Arithmetic Expressions consist of numeric literals, arithmetic operators, and numeric variables. They simplify to a single value, when evaluated.

Here is an example of an arithmetic expression with no variables:

3.14*10*10

This expression evaluates to 314, the approximate area of a circle with radius 10. Similarly, the expression

3.14*radius*radius

would also evaluate to 314, if the variable radius stored the value 10.

Note that the parentheses in the last expression helps dictate which order to evaluate the expression.

Multiplication and division have a higher order of precedence than addition and subtraction. In an arithmetic expression, it is evaluated left to right, only performing the multiplications and divisions.

After doing this, process the expression again from left to right, doing all the additions and subtractions.

 So,

 3+4*5

first evaluates to

 3+20 which then evaluates  to 23.

Consider this expression:

3 + 4*5 - 6/3*4/8 + 2*6 - 4*3*2

First go through and do all the multiplications and divisions:

3 + 20 - 1 + 12 - 24

Integer Division: In particular, if the division has a leftover remainder or fraction, this is simply discarded.

For example:

13/4 evaluates to 3

19/3 evaluates to 6 but

Similarly, if you have an expression with integer variables part of a division, this evaluates to an integer as well.

For example, in this segment of code, y gets set to 2.

int x = 8;

int y = x/3;

However, if we did the following,

double x = 8;

double y = x/3;

y would equal 2.66666666 (approximately).

The way C decides whether it will do an integer division (as in the first example), or a real number division (as in the second example), is based on the TYPE of the operands.

If both operands are ints, an integer division is done.

 If either operand is a float or a double, then a real division is done. The compiler will treat constants without the decimal point as integers, and constants with the decimal point as a float. Thus, the expressions 13/4 and 13/4.0 will evaluate to 3 and 3.25 respectively.

The mod operator (%)

The one new operator is the mod operator, which is denoted by the percent sign(%). This operator is ONLY defined for integer operands. It is defined as follows:

a%b evaluates to the remainder of a divided by b.

For example,

12%5 = 2

19%6 = 1

14%7 = 0

19%200 = 19

The precedence of the mod operator is the same as the precedence of multiplication and division.

2.1.1 Operators and expression using numeric and relational operators

Every expression in C language contains set of operators and operands. Operators are the special symbols which are used to indicate the type of operation whereas operands are the data member or variables operating as per operation specified by operator. One expression contains one or more set of operators and operands. So to avoid the ambiguity in execution of expression, C compiler fixed the precedence of operator. Depending on the operation, operators are classified into following category.

1. Arithmetic Operator: These are the operators which are useful in performing mathematical calculations. Following are the list of arithmetic operator in C language. To understand the operation assume variable A contains value 10 and variable contains value 5.

 Example:

 #include<stdio.h>

 #include<conio.h>

 void main()

 {

  int a,b,c;

  clrscr();

  printf("Enter two numbers");

  scanf("%d %d",&a,&b);

  printf("\n Result of addition of  %d and  %d is %d",a,b,a+b);

  printf("\n Result of subtraction of %d and %d is %d",a,b,a-b);

  printf("\n Result of multiplication %d and %d is %d",a,b,a*b);

  printf("\n Result of division of %d and %d is %d",a,b,a/b);

  printf("\n Result of modulus of  %d and %d is %d",a,b,a%b);

  getch();

 }

 Output:

 Enter two numbers

 5

 3

 Result of addition of 5 and 3 is 8

 Result of subtraction of 5 and 3 is 2

 Result of multiplication of 5 and 3 is 15

 Result of division of 5 and 3 is 1

 Result of modulus of 5 and 3 is 2

2.     Relational Operators: Relational operator used to compare two operands. Relational operator produce result in terms of binary values. It returns 1 when the result is true and 0 when result is false. Following are the list of relational operator in C language. To understand the operation assume variable A contains value 10 and variable contains value 5.

Example:

 #include<stdio.h>

 #include<conio.h>

 void main()

 {

  int a,b,c;

  clrscr();

  printf("Enter two numbers");

  scanf("%d %d",&a,&b);

  printf("\n Result of less than operator of  %d and %d is %d",a,b,a<b);

  printf("\n Result of greater than operator of %d and %d is %d",a,b,a>b);

  printf("\n Result of leass than or equal to operator %d and %d is %d",a,b,a<=b);

 printf("\n Result of greater than or equal to operator of %d and %d is %d",               a,b,a>=b);

  printf("\n Result of double equal to operator of  %d and %d is %d",a,b,a==b);

  printf("\n Result of not equal to operator of  %d and %d is %d",a,b,a!=b);

  getch();

 }

Output:

 Enter two numbers

 5

 3

 Result of less than operator of 5 and 3 is 0

 Result of greater than operator of 5 and 3 is 1

 Result of less than or equal to operator of 5 and 3 is 0

 Result of greater than or equal to operator of 5 and 3 is 1

 Result of double equal to operator of 5 and 3 is 0

 Result of not equal to operator of 5 and 3 is 1

2.1.2 Mixed operands

In a statement or expression if one the operand is real (float) and another one is integer then expression is called as Mixed Mode Arithmetic Expression. If in an expression either operand is of real then output is always in real format. If both operands are real then output will be in real formats.

Example

Real operand and Integer operand = Real operand (Output)
Real operand and Real operand = Real operand (Output).

Types of Arithmetic Operators used in Mixed Mode Expression

"*" - Multiply use for Multiplication
"/"  - Divide use for division
"+" - Plus use for addition
"-" - Minus use for subtraction
"%" - Modulus use for getting a reminder
"**" - Square  use for getting square number

Rules for Evaluation Mixed Mode Arithmetic Expression

Rule 1

Evaluate Expressions always from Left to Right

For Example: 3 + 5 - 4 = 4

Rule 2

Priority of an operator is also considered while calculating an expression

Operator Priorities in descending order

1. (**) Known as Square operator which executes From Right To Left .
   
For example 5**2 is equal to 25

2. (*) Known as multiplication operator which executes From Left to Right
   
For example 5 * 2 is equal to 10

3. (/) Known as Division operator which executes From Left to Right
   
For example 6 / 2 is equal to 3

4. (+) Known as Plus or Addition operator which executes From Left to Right
   
For example 6 + 2 is equal to 8

5. (-) Known as Minus or Subtraction operator which executes From Left to Right
   
For example 6 - 2 is equal to 4

Mixed mode operator example
 
2 + 2 * 5 ** 3

==> 2 + 2 * (5**3)
==> 2 + 2 * 125
==> 2 + (2 * 125)
==> 2 + 250 = 252

Rule 3

If the operands of this operator are of the same type means either Integer or Real, compute the same for result in that operator only.

For Example

Both Real Numbers

double a = 2.0;
double b = 3.0;

Double add = 2.0 + 3.0 = 5.0 (Result in Real Number only)

Both Integer Number

int a = 2;
int b = 3;
int add = 2 + 3 = 5 (Result in Integer Number only)

Rule 4

If one of the operator is Integer and other one is real then convert integer number to real number and compute the result in real number only.

For Example

double a = 5.0;

int b = 5;

Result = 5.0 = 5 = 10.0 (Result in Real Number only).

2.1.3 Type conversion

Implicit type conversion:

Also known as ‘automatic type conversion’.

• Done by the compiler on its own, without any external trigger from the user.
• Generally, takes place when in an expression more than one data type is present. In such condition type conversion (type promotion) takes place to avoid to loose data.
• All the data types of the variables are upgraded to the data type of the variable with largest data type.

bool -> char -> short int -> int ->

       unsigned int -> long -> unsigned ->

       long long -> float -> double -> long double

It is possible for implicit conversions to lose information, signs can be lost (when signed is implicitly converted to unsigned), and overflow can occur (when long is implicitly converted to float).

Example of Type Implicit Conversion:

Output:

x=107, z = 108.000000

Explicit Type Conversion–

This process is also called type casting and it is user defined. Here the user can type cast the result to make it of a particular data type.

The syntax in C:

(type) expression

Type indicated the data type to which the result is converted.

2.1.4 Logical operators

Logical Operators: Logical operators are used to compare logical values of two operands. Following are the list of logical operator in C language. To understand the operation assume variable A contains value 10 and variable contains value 5.

Example:

#include<stdio.h>

#include<conio.h>

void main()

{

 int a,b,c;

 clrscr();

 printf("Enter two numbers");

 scanf("%d %d",&a,&b);

 printf("\n Result of logical and operator of  %d and  %d is %d",a,b,a&&b);

 printf("\n Result of logical or  operator of %d and %d is %d",a,b,a||b);

 printf("\n Result of logical not operator of %d and and %d is %d",a,b,!(a&&b));

 getch();

}

Output:

Enter two numbers

5

3

Result of logical and operator of 5 and 3 is 1

Result of logical or operator of 5 and 3 is 1

Result of logical not operator of 5 and 3 is 0

2.1.5 Bit operations

1. These operators are used to work on the each bits of data. These operators can work on the binary data. If the data is non binary then computer first of all convert it into binary form and then perform the operation. Following are the list of logical operator in C language. To understand the operation assume variable A contains value 10 and variable contains value 5. So the binary values of

A = 0000 1010 and

B = 0000 0101

Example:

#include<stdio.h>

#include<conio.h>

void main()

{

 int a,b,c;

 clrscr();

 printf("Enter two numbers");

 scanf("%d %d",&a,&b);

 printf("\n Result of bitwise and operator of  %d and  %d is %d",a,b,a&b);

 printf("\n Result of bitwise or  operator of %d and %d is %d",a,b,a|b);

 printf("\n Result of bitwise exclusive operator of %d and %d is %d",a,b,a^b);

 printf("\n Result of bitwise left shift operator of %d and %d is %d",a,b,a<<b);

 printf("\n Result of bitwise right shift  operator of %d and %d is %d",a,b,a>>b);

 getch();

}

Output:

Enter two numbers

5

3

Result of bitwise and operator of 5 and 3 is 1

Result of bitwise or operator of 5 and 3 is 7

Result of bitwise exclusive operator of 5 and 3 is 6

Result of bitwise left shift operator of 5 and 3 is 40

Result of bitwise right shift operator of 5 and 3 is 0

2.1.6 Assignment operator

Assignment Operators: Assignment operator is used to assign the value to variable. To understand the operation assume variable A contains value 10 and variable contains value 5.

Example: A=B;

In the above example value of variable B is assign to variable A. Result of this expression is value of A is 5 and value of B is 5.

2.1.7 Operator precedence and associativity

Expression may have one or more operators in it. If expression has multiple operators then these operators are solved according to hierarchy of operators. Hierarchy determines the order in which these operators are executed.

Table : Hierarchy of operators

Ex. 1 

Find the result of the following operations.

Soln. :

Ex. 2

Using Hierarchy chart, list the order in which following operations would be processed?

1. +,-,*   2. OR,*,<  

3. NOT, AND,*  4. AND,OR,NOT 

5. NOT,+,\  6. MOD,\,< 

7. <,AND,>,+

Soln. :

In conditional branching decision point is based on the run time logic. Conditional branching makes use of both selection logic and iteration logic. In conditional branching flow of program is transfer when the specified condition is satisfied.

Fig. Flowchart for conditional branching

2.2.1 Applying if and switch statements, nesting if and else

In conditional branching change in sequence of statement execution is depends upon the specified condition. Conditional statements allow programmer to check a condition and execute certain parts of code depending on the result of conditional expression. Conditional expression must be resulted into Boolean value. In C language, there are two forms of conditional statements:

1. if-----else statement: It is used to select one option between two alternatives

2. switch statement: It is used to select one option between multiple alternative

•   if Statements

This statement permits the programmer to allocate condition on the execution of a statement. If the evaluated condition found to be true, the single statement following the "if" is execute. If the condition is found to be false, the following statement is skipped. Syntax of the if statement is as follows

In the above syntax, “if” is the keyword and condition in parentheses must evaluate to true or false. If the condition is satisfied (true) then compiler will execute statement1 and then statement2. If the condition is not satisfied (false) then compiler will skip statement1 and directly execute statement2.

                 if-----else statement

This statement permits the programmer to execute a statement out of the two statements. If the evaluated condition is found to be true, the single statement following the "if" is executed and statement following else is skipped. If the condition is found to be false, statement following the "if" is skipped and statement following else is executed. 

In this statement “if” part is compulsory whereas “else” is the optional part. For every “if” statement there may be or may not be “else” statement but for every “else” statement there must be “if” part otherwise compiler will gives “Misplaced else” error. 

Syntax of the “if----else” statement is as follows

In the above syntax, “if” and “else” are the keywords and condition in parentheses must evaluate to true or false. If the condition is satisfied (true) then compiler will execute statement1 and skip statement2. If the condition is not satisfied (false) then compiler will skip statement1 and directly execute statement2.

Nested if-----else statements :

Nested “if-----else” statements are used when programmer wants to check multiple conditions. Nested “if---else” contains several “if---else” a statement out of which only one statement is executed. Number of “if----else” statements is equal to the number of conditions to be checked. Following is the syntax for nested “if---else” statements for three conditions

In the above syntax, compiler first check condition1, if it trues then it will execute statement1 and skip all the remaining statements. If condition1 is false then compiler directly checks condition2, if it is true then compiler execute statement2 and skip all the remaining statements. If condition2 is also false then compiler directly checks condition3, if it is true then compiler execute statement3 otherwise it will execute statement 4.

Note:

If the test expression is evaluated to true,

• Statements inside the body of if are executed.

• Statements inside the body of else are skipped from execution.

If the test expression is evaluated to false,

• Statements inside the body of else are executed

• Statements inside the body of if are skipped from execution.

// Check whether an integer is odd or even

#include <stdio.h>

int main() {

    int number;

    printf("Enter an integer: ");

    scanf("%d", &number);

    // True if the remainder is 0

    if  (number%2 == 0) {

        printf("%d is an even integer.",number);

    }

    else {

        printf("%d is an odd integer.",number);

    }

    return 0;

}

Program to relate two integers using =, > or < symbol

#include <stdio.h>

int main() {

    int number1, number2;

    printf("Enter two integers: ");

    scanf("%d %d", &number1, &number2);

    //checks if the two integers are equal.

    if(number1 == number2) {

        printf("Result: %d = %d",number1,number2);

    }

    //checks if number1 is greater than number2.

    else if (number1 > number2) {

        printf("Result: %d > %d", number1, number2);

    }

    //checks if both test expressions are false

    else {

        printf("Result: %d < %d",number1, number2);

    }

    return 0;

}

•   Switch Statements

This statement permits the programmer to choose one option out of several options depending on one condition. When the “switch” statement is executed, the expression in the switch statement is evaluated and the control is transferred directly to the group of statements whose “case” label value matches with the value of the expression. Syntax for switch statement is as follows:

In the above, “switch”, “case”, “break” and “default” are keywords. Out of which “switch” and “case” are the compulsory keywords whereas “break” and “default” is optional keywords.

• “switch” keyword is used to start switch statement with conditional expression.
• “case” is the compulsory keyword which labeled with a constant value. If the value of expression matches with the case value then statement followed by “case” statement is executed.
• “break” is the optional keyword in switch statement. The execution of “break” statement causes the transfer of flow of execution outside the “switch” statements scope. Absence of “break” statement causes the execution of all the following “case” statements without concerning value of the expression.
• “default” is the optional keyword in “switch” statement. When the value of expression is not match with the any of the “case” statement then the statement following “default” keyword is executed.

Example: Program to spell user entered single digit number in English is as follows

Output

Enter a number

5

Five

2.2.2 Use of break and default with switch

In unconditional branching statements are executed without concerning the condition. Unconditional statements allow programmer to transfer the flow of execution to any part of the program. In C language, there are four types of unconditional statements:

1. Break statement: It is the unconditional jump instruction. It is used mainly with “switch” and loop statements. The execution of “break” instruction, transfer the flow of program outside the loop or “switch” statement Syntax of “break” statement is as follows                                                                     

 When “break” statement used inside loops then execution of “break” statement causes the immediate termination of loop and compiler will execute next statement after the loop statement.             

2.     Goto statement: “goto” statement is used to transfer the flow of program to any part of the program. The syntax of “go to” statement is as follows              

 In the above syntax “goto” is keyword which is used to transfer the flow of execution to the label specified after it. Label is an identifier that is used to mark the target statement to which the control is transferred. The target statement must be labeled and the syntax is as follows

 In the above syntax label name can be anything but it should be same as that of name of the label specified in “goto” statement, a colon must follow the label. Each labeled statement within the function must have a unique label, i.e., no two statements can have the same label.

3.     Continue statement: It is used mainly with “switch” and “loop” statements. The execution of “continue” instruction, skip the remaining iteration of the loop and transfer he flow of program to the loop control instruction. Syntax of “continue” statement is as follows

4. Return statement: The “return” statement terminates the execution of the current function and return control to the calling function. The “return” statement immediately ends the function, ignoring everything else in the function after it is called. It immediately returns to the calling function and continue from the point that it is called. Return also able to "return" a value which can be use in the calling function.