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APP. G]
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HEXADECIMAL NUMBERS
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Base 16: n = 1ff Enter a hexadecimal numeral (use 0x prefix): 0x1ff Base 8: n = 777 Base 10: n = 511 Base 16: n = 1ff
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Algorithm G.1 Decimal Integer to Hexadecimal To convert the integer x into its equivalent hexadecimal numeral: 1. Assert x > 0. 2. Set k = 0. 3. Divide x by 16, setting x equal to the (integer) quotient. 4. Set h k equal to the remainder from the previous division. Use one of the 16 hexadecimal digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, representing the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, for h k. 5. Add 1 to k. 6. If x > 0, repeat steps 3 6. 7. Return h k h 2h 1h 0 (i.e., the hexadecimal numeral whose jth hex symbol is h j)
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EXAMPLE G.3 Converting the Decimal Numeral 100,000 to Hexadecimal
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Applying Algorithm G.1 to the decimal number 100,000 yields 100000 10 = h 4h 3h 2h 1h 0 = 186a0 16 :
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k x 0 100000 1 6250 2 390 3 24 4 1 8 0 hk 0 a 6 8 1
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Algorithm G.2 Hexadecimal Integer to Decimal To convert the hexadecimal integer hk h2h1h0 into its equivalent decimal numeral: 1. Set x = 0. 2. Set j = k + 1 (the actual number of bits in the hexadecimal string). 3. Subtract 1 from j. 4. Multiply x by 16. 5. Add h j to x. 6. If j > 0, repeat steps 3 6. 7. Return x.
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EXAMPLE G.4 Converting the Hexadecimal Numeral f4d9 to Decimal
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Convert f4d9 to decimal:
j 4 3 2 1 0 hj f 4 d 9 x = 2x + hj 0 16 0 + f = 15 16 15 + 4 = 244 16 244 + 13 = 3917 16 3917 + 9 = 62,681
HEXADECIMAL NUMBERS
[APP. G
So f4d916 = 62,68110 .
EXAMPLE G.5 Converting the Hexadecimal Numeral 543ab to Decimal
Converting 543ab to decimal:
j 5 4 3 2 1 0 hj x = 2x + hj 0 5 16 0 + 5 = 5 4 16 5 + 4 = 84 3 16 84 + 3 = 1347 a 16 1347 + a = 21,562 b 16 21,562 + b = 345,003
So 543ab16 = 345,00310 .
TeamLRN
Appendix H
References
[Adams]
C++ An Introduction to Computing, by Joel Adams, Sanford Leestma, and Larry Nyhoff. Prentice Hall, Englewood Cliffs, NJ (1995) 0-02-369402-5.
[Barton]
Scientific and Engineering C++, by John J. Barton and Lee R. Nackman. Addison-Wesley Publishing Company, Reading, MA (1994) 0-201-53393-6.
[Bergin]
Data Abstraction, the Object-Oriented Approach Using C++, by Joseph Bergin. McGraw-Hill, Inc., New York, NY (1994) 0-07-911691-4.
[Bronson]
A First Book of C++, by Gary J. Bronson. West Publishing Company, St. Paul, MN (1995) 0-314-04236-9.
[Budd]
Classic Data Structures in C++, by Timothy A. Budd. Addison-Wesley Publishing Company, Reading, MA (1994) 0-201-50889-3.
[Capper]
Introducing C++ for Scientists, Engineers and Mathematicians, by D. M. Capper. Springer-Verlag, London (1994) 3-540-19847-4.
[Cargill]
C++ Programming Style, by Tom Cargill. Addison-Wesley Publishing Company, Reading, MA (1992) 0-201-56365-7.
[Carrano]
Data Abstraction and Problem Solving with C++, by Frank M. Carrano. Benjamin/Cummings Publishing Company, Redwood City, CA (1993) 0-8053-1226-9.
[Carroll]
Designing and Coding Reusable C++, by Martin D. Carroll and Margaret A. Ellis. Addison-Wesley Publishing Company, Reading, MA (1995) 0-201-51284-X.
[Cline]
C++ FAQs, Second Edition, by Marshall Cline, Greg Lomow, and Mike Girou. Addison-Wesley Publishing Company, Reading, MA (1999) 0-201-30983-1.
[Coplien]
Advanced C++, Programming Styles and Idioms, by James O. Coplien. Addison-Wesley Publishing Company, Reading, MA (1992) 0-201-54855-0.
[Deitel]
C++ How to Program, Second Edition by H. M. Deitel and P. J. Deitel. Prentice Hall, Englewood Cliffs, NJ (1998) 0-13-528910-6.
Copyright 2000 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
REFERENCES
[APP. H
[Dewhurst]
Programming in C++, Second Edition, by Stephen C. Dewhurst and Kathy T. Stark. Prentice Hall, Englewood Cliffs, NJ (1995) 0-13-182718-9.
[Ellis]
The Annotated C++ Reference Manual, by Margaret A. Ellis and Bjarne Stroustrup. Addison-Wesley Publishing Company, Reading, MA (1992) 0-201-51459-1.
[Friedman]
Problem Solving, Abstraction, and Design Using C++, by F. L. Friedman and E. B. Koffman. Addison-Wesley Publishing Company, Reading, MA (1994) 0-201-52649-2.
[Hansen]
The C++ Answer Book, by Tony L. Hansen. Addison-Wesley Publishing Company, Reading, MA (1990) 0-201-11497-6.
[Headington]
Data Abstraction and Structures Using C++, by Mark R. Headington and David D. Riley. D. C. Heath and Company, Lexington, MA (1994) 0-669-29220-6.
[Horowitz]
Fundamentals of Data Structures in C++, by Ellis Horowitz, Sartaj Sahni, and Dinesh Mehta. W. H. Freeman and Company, New York, NY (1995) 0-7167-8292-8.
[Hubbard1]
Fundamentals of Computing with C++, by John R. Hubbard. McGraw-Hill, Inc, New York, NY (1998) 0-07-030868-3.
[Hubbard2]
Data Structures with C++, by John R. Hubbard. McGraw-Hill, Inc, New York, NY (1999) 0-07-135345-3.
[Hughes]
Mastering the Standard C++ Classes, by Cameron Hughes and Tracey Hughes. John Wiley & Sons, Inc, New York, NY (1999) 0-471-32893-6.
[Johnsonbaugh]
Object-Oriented Programming in C++, by Richard Johnsonbaugh and Martin Kalin. Prentice Hall, Englewood Cliffs, NJ (1995) 0-02-360682-7.
[Josuttis]
The C++ Standard Library, by Nicolai M. Josuttis. Addison-Wesley Publishing Company, Reading, MA, 1999, 0-201-37926-0.
[Knuth1]
The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Third Edition, by Donald E. Knuth. Addison-Wesley Publishing Company, Reading, MA, 1997, 0-201-89683-4.
[Knuth2]
The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Third Edition, by D. E. Knuth. Addison-Wesley Publishing Company, Reading, MA, 1998, 0-201-89684-2.
[Knuth3]
The Art of Computer Programming, Vol. 3: Sorting and Searching, Second Edition, by Donald E. Knuth. Addison-Wesley Publishing Company, Reading, MA, 1998, 0-201-89685-0.
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