chapter 7 simple date types j. h. wang ( 王正豪 ), ph. d. assistant professor dept. computer...

Chapter 7Simple Date Types

J. H. Wang (王正豪 ), Ph. D.

Assistant Professor

Dept. Computer Science and Information Engineering

National Taipei University of Technology

Copyright ©2004 Pearson Addison-Wesley. All rights reserved. 7-2

Representation and Conversion of Numeric Types

• Simple data type – a data type used to store a single value

• Differences between numeric types– integers are faster– storage space– loss of accuracy with type double numbers– data represented in memory is computer

dependent


Floating-point Format

• double

• divided into two sections: the mantissa and the exponent

• mantissa– between 0.5 and 1.0 for positive numbers and

between -0.5 and -1.0 for negative– real number = mantissa X 2exponent


Figure 7.1 Internal Formats of Type int and Type double


Floating-point Format (Cont’d)

• Actual ranges vary from one implementation to another

• The ANSI standard for C specifies the minimum range of positive values of type int is from 1 to 32,767.

• The minimum range specified for positive values of type double is from 10-37 to 1037.


Figure 7.2 Program to Print Implementation-Specific Ranges for Positive Numeric Data


Numerical Inaccuracies

• Some fractions cannot be represented exactly as binary numbers in the mantissa

• Representational error – an error due to coding a real number as a finite

number of binary digits

• The representational error (sometimes called roundoff error) will depend on the number of binary digits (bits) used in the mantissa.


Numerical Inaccuracies (Cont’d)

• The result of adding 0.1 one hundred times may not be exactly 10.0, so the following loop may fail to terminate.for (trial = 0.0; trial != 10.0; trial = trial + 0.1) {. . .}

• If the loop repetition test is changed to trial < 10.0, the loop may execute 100 times on one computer and 101 times on another.

• It is best to use integer variables for loop control


Numerical Inaccuracies (Cont’d)

• When you add a large real number and a small number, the larger number may “cancel out” the smaller number.

• cancellation error – an error resulting from applying an arithmetic operation to operands

of vastly different magnitudes; effect of smaller operand is lost

• arithmetic underflow – an error in which a very small computational result is represented

as zero

• arithmetic overflow – an error that is an attempt to represent a computational result that

is too large


Automatic Conversion of Data Types

• int k = 5, m = 4, n;• double x = 1.5, y = 2.1, z;


Explicit Conversion of Data Types

• cast – an explicit type conversion operation

• Assume int nt, d1; Compare– frac = (double)n1 / (double)d1;– frac = n1 / d1;

• converting only one would be sufficient, because the rules for evaluation of mixed-type expressions would then cause the other to be converted as well. – Note: assignment is not included in this rule

• But, frac = (double)(n1 / d1); resulting in the loss of the fractional part!! Why?


Explicit Conversion of Data Types (Cont’d)

• We sometimes include casts that do not affect the result but simply make clear to the reader the conversions that would occur automatically.

• Equivalent (int sqrt_m, m;)– sqrt_m = sqrt(m);– sqrt_m = (int)sqrt((double)m);


Representation and Conversion of Type char

• Character values may also be compared, scanned, printed, and converted to type int.

• Each character has its own unique numeric code; the binary form of this code is stored in a memory cell.

• Character Codes in Appendix A: ASCII, EBCDIC, CDC


Representation and Conversion of Type char (Cont’d)

• Order relationship– '0' < '1' < '2' < '3' < '4' < '5' < '6' < '7' < '8' < '9'– 'A' < 'B' < 'C' < ... < 'X' < 'Y' < 'Z'– 'a' < 'b' < 'c' < ... < 'x' < 'y' < 'z'

• not necessarily consecutive.


Representation and Conversion of Type char (Cont’d)

• In ASCII, the printable characters have codes from 32 (code for a blank or space) to 126 (code for the symbol ~).

• The other codes represent nonprintable control characters. – Sending a control character to an output device causes the device

to perform a special operation such as returning the cursor to column one.

• C permits conversion of type char to type int and vice versa.

• collating sequence – a sequence of characters arranged by character code number


Figure 7.3 Program to Print Part of the Collating Sequence


Enumerated Types

• Enumerated type – a data type whose list of values is specified by

the programmer in a type declaration

• Exampletypedef enum

{entertainment, rent, utilities, food, clothing,automobile, insurance, miscellaneous}

expense_t;expense_t expense_kind;


Enumerated Types (Cont’d)

• Enumeration constant – an identifier that is one of the values of an

enumerated type

• expense_t causes the enumeration constant entertainment to be represented as the integer 0, rent to 1, utilities to 2, and so on.


Figure 7.4 Enumerated Type for Budget Expenses


Figure 7.4 Enumerated Type for Budget Expenses (cont’d)



• Enumeration constants must be identifiers; they cannot be numeric, character, or string literals.

• An identifier cannot appear in more than one enumerated type definition.

• Relational, assignment, and even arithmetic operators can be used with enumerated types.



• Example– sunday < monday– wednesday != friday– tuesday >= Sunday

• Exampleday_t tomorrow;if (today == saturday)

tomorrow = sunday;else

tomorrow = (day_t)(today + 1);



• C handles enumerated type values just as it handles other integers, no range checking to verify that the value stored in an enumerated type variable is valid.– today = saturday + 3; is invalid


Figure 7.5 Accumulating Weekday Hours Worked


Figure 7.6 Six Roots for the Equation f(x) = 0


Figure 7.7 Using a Function Parameter


Figure 7.8 Change of Sign Implies an Odd Number of Roots


Figure 7.9 Three PossibilitiesThat Arise When the Interval [xleft, xright] Is Bisected


Figure 7.10 Finding a Function Root Using the Bisection Method


Figure 7.10 Finding a Function Root Using the Bisection Method (cont’d)


Figure 7.11 Sample Run of Bisection Program with Trace Code Included


Figure 7.12 Geometric Interpretation of Newton's Method


Figure 7.13 Approximating the Area Under a Curve with Trapezoids


Figure 7.14 Finite State Machine for Numbers and Identifiers

chapter 7 simple date types j. h. wang ( 王正豪 ), ph. d. assistant professor dept. computer...

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