Page 101 - Engineering Digital Design

72 CHAPTER 2 / NUMBER SYSTEMS, BINARY ARITHMETIC, AND CODES

alphabet letters, and a variety of printer and typewriter control abbreviations. An eighth bit
(not shown) is often used with the ASCII code for error detection purposes.
Another common character code is known as EBCDIC (pronounced "ebb-see-dick"),
the acronym for extended BCD interchange code. It uses 8-bit BCD strings so as to encode
a 256-character set.

FURTHER READING

Literature on number systems and arithmetic is extensive. Many journal articles and most
texts on digital logic design cover these subjects to one extent or another. Portions of this
chapter regarding number systems are taken from contributions by Tinder to The Electrical
Engineering Handbook, cited here. Recognized classic treatments of number systems and
arithmetic include those of Gamer, Hwang, and Knuth. The IEEE publication on the standard
for floating-point arithmetic is also frequently cited. These references, together with recent
texts covering the subject areas, are cited here.

[1] H. L. Garner, "Number Systems and Arithmetic," in Advances in Computers, Vol. 6. Academic
Press, New York, 1965, pp. 131-194.
[2] K. Hwang, Computer Arithmetic. John Wiley & Sons, New York, 1978.
[3] IEEE, IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985) The
Institute of Electrical and Electronic Engineers, New York, 1985.
[4] D. E. Knuth, The Art of Computer Programming: Seminumerical Algorithms, Vol. 2. Addison-
Wesley, Reading, MA, 1969.
[5] V. P. Nelson, H. T. Nagle, B. D. Carroll, and J. D. Irwin, Digital Logic Circuit Analysis and
Design. Prentice Hall, Englewood Cliffs, NJ, 1995.
[6] L. H. Pollard, Computer Design and Architecture. Prentice Hall, Englewood Cliffs, NJ, 1990.
[7] A. W. Shaw, Logic Circuit Design. Saunders College Publishing, Fort Worth, TX, 1993.
[8] R. F. Tinder, Digital Engineering Design: A Modern Approach, Prentice Hall, Englewood Cliffs,
NJ, 1991.
[9] R. F. Tinder, "Number Systems," in The Electrical Engineering Handbook, 2nd ed. (R. C. Dorf,
Ed.). CRC Press, 1997, pp. 1991-2006.
[10] C. Tung, "Arithmetic," Computer Science (A. F. Cardenas et al, Eds.), Chapter 3. Wiley-
Interscience, New York, 1972.
[11] J. F. Wakerly, Digital Design Principles and Practice, 2nd ed. Prentice Hall, Englewood Cliffs,
NJ, 1994.

PROBLEMS

Note: Use Tables P2.1, P2.2, and P2.3 as needed in working the following problems.

2.1 Convert the following decimal numbers to binary:
(a) 5
(b) 14
(c) 39
(d) 107.25
(e) 0.6875