be called as a whole

number). 6.5 is a real number (it has a decimal point). Similarly, in programming we have what are called as

data types. When a variable is declared, the programmer has to specify which data type it belongs to. Only

then will the compiler know how many bytes it should allocate for that particular variable. Or in other words,

each data type occupies a different memory size and if a variable is declared as belonging to one particular

data type it cannot be assigned a different data type value. In simpler terms, suppose the variable x is

declared such that it can hold only whole numbers; then it cannot (and should not) be assigned some alphabet.

There are two categories of data types: fundamental data types and user-defined data types. The second

category of data types will be dealt with later.

The fundamental (or built-in or primitive) data types are:

Integer

Floating Point

Character

Double

Bool

The first three data types: integer, floating point and character are used frequently.

Integer (int):

An integer can contain only digits (numbers) from 0 to 9. Examples of integers are:

Data Types http://www.sstutor.com/cpp/datatype.htm

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010

345

6789

-23

-600

It includes positive and negative numbers but the numbers have to be whole numbers. It does accept the

decimal point. Hence the following numbers are not integer data types:

3.5

4.8

0.23

These numbers come under the second category (floating point type) and not under integers. If the program

has to accept such values from the user do not declare the variable as an integer. If a variable is declared as

an integer and the user enters a value of 2.3, the program will assign 2 as the value for that integer variable.

Similarly, if the user enters 3.2, the program will assign 3 to the integer variable.

Remember: Once a variable is declared as an integer, it will only store whole numbers (if the user types a

value with the decimal point, the program will ignore everything that is typed after the decimal point).

How to declare a variable as belonging to the type integer? The syntax is:

int variable-name;

Each data type occupies a certain amount of memory space. An integer will occupy 2 bytes of memory

(which means 16 bits). From this it is possible to calculate the maximum and minimum values that an integer

can store. 2^16 = 65536 (hence 65536 different combinations of 16 bits are possible). Divide this by 2

because integers (by default) range from negative to positive values. We have a 0 in between and so subtract

one from this to get 32,767. Hence an integer can take values from 32,768 up to +32,767 (a total of 65536

different values).

A natural question springs to mind, "What would happen if a value greater than 32,767 is entered?" Since this

value cannot be accommodated within the allocated two bytes, the program will alter the value. Its not

exactly altering the value; it will basically change your value into something different. The user might enter

123456 as the integer value but the program will store it as 7623 or something like that. Whenever you use

variables ensure that you have declared them as belonging to the correct data type.

This restriction on maximum range might seem to be a problem. In C++ qualifiers can be used to vary the

range of fundamental data types. Qualifiers are only supplements to the basic data types and they cannot be

used separately on their own. They work only with a basic (or fundamental) data type. The 4 qualifiers

available in C++ are:

Short1.

Long2.

Signed3.

Unsigned4.


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Signed and unsigned integers were discussed in the first chapter. When an integer is specified as signed, then

automatically the most significant bit of the number is used as a sign bit (to denote the sign of the number).

Hence it can be used if the programmer needs positive and negative number values for the variable. By

declaring a variable as an integer, by default you can specify both positive and negative values. By default an

integer is a signed integer. In other words,

int variable-name;

is the same as

signed int variable-name;

In the second form, signed is the qualifier and it is used to explicitly state that the variable is a signed

integer. For an unsigned integer the syntax will be:

unsigned int variable-name;

An unsigned integer can hold a value up to 65,535 (a signed integer can hold only up to 32,767). Of course, in

an unsigned integer you cannot assign a negative value. The range is from 0 to 65,535. To go beyond 65,535

and make use of both positive and negative values as well, the qualifier long should be used.

long int variable-name;

Long integers occupy 4 bytes of memory (32 bits). Remember, long int actually means signed long int (you

can give positive and negative values).

If you specify

unsigned long int variable-name;

you can only assign positive values to the variable. Thus, two qualifiers can be used together with a basic data

type.

What about the short qualifier? Short integer is the same as a signed integer. It occupies two bytes and has

the same range of positive and negative values as the normal integer case.

int x;

is usually the same as

short int x;

Compilers (depending on the operating system) will assume int as a long int or a short int. VC++ (since it

works in the Windows OS) will default to long int if you specify a variable as type int (i.e. it will allocate 4

bytes to an int variable). Turbo C++ (which is a DOS based compiler) will default to short int when you

specify a variable as type int. Thus the statement:

int var;

will allocate var 4 bytes if you are using VC++ but the same statement will allocate 2 bytes if you are using

Turbo C++ compiler.

Programmers sometimes prefer to explicitly state what type of integer they want to use by making use of the

short and long qualifiers. short int always occupies only 2 bytes (irrespective of whether the OS is


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Windows or DOS) while a long int always occupies 4 bytes.

Two qualifiers can be used together, but do not try using:

short long int variable-name;

This will cause a compile-time error. So be careful with what qualifiers you use. And remember that the

default for int is equivalent to short signed integer.

Floating Types (float):

Floating type data include integers as well as numbers with a decimal point. It can also have an exponent.

Exponent means 10 to the power of some integer value (whole number). 20000 = 2 x 10^4 = 2e4 = 2E4.

If you specify decimal numbers, floating point data type will store up to a precision of 6 digits after the

decimal point. Suppose 0.1234567 is assigned to a floating-point variable, the actual value stored would be

0.123457 (it will round up to the sixth digit after the decimal place). Valid floating-point numbers are:

0.1276

1.23

1.0

10.2

2e5 (this will be typed in your code as 2e5)

Do not use an exponent with a decimal point. For example: 2e2.2 is an invalid floating point because the

exponent has to be an integer. Floating point numbers use 4 bytes of memory and has a much greater range

than integers because of the use of exponents. They can have values up to 10^38 (in positive and negative

direction). The same qualifiers used for an integer can be applied to floating point numbers as well. To declare

a floating variable, the syntax is:

float variable-name;

Double (double):

This is similar to the floating-point data type but it has an even greater range extending up to 10308. The

syntax to declare a variable of type double is:

double variable-name;

Beware: Visual C++ (VC++) usually uses its default as double instead of float. Suppose we type:

float x=31.54;

you will get a warning message saying that a double (i.e. 31.54) is being converted into a floating point. It is

just to warn you that you are using a float and not a double. (Even if there are warnings, there wont be

any problem in running your program).

Character (char):


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A character uses just one byte of memory. It can store any character present on the keyboard (includes

alphabets and numbers). It can take numbers from 0 to 9 only. The following are valid characters:

A

B

3

a

:

/

If the number 13 is entered as the value for a character, the program will only store 1 (i.e it will store the first

character that it encounters and will discard the rest). A character is stored in one byte (as a binary number).

Thus whatever the user enters is converted into a binary number using some character set to perform this

conversion. Mostly all computers make use of the ASCII (American Standard Code for Information

Interchange). For example, according to the ASCII coding, the letter A has a decimal value of 65 and the

letter a has a value of 97.

There is another form of coding called the EBCDIC (Extended Binary Coded Decimal Information Code)

which was developed by IBM and used in IBM computers. However, ASCII remains the most widely used

code in all computers. The table at the end of the book gives a listing of the ASCII values and their equivalent

characters. The syntax to declare a variable which can hold a character is:

char variable-name;

Boolean Type (bool)

This data type will only accept two values: true or false. In C++, true and false are keywords. Actually a

value of true corresponds to 1 (or a non-zero value) and a value of false corresponds to 0.

#include

int main( )

{

bool check;

check = true;

cout

(Compiler

dependent)bytes)

char 1 Character or 8 bit integer.signed: -128 to 127

unsigned: 0 to 255

bool 1Boolean type. It takes only

two values. true or false

short 2 16 bit integer.signed: -32768 to 32767

unsigned: 0 to 65535

long 4 32 bit integer.signed:-2147483648 to

2147483647

int 2/4

Integer. Length depends on

the size of a word used by

the Operating system. In

MSDOS a word is 2 bytes and

so an integer is also 2 bytes.

Depends on whether 2/4 bytes.

float 4 Floating point number. 3.4e + / - 38 (7 digits)

double 8double precision floating point

number.1.7e + / - 308

Remember: short int always occupies only 2 bytes (irrespective of whether the OS is Windows or DOS)

while a long int always occupies 4 bytes.

Determining the range:

You might be wondering why the ranges are from -128 to 127 or from -32768 to 32767?

Why not from 128 to 128? Well take the case of signed characters to understand the range. A character

occupies one byte (8 bits). In a signed character the MSB (i.e. the 7th bit is used to denote the sign; if the

MSB is 1 then the number is negative else it is positive). The binary number: 0111 1111 represents +127 in

decimal value (weve seen about conversion from binary to decimal numbers in the first chapter). The

number 0000 0000 represents 0 in decimal. But what about 1000 0000? Since the MSB denotes a negative

number, does this stand for 0? Since there is no point in having a 0 and a +0, computers will take 1000

0000 as 128. 0000 0000 is taken to be zero. Thus in the negative side we have a least value of 128 possible

while in the positive side we can have a maximum of only +127.

Another point to note is that negative numbers in computers are usually stored in 2s complement format. For

example: 1000 0001 actually stands for 1 but if this number is stored in 2s complement format then it stands

for 127. Similarly 1000 0010 would appear to be 2 but is actually 126. To understand 2s complement you

should know about 1s complement. Let us say we have a signed binary number: 1000 0001. The 1s

complement of this number is 1111 1110 (i.e. to find the 1s complement of a binary number just change the

1s to 0s and 0s to 1s but do not change the sign bit). To find the 2s complement just add 1 to the 1s

complement. Hence the 2s complement of 1000 0001 is 1111 1111 (or 127). In the same way the 2s

complement of 1111 1111 (-127) is 1000 0001 (or 1). Thus the computer instead of storing 1111 1111 (for

127) will store the 2s complement of the number (i.e. it will store 1000 0001).


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Remember: When converting a number to its 2s complement leave its sign bit unchanged. And numbers are

stored in 2s complement format only if they are negative. Positive numbers are stored in the normal format.

More on Binary Numbers:

Everything in the computer is stored in binary format. Even if we ask the computer to store an octal

number or a hexadecimal number in a variable, it will still be stored in binary format (well see this later)

because computers only understand 0s and 1s. How does a computer perform calculations? Yes, it has to do it

in binary format. Lets take an example of binary addition:

0 1 1 0 1 0 1 0 (106)10

0 0 1 1 0 1 0 0 (52)10

-----------------------------------------------------------------

1 0 0 1 1 1 1 0

First of all, what 2 decimal numbers are we adding? Convert them to decimal and youll get: 106 and 52.

When the computer has to add 106 and 52, it would in effect be adding the 2 binary numbers as shown above.

Binary arithmetic is simple:

0 + 0 = 0

1 + 0 = 1

0 + 1 = 1

1 + 1 = 0 and a carry of 1

Use this and try out the addition of 106 and 52. Voila! Youll get the answer of 158.

Proceeding further, we need to investigate as to how negative numbers are really stored in computers. We

discussed earlier that if +10 is represented as 0000 1010 then -10 would be represented as 1000 1010 (since

the MSB is considered as the sign bit). Right? Lets check it out.

If we add -10 to 10 then we should get the answer as zero.

0 0 0 0 1 0 1 0

1 0 0 0 1 0 1 0

-----------------------------------------------------------------

1 0 0 1 0 1 0 0

And the answer is? -20.


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So, where did we go wrong? One question you might have is why did we add the sign bit also? The computer

isnt smart enough (or rather it doesnt have the circuitry) to separate the sign bit from the rest of the number.

The 2 numbers that you want to add, are fed as input to an adder circuit which will blindly add up both the

numbers and give the result. To overcome this problem, we can make use of 2s complement.

For example: 1000 0001 actually stands for 1 but if this number is stored in 2s complement format

then it stands for 127. Similarly 1000 0010 would appear to be 2 but is actually 126. To understand 2s

complement you should know about 1s complement. Let us say we have a signed binary number:

1 0 0 0 0 0 0 1

The 1s complement of this number is

1 1 1 1 1 1 1 0

To find the 1s complement of a binary number just change the 1s to 0s and 0s to 1s but do not change the

sign bit.

Next, to find the 2s complement just add 1 to the 1s complement.

1 1 1 1 1 1 1 0

1

-----------------------------------------------------------------

1 1 1 1 1 1 1 1

Hence the 2s complement of 1000 0001 is 1111 1111 (or 127). In the same way the 2s complement of 1111

1111 (-127) is 1000 0001 (or 1). Thus the computer instead of storing 1111 1111 (for 127) will store the 2s

complement of the number (i.e. it will store 1000 0001). Why? Lets go back to our initial problem of adding

+10 and -10. Now lets assume that the computer stores -10 in 2s complement format. The addition will now

be:

0 0 0 0 1 0 1 0 (+10)

1 1 1 1 0 1 1 0 (-10)

-----------------------------------------------------------------

0 0 0 0 0 0 0 0

Voila! The answer is 0. But you may ask what about the carry of 1?. Well, since it is an extra bit, it

overflows (which means it is lost and we neednt worry about it). Im not going to get into more details of 2s

complement since this should be sufficient for learning C++. To learn more on this subject, you can check out

books on digital systems or computer system architecture.

Note: When you perform binary addition, 1 + 1 is equal to 0 and a carry of 1 (because in the binary system

we only have 2 states: 1 and 0; so we cant have 1 + 1 = 2 in binary).


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Remember: When converting a number to its 2s complement its sign bit is unchanged. Numbers are stored

in 2s complement format only if they are negative. Positive numbers are stored in the normal format.

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Copyright 2004 Sethu Subramanian All rights reserved.


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c++ data types

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