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3. Basic Types, Operators and Expressions

Table of Contents


Variables

Like in other high-level programming languages, in C, we can assign symbolic names, known as variables, for storing information in memory. Then we can refer to those pieces of information in memory by using the symbolic variable name, instead of having to use the raw address in memory. Variables can be used to store floating-point numbers, characters, and even pointers to other locations in memory.

Variable names

There are some restrictions on the names of variables in C. Names are made up of letters and digits, but the first character must be a letter (not a digit). The underscore "_" counts as a letter. Also remember in unix, uppercase and lowercase letters are distinct and so Age is distinct from age.

Here is a list of reserved keywords in C that cannot be used as variable names:

_Bool default if sizeof while
_Complex do inline static  
_Imaginary double int struct  
auto else long switch  
break enum register typedef  
case extern restrict union  
char float return unsigned  
const for short void  
continue goto signed volatile  

Data Types and Sizes

There are four basic data types in C, their meaning, and their size (on my MacBook Pro 15-inch, Mid 2010):

Type Meaning Size (bytes) Size (bits)
char a single byte, capable of holding one character 1 byte 8 bits
int an integer 4 bytes 32 bits
float single-precision floating point number 4 bytes 32 bits
double double-precision floating point number 8 bytes 64 bits

Binary representation

There are also qualifiers short, long, signed and unsigned, that can be applied to these basic types.

Qualifier Size (bytes) Size (bits)
short int 2 bytes 16 bits
long int 8 bytes 64 bits
long double 16 bytes 128 bits
     

We have been talking about variable types and how many bytes they take up in memory. An important quantity to know about is that one byte is made up of 8 bits. One bit can take on two possible values: 0 or 1. An unsigned 8-bit variable can take on values between 0 and (2^{8})-1 = 255. A signed 8-bit variable can take on values between -127 and +127.

So when a variable is signed, it can take on negative values, and half of it's total range is spread below zero, and the other half above zero.

A signed int can take on values between -2,147,483,648 and +2,147,483,648. If we want to be able to represent integers larger than +2,147,483,648 then we can either use more bits (e.g. by using a long int), or by forcing all 32 bits of our int to be used on the positive side of zero. An unsigned int (4 bytes or 32 bits) can take on values between 0 and 4,294,967,295.

How many bytes on your machine?

Here is a small C program that will print out the size of some basic C types on your machine. Enter it into your source code editor, and save it to a file called my_types.c

#include <stdio.h>

int main(int argc, char *argv[]) {
  printf("a char is %ld bytes\n", sizeof(char));
  printf("an int is %ld bytes\n", sizeof(int));
  printf("an float is %ld bytes\n", sizeof(float));
  printf("a double is %ld bytes\n", sizeof(double));
  printf("a short int is %ld bytes\n", sizeof(short int));
  printf("a long int is %ld bytes\n", sizeof(long int));
  printf("a long double is %ld bytes\n", sizeof(long double));
  return 0;
}

Then compile and run using the following commands:

gcc -o my_types my_types.c
./my_types

and you should see something like the following output:

a char is 1 bytes
an int is 4 bytes
an float is 4 bytes
a double is 8 bytes
a short int is 2 bytes
a long int is 8 bytes
a long double is 16 bytes

Constants

Constants are values that that do not change after they have been defined.

Numeric Constants

An example of an int constant is the number 1234. An example of a floating-point constant (by default typed as a double) is 123.4 and 1e-2. We can write numbers in octal or hexadecimal instead of decimal: octal by using a leading zero (0) and hexadecimal by using a leading zero-x (0x). Decimal 31 can be written as 037 in octal and 0x1f or 0X1F in hexadecimal. Here are some examples of defining numeric constants:

int year = 1984;       // integer constant 1984
int octalYear = 03700; // 1984 in octal
int hexYear = 0x7c0;   // 1984 in hexadecimal

Here is some code to show how to print integers in various representations. Type it into your source code editor, and save it as numerics.c.

#include <stdio.h>

int main() {
  printf("1984 in decimal is %d\n", 1984);
  printf("1984 in octal is 0%o\n", 1984);
  printf("1984 in hexadecimal is 0x%x\n", 1984);
  printf("0123 is octal for %d\n", 0123);
  printf("0x12f is hexadecimal for %d\n", 0x12f);
  return 0;
}
gcc -o numerics numerics.c
./numerics
1984 in decimal is 1984
1984 in octal is 03700
1984 in hexadecimal is 0x7c0
0123 is octal for 83
0x12f is hexadecimal for 303

Character Constants

A character constant is written between single quotes, for example, 'x'. Characters in C are represented using integer values, from the ASCII character set. ASCII codes range between 0 and 255. The upper-case alphabet starts at 65 (A) and ends at 90 (Z); the lowercase alphabet starts at 97 (a) and ends at 122 (z). Other symbols such as (, !, tab, carriage return, etc, are also represented in the ASCII table. See ASCII (wikipedia) and AsciiTable for the mapping between characters and integer ascii codes.

An important character constant to know about is the constant '\0' which represents the character with value zero, sometimes called the NULL character. We will see later when we talk about string handling in C that '\0' is used to terminate variable-length strings.

String Constants

String constants can be specified using a sequence of zero or more characters enclosed within double quotes, e.g. "C is fun". A string constant is technically an array of characters that is terminated by a null character '\0' at the end. This means that the storage required to represent a string of length n is actually n+1. Thus we can store strings of arbitrary length in memory as long as they are terminated by a null character (so we know when they stop). We will talk about arrays later.

Enumeration Constants

An enumeration constant is a list of constant integer values, that you can assign to arbitrary labels. They provide a convenient way to associate constant values with names. For example you could store the months of the year like this:

enum months { JAN=1, FEB, MAR, APR, MAY, JUN,
              JUL, AUG, SEP, OCT, NOV, DEC };

Now you have defined a new enumerated constant data type called months. Now a variable of type months can only take on values as defined above. You can use the symbolic names (e.g. JAN) in place of their integer counterparts, for example like this:

months the_month;
...
if (the_month == JAN) {
  printf("it's January\n");
}

Why not just use strings to represent months? One reason is that in C strings are slightly clunky to work with, especially compared to interpreted languages like Python, R, etc. Comparing two strings in C is not as easy as typing if (the_month == "JAN") … it requires a call to a function in string.h called strcmp().

Another reason is that because enum data types are represted as integers, you can do integer operations (comparisons, arithmetic, etc) on them… so for example you could do something clever like:

if ((the_month > APR) && (the_month < SEP)) {
  printf("it's summer!\");
}

Declarations

Unlike in languages like Python, R, Octave/Matlab, etc, which are dynamically typed languages, the C language is a statically typed language. From a practical point of view, this means in C, we have to declare, up front, the type of every variable we use. In languages like Python we can do crazy stuff like this:

a = 123.456
b = 50.2
c = 100.0
d = [a, b, c]
print a, b, c, d
123.456 50.2 100.0 [123.456, 50.2, 100.0]

The Python interpreter will figure out what type to assign to a, b, c and d based on evaluating the right-hand side of each declaration. In C, we have to explicitly declare the type of each variable like this:

#include <stdio.h>

int main() {
  double a = 123.456;
  double b = 50.2;
  double c = 100.0;
  double d[] = {a, b, c};
  printf("a=%.3f, b=%.3f, c=%.3f, d=[%.3f, %.3f, %.3f]\n", 
                a, b, c, d[0], d[1], d[2]);
  return 0;
}
a=123.456, b=50.200, c=100.000, d=[123.456, 50.200, 100.000]

We haven't talked about arrays yet but we will later in the tutorial.

Expressions

Like in any other programming language, in C, there are a number of arithmetic relational and logical operators we can use to write expressions that are made up of simpler basic types.

Arithmetic Operators

The following binary arithmetic operators can be used in C: +, -, *, / and the modulus operator %. When writing arithmetic expressions we must always be aware of operator precedence, which is the order in which operators are applied when evaluating an expression.

For example 4+5*6 evaluates to 34, because the * operator has precedence over the + operator, and so the expression is evaluated as 4 + (5*6), not (4+5)*6. My own strategy to deal with this is to always use brackets to explicitly denote desired precedence in arithmetic expressions. So instead of writing:

double q = a*x*x+b*x+c;

which is a perfectly accurate expression of the quadratic equation:

\begin{equation} ax^{2} + bx + c \end{equation}

I would rather code it like this:

double q = (a*x*x) + (b*x) + c;

Another illustration of operator precedence: What are the values of the result1, result2 and result3 variables in the following code?

#include <stdio.h>
int main() {
  int a=100, b=2, c=25, d=4;
  int result1, result2, result3;
  result1 = a * b + c * d;
  result2 = (a * b) + (c * d);
  result3 = a * (b + c) * d;
  printf("result1=%d, result2=%d, result3=%d\n",
         result1, result2, result3);
  return 0;
}

Always using brackets will avoid cases where operator precedence messes up your calculations. These errors are very hard to debug.

Wikipedia provides a chart showing operator precedence.

Relational and Logical Operators

The relational operators are >, >=, < and <=, which all have equal precedence. There are also two equality operators: == and !=.

A very common gotcha in C programming is to erroneously use the assignment operator = when you mean to use the equality operator ==, for example:

if (grade = 49) grade = grade + 1; // INCORRECT !!!
if (grade == 49) grade = grade + 1; // CORRECT

In line 1 above, the expression grade=49 doesn't test for the equality of the variable grade and the constant 49, it assigns the value 49 to the variable grade. What we really want is in line 2 where we use the equality operator == to test if grade==49. This bug is a tough one to spot when it happens.

There are two logical operators && (logical AND) and || (logical OR).

By default in C, the results of relational and logical operators are evaluated to integer values: 0 for FALSE and 1 for TRUE.

Increment and Decrement Operators

You may come across two unusual-looking operators that may be used as a shorthand for incrementing and decrementing variables. The ++ and -- operators add 1 and subtract 1, respectively, from their operands. For example in the following code snippet, we increment the int variable a and we decrement the int variable b:

#include <stdio.h>

int main(int argc, char *argv[]) {

  int a = 0;
  int b = 0;

  printf("a=%d, b=%d\n", a, b);

  a++;
  b--;

  printf("a=%d, b=%d\n", a, b);

  return 0;
}
a=0, b=0
a=1, b=-1

A note of caution, you can also use these two operators in a different way, by putting the operator before the operand, e.g. ++a and --b. When the operand is used before the operand this is called a prefix operator, and when it is used after the operand it is called a postfix operator. When using ++ and -- as a prefix operator, the increment (or decrement) happens before its value is used. As postfix operators, the increment (or decrement) happens after its value has been used. Here is a concrete example:

#include <stdio.h>

int main(int argc, char *argv[]) {

  int n, x;

  n = 3;
  x = 0;
  printf("n=%d, x=%d\n", n, x);
  x = n++;
  printf("n=%d, x=%d\n\n", n, x);

  n = 3;
  x = 0;
  printf("n=%d, x=%d\n", n, x);
  x = ++n;
  printf("n=%d, x=%d\n", n, x);

  return 0;
}
n=3, x=0
n=4, x=3

n=3, x=0
n=4, x=4

In lines 7 to 11, x is set to 3 (the value of n), and then n is incremented by 1. In lines 13 to 17, n is incremented first and becomes 4, and then x is set to the resulting value (also 4).

If you think this is all a bit unnecessarily confusing, then you agree with me. I typically don't use these operators because of the risk of mis-using them, and so when I want to increment or decrement a value by 1, I just write it out explicitly:

int x;
x = x + 1;

Type Conversions

There are two kinds of type conversion we need to talk about: automatic or implicit type conversion and explicit type conversion.

Implicit Type Conversion

The operators we have looked at can deal with different types. For example we can apply the addition operator + to an int as well as a double. It is important to understand how operators deal with different types that appear in the same expression. There are rules in C that govern how operators convert different types, to evaluate the results of expressions.

For example, when a floating-point number is assigned to an integer value in C, the decimal portion of the number gets truncated. On the other hand, when an integer value is assigned to a floating-point variable, the decimal is assumed as .0.

This sort of implicit or automatic conversion can produce nasty bugs that are difficult to find, especially for example when performing multiplication or division using mixed types, e.g. integer and floating-point values. Here is some example code illustrating some of these effects:

#include <stdio.h>
int main() {
  int a = 2;
  double b = 3.5;
  double c = a * b;
  double d = a / b;
  int e = a * b;
  int f = a / b;
  printf("a=%d, b=%.3f, c=%.3f, d=%.3f, e=%d, f=%d\n",
          a, b, c, d, e, f);
  return 0;
}

Explicit Type Conversion

Type Casting

There is a mechanism in C to perform type casting, that is to force an expression to be converted to a particular type of our choosing. We surround the desired type in brackets and place that just before the expression to be coerced. Look at the following example code:

#include <stdio.h>
#include <stdio.h>
int main() {
  int a = 2;
  int b = 3;
  printf("a / b = %.3f\n", a/b);
  printf("a / b = %.3f\n", (double) a/b);
  return 0;
}

String Conversion Library Functions

There are some built-in library functions in C to perform some basic conversions between strings and numeric types. Two useful functions to know about convert ascii strings to numeric types: atoi() (ascii to integer) and atof() (ascii to floating-point). We need to #include the library stdlib.h in order to use these functions.

To convert from numeric types to strings things are a bit more difficult. First we have to allocate space in memory to store the string. Then we use the sprintf() built-in function to "print" the numeric type into our string.

Here is some example code (typeConvert.c) illustrating conversion of strings to numerics, and vice-versa:

#include <stdio.h>
#include <stdlib.h>

int main() {
  char intString[] = "1234";
  char floatString[] = "328.4";
  int myInt = atoi(intString);
  double myDouble = atof(floatString);
  printf("intString=%s, floatString=%s\n", intString, floatString);
  printf("myInt=%d, myDouble=%.1f\n\n", myInt, myDouble);

  int a = 2;
  double b = 3.14;
  char myString1[64], myString2[64];
  sprintf(myString1, "%d", a);
  sprintf(myString2, "%.2f", b);
  printf("a=%d, b=%.2f\n", a, b);
  printf("myString1=%s, myString2=%s", myString1, myString2);
  return 0;
}
intString=1234, floatString=328.4
myInt=1234, myDouble=328.4

a=2, b=3.14
myString1=2, myString2=3.14

Defining your own type names using typedef

In C you can assign an alternate name to a data type, any name you want. The typedef statement allows you to do this.

For example we can use typedef to define a type called "Counter" which is an alternate name for an integer, like this:

typedef int Counter;

Now we can declare variables to be of type "Counter":

typedef int Counter;
Counter i, j, k;

Typedef isn't used particularly often in most basic C code, but you may come across it in applications requiring a high degree of portability. New types may be defined for basic variables and typedef may be used in header files to tailor the program to the target machine.

One place you may see typedef used more often is to simplify the declaration of compound types such as the struct type (which we will see later).

Exercises

  • 1 Write a program that converts 27^{°} from degrees Fahrenheit (F) to degrees Celsius (C) using the following formula, and write the result to the screen:
\begin{equation} C = \frac{(F-32)}{1.8} \end{equation}
  • 2 Write a program that computes the (two) roots of the quadratic equation:

    \begin{equation} a x^{2} + bx + c = 0 \end{equation}

    where \(a=1.2\), \(b=2.3\) and \(c=-3.4\).

    You can hard-code values of \(a\), \(b\) and \(c\) and then compute and print the two solutions for \(x\), to 5 decimal places. You can use WolframAlpha to check your arithmetic.

Solutions


Paul Gribble | Summer 2012
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