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Chapter 6 Fundamental Types

Chapter 6 Fundamental Types. Dept of Computer Engineering Khon Kaen University. Major Concepts. Data types Numeric types Boolean type Enumeration type Character type Arithmetic operations Type conversions Run-time errors: Numeric overflow Round-off error. Numeric Data Types.

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Chapter 6 Fundamental Types

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  1. Chapter 6 Fundamental Types Dept of Computer Engineering Khon Kaen University

  2. Major Concepts • Data types • Numeric types • Boolean type • Enumeration type • Character type • Arithmetic operations • Type conversions • Run-time errors: • Numeric overflow • Round-off error 178110: Computer Programming (II/2546)

  3. Numeric Data Types • There are two kinds of numbers • Whole numbers, Integers (จำนวนเต็ม) • Including negative whole numbers, 0, and positive whole numbers • Examples: 0, 1, 2, -1, -2 • Decimal numbers • Fraction where the denominator is a power of ten and is therefore expressed using a decimal point. • Examples: 0.37 • Rational numbers: จำนวนจริงเป็นตัวเลขที่สามารถเขียนอยู่ในรูปทศนิยม, such as 2/10 • Irrational numbers: cannot be expressed as a fraction, such as 178110: Computer Programming (II/2546)

  4. Fundamental Types • Standard C++ has 14 different fundamental types: 11 integral types and 3 floating-point types • Integral Types • Boolean Type • bool • Enumeration Type • enum 178110: Computer Programming (II/2546)

  5. Fundamental Types (Cont.) • Integral Types • Character Types • char • unsigned char • wchar_t • Integer Types • short • int • long 178110: Computer Programming (II/2546)

  6. Fundamental Types (Cont.) • Integral Types • Integer Types • unsigned short • unsigned int • unsigned long • Floating-point Types • float • double • long double 178110: Computer Programming (II/2546)

  7. The Boolean Type • A boolean type is an integral type whose variables can have only two values: • False and true • These values are stored as the integers • 0 and 1 • The boolean type in Standard C++ is named bool 178110: Computer Programming (II/2546)

  8. Boolean Variables #include <iostream> using namespace std; int main() {// print the value of a boolean variable bool flag = false; cout << “flag = “ << flag << endl; flag = true; cout << “flag = “ << flag << endl; } 178110: Computer Programming (II/2546)

  9. Enumeration Types • An enumeration type is an integral type that is defined by the user with the syntax enum typename { enumerator-list }; • enum is a C++ keyword • typename is an identifier that names the type being defined • enumerator-list is a list of acceptable values of the variable that has that typename 178110: Computer Programming (II/2546)

  10. Enumeration Types (Cont.) • Example: enum Semester {FALL, WINTER, SPRING, SUMMER}; • We can then declare variables of this type • Semester s1, s2; • We can use those variables and those type values as we would with predefined types • s1 = FALL; • s2 = WINTER; 178110: Computer Programming (II/2546)

  11. Enumeration Types • The actual values defined in the enumerator-list are called enumerators • In fact, they are ordinary integer constants • Example: the enumerators FALL, WINTER, SPRING, and SUMMER that are defined for the semester type could have been defined like this: • const int FALL = 0; • const int WINTER = 1; • const int SPRING = 2; • const int SUMMER = 3; 178110: Computer Programming (II/2546)

  12. Enumeration Types (Cont.) • The values 0, 1, … are assigned automatically when the type is defined • These default values can be overridden in the enumerator-list: • enum Coin {PENNY = 1, NICKEL = 5, DIME = 10, QUARTER = 25}; 178110: Computer Programming (II/2546)

  13. Enumeration Types (Cont.) • If integer values are assigned to only some of the enumerators, then the ones that follow are given consecutive values • enum Month {JAN=1, FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT, NOV, DEC}; • Since enumerators are simply integer constants, it is legal to have several different enumerators with the same value: • enum Answer {NO = 0, FALSE = 0, YES = 1, TRUE = 1, OK = 1} 178110: Computer Programming (II/2546)

  14. Enumeration Types (Cont.) • Enumeration types are usually defined to make code more self-documenting, i.e., easier for humans to understand • enum Sex {FEMALE, MALE}; • enum Day {SUN, MON, TUE, WED, THU, FRI, SAT}; • enum Radix {BIN=2, OCT=8, DEC=10, HEX=16}; 178110: Computer Programming (II/2546)

  15. Enumeration Types (Cont.) • Enumerators must be valid identifiers • This following definition would not be valid • enum Grade {F, D, C-, C, C+, B-, B, A-, A}; • Why is it invalid? • ‘+’ and ‘-’ cannot be used in identifiers • Same values cannot be used in the same scope (same place) • enum Month {JAN, …, OCT, …} • enum Radix {BIN, OCT, …} 178110: Computer Programming (II/2546)

  16. Character Types • A character type is an integral type whose variables represent characters like the letter ‘A’ or the digit ‘s’ • Characters are delimited by the apostrophe (‘) • Like all integral type values, character values are stored as integers • In C++, the type name for a character is char 178110: Computer Programming (II/2546)

  17. Character Types (Cont.) • Using the ASCII encoding standard, the examples of the values that represent these characters are as follow: ‘ ’ represented by 32 ‘+’ represented by 43 ‘A’ represented by 65 ‘a’ represented by 97 178110: Computer Programming (II/2546)

  18. Escape Sequences • Escape sequences are used to print out special characters • \‘ Single quote • \“ Double quote • \\ Backslash • \n Newline • \t Horizontal tab • \v Vertical tab 178110: Computer Programming (II/2546)

  19. Integer Types • There are 6 integer types in Standard C++ • short: 2 bytes • int: 4 bytes • long: 4 bytes • unsigned short: 2 bytes • unsigned int: 4 bytes • unsigned long:4 bytes • The least value of variables with unsigned types are 0 178110: Computer Programming (II/2546)

  20. Integer Type Ranges • This program prints the numeric ranges of the 6 integer types in C++ #include <iostream> #include <limits> // defines the constants SHRT_MIN, etc. using namespace std; int main() { // prints some of the constants stored in the <limits> header: cout << "minimum short = " << SHRT_MIN << endl; cout << "maximum short = " << SHRT_MAX << endl; cout << "minimum unsigned short = 0" << endl; cout << "maximum unsigned short = " << USHRT_MAX << endl; cout << "minimum int = " << INT_MIN << endl; cout << "maximum int = " << INT_MAX << endl; cout << "minimum unsigned int = 0" << endl; cout << "maximum unsigned int = " << UINT_MAX << endl; cout << "minimum long= " << LONG_MIN << endl; cout << "maximum long= " << LONG_MAX << endl; cout << "minimum unsigned long = 0" << endl; cout << "maximum unsigned long = " << ULONG_MAX << endl; } 178110: Computer Programming (II/2546)

  21. Integer Type Ranges (Cont.) • The output of the program minimum short = -32768 maximum short = 32767 minimum unsigned short = 0 maximum unsigned short = 65535 minimum int = -2147483648 maximum int = 2147483647 minimum unsigned int = 0 maximum unsigned int = 4294967295 minimum long= -2147483648 maximum long= 2147483647 minimum unsigned long = 0 maximum unsigned long = 4294967295 178110: Computer Programming (II/2546)

  22. Arithmetic Operations • C++ performs its numerical calculations by means of the five arithmetic operators: +, -, *, /, and % • Operations are performed in this order • 1. ( ) Perform the operation inside ( ) first • 2. +,- Then, perform unary plus and unary minus, such as +32, -16 • 3. *,/,% • 4. +, - • If there is more than one operation with the same order, perform from left to right 178110: Computer Programming (II/2546)

  23. Arithmetic Operations (Cont.) • Math: a = bc/de • C++: a = (b*c)/(d*e) • Is b*c/d*e == (b*c)/(d*e)? • Is b*c*d*e == (b*c)*(d*e)? • Math: m = • C++: m = (y-b)/(x-a) • Is y-b/x-a == (y-b)/(x-a)? • Is y-b-x-a == (y-b)-(x-a)? 178110: Computer Programming (II/2546)

  24. Arithmetic Operations (Cont.) • -34*32 = ? • Choice a: (-34)*32 • Choice b: -(34*32) • 7 – 2 % 3 = ? • Choice a: (7-2)% 3 • Choice b: 7 – (2 %3) • 3 + 2 / 4 = ? • Choice a: 3 + (2/4) • Choice b: (3 + 2)/ 4 178110: Computer Programming (II/2546)

  25. Arithmetic Operations (Cont.) #include <iostream> using namespace std; int main() { // tests operators +, -, *, /, and %: int m=54; int n=20; cout << "m = " << m << " and n = " << n << endl; cout << "m+n = " << m+n << endl; // 54+20 = 74 cout << "m-n = " << m-n << endl; // 54-20 = 34 cout << "m*n = " << m*n << endl; // 54*20 = 1080 cout << "m/n = " << m/n << endl; // 54/20 = 2 cout << "m%n = " << m%n << endl; // 54%20 = 14 return 0; } 178110: Computer Programming (II/2546)

  26. Increment & Decrement Operators • The values of integral objects can be incremented by one with the ++ operator and decremented by one with the – operator • Each of “++” and “--” operator has two versions: • A “pre” version • A “post” version 178110: Computer Programming (II/2546)

  27. ++ & -- Operators • The “pre” version performs the operation on the object before the resulting value is used in its context • Example: n = ++m  m= m + 1, n = m • The “post” version performs the operation on the operation after the object’s current value ahs been used • Example: n = m++  n = m, m = m + 1 178110: Computer Programming (II/2546)

  28. ++ & -- Operators (Cont.) int main() { // shows the difference between m++ and ++m m = 44; n = ++m; cout << “m = “ << m << “, n = “ << n << endl; m = 44; n = m++; cout << “m = “ << m << “, n = “ << n << endl; } 178110: Computer Programming (II/2546)

  29. Composite Assignment Operators • The standard assignment operator in C++ is the equal sign ‘=‘ • C++ also includes the composite assignment operators: ‘+=‘, ‘-=‘, ‘*=‘, ‘/=‘, and ‘%=‘ • Examples: • A += B;  A = A + B; • A *= B;  A = A * B; 178110: Computer Programming (II/2546)

  30. Composite Assignment Operators #include <iostream> using namespace std; int main() { // tests arithmetic assignment operators: int n=22; cout << "n = " << n << endl; n += 9; // adds 9 to n cout << "After n += 9, n = " << n << endl; n %= 7; // mod n with 7 cout << "After n %= 7, n = " << n << endl; } 178110: Computer Programming (II/2546)

  31. Floating-Point Types • C++ has three types for storing values with floating-point • float: use 4 bytes • double: use 8 bytes • long double: use 8, 10, 12, or 16 bytes • On most systems, double uses twice as many bytes as float 178110: Computer Programming (II/2546)

  32. Floating-Point Arithmetic int main() { double x = 54.0; double y = 20.0; cout << “x*y = “ << x*y << endl; // 1080 cout << “x/y = “ << x/y << endl; // 2.7 } • If x and y have type ‘int’, what is the value of x/y? • 2 178110: Computer Programming (II/2546)

  33. Using the sizeof Operator • The programs use the sizeof operator which returns the size in bytes of the type specified • Examples: cout << “size of integer is “ << sizeof(int) << endl; cout << “size of float is “ << sizeof(float) << endl; • Output: • size of integer is 4 • size of float is 4 178110: Computer Programming (II/2546)

  34. Type Conversions int n = 22; float x = 3.14159; n += x; x += n; cout << “n is “ << n << endl; cout << “x is “ << x << endl; • What are the values of n and x? n is 25 x is 28.1416 178110: Computer Programming (II/2546)

  35. Type Conversions (Cont.) • If T is one type and v is a v value of another type, then the expression • T(v) converts v to type T • This process is called type casting • Example: double v = 1234.56789; int n = (int) v; cout << “n is “ << n endl; • What is the value of n? • n is 1234 178110: Computer Programming (II/2546)

  36. Numeric Overflow • Computers are finite, so the range of any type must also be finite • But in mathematics, there are infinitely many integers • Consequently, computers are manifestly prone to error when their numeric values become too large • This kind of error is called numeric overflow 178110: Computer Programming (II/2546)

  37. Numeric Overflow (Cont.) int main() { // print n until it overflows int n = 10000; cout << “sizeof(int) is “ << sizeof(int) << endl; cout << “n is “ << n << endl; n *= 10000; cout << “n is “ << n << endl; n *= 10000; cout << “n is “ << n << endl; return 0; } • What is the maximum n can be? • 2147483647 178110: Computer Programming (II/2546)

  38. Integer Overflow (Cont.) • What is the size of an integer in bits? • 32 bits • 232 = 4,294,967,296 • What is the maximum value of a variable with type ‘int’? • 2,147,483,647 • ((232)/2) - 1 • What is the minimum value of a variable with type ‘int’? • -(232)/2 178110: Computer Programming (II/2546)

  39. Floating-Point Overflow #include <iostream> using namespace std; int main() { // prints x until it overflows: float x=1000.0; cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; x *= x; // multiplies n by itself; i.e., it squares x cout << "x = " << x << endl; } 178110: Computer Programming (II/2546)

  40. Floating-Point Overflow (Cont.) • Output • x = 10000 • x = 1e+08 • x = 1e+16 • x = 1e+32 • x = inf • Integer overflow “wrap around” to negative integers • Floating-point overflow “sinks” into the abstract notion of infinity 178110: Computer Programming (II/2546)

  41. Round-off Error • Round-off error is another kind of error that often occurs when computers do arithmetic on rational numbers • Example: • The number 1/3 might be stored as 0.33333, which is not exactly equal to 1/3 • The difference is called round-off error • In some cases, these errors can cause serious problems 178110: Computer Programming (II/2546)

  42. Round-Off Error (Cont.) // Example 2.14 on page 28 // Round-off Error #include <iostream> using namespace std; int main() { // illustrates round-off error:: double x = 1000/3.0; cout << "x = " << x << endl; // x = 1000/3 double y = x - 333.0; cout << "y = " << y << endl; // y = 1/3 double z = 3*y - 1.0; cout << "z = " << z << endl; // z = 3(1/3) - 1 if (z == 0) cout << "z == 0.\n"; else cout << "z does not equal 0.\n"; // z != 0 } 178110: Computer Programming (II/2546)

  43. Round-Off Error (Cont.) • Program output • x = 1000/3 = 333.333 // x = 1000/3 • y = x – 333 = 0.333333 // y = 1/3 • z = 3*y – 1.0 = -5.68434e-14 // z = 3(1/3) - 1 • z does not equal 0. // z != 0 • It is better to avoid tests for equality with floating-point types • Overflow and round-off errors are run-time errrors 178110: Computer Programming (II/2546)

  44. E-Format for Floating-Point Values • When input or output, floating-point values may be specified in either of two formats: • Fixed-point format Example: 333.333, 0.1 • Scientific format Example: -5.68434x10-14 = -5.68434e-14 178110: Computer Programming (II/2546)

  45. E-Format (Cont.) • Letter e stands for “exponent on 10” • Thus, e-14 means 10-14 • The scientific format is thus usually used to express very small or very large numbers • You can use either e or E in the scientific format 178110: Computer Programming (II/2546)

  46. Scope • The scope of an identifier is that part of the program where it can be used • Variables cannot be used before they are declared • The scope of a variable extends from the point where it is declared to the end of the internal block within which it is declared { int a = 2; // a can be used from this point } a cannot be used here 178110: Computer Programming (II/2546)

  47. Scope (Cont.) #include <iostream> using namespace std; int main() { // illustrates the scope of variables: x = 11; // Is this line OK? int x; { x = 22; // Is this line OK? y = 33; // Is this line OK? int y; y = 11; // Is this line OK? } x = 66; // Is this line OK? y = 77; // Is this line OK? } 178110: Computer Programming (II/2546)

  48. Scope (Cont.) int x = 11; int main() { int x = 22; { int x = 33; cout << “In block inside main(): x = “ << x << endl; } cout << “In main(): x = “ << x << endl; cout << “In main(): ::x = “ << ::x << endl; } • The scope resolution operator :: is to access the global x that is otherwise hidden in main() 178110: Computer Programming (II/2546)

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