[...]... performance in the future This book can be used as a text of an introductory course for graduate students or senior undergraduate students in electrical engineering, and computer and mathematical sciences It can also be used as a reference book for practicing engineers and computer scientists involved in the design, application and development of computer arithmetic units For the number systems covered in Sections... Lu received the M.S and Ph.D degrees in electrical engineering from Rice University, Houston, in 1984 and 1987, respectively She joined the Department of Electrical Engineering at Texas A&M University in 1987, where she is currently a professor Lu’s research interests include computer arithmetic, parallel computing, computer architectures, VLSI algorithms and computer networks, and she has published... conventional computer arithmetic methods, but also the unconventional ones are worth investigation in new designs Numbers play an important role in computer systems Numbers are the basis and object of computer operations The main task of computers is computing, which deals with numbers all the time Humans have been familiar with numbers for thousands of years, whereas representing numbers in computer systems. .. DifSerent Number Systems 12 1.2 Finding Signed Digits 14 1.3 Resewed Representation in IEEE Standard 21 2.1 f Delay Time and Area o Logic Gates 30 2.2 Logic Function o a Half-Adder f 32 2.3 f Logic Function o a Full-Adder 33 2.4 Single-Bit Subtractor 35 2.5 Negation in One’s Complement System 36 3.1 Maximum Inputs o CSA Trees f 71 4.1 Recoding the Triplets 92 5.1 Combination and Delay of k-input Wallace... technical papers in these areas In addition, Professor Lu has served as associate editor of the Journal of Computing and Information and the Information Sciences Journal, and was conference chairman of the Fifth, Sixth and Seventh International Conferences on Computer Science and Informatics She served on the panel of the National Science Foundation and the panel of the IEEE Workshop on Imprecise and Approximate... advisory committees for Ph.D and Masters students, is a registered professional engineer, and is a senior member of the Institute of Electrical and Electronics Engineers She is recognized in Who’s Who in the World (2001, 2003), Who‘s Who in America (2002-2003) and Who’s Who of American Women (2002-2003) xxi This Page Intentionally Left Blank 1 Computer Number Systems As the arithmetic applications grow... remainder do and the quotient d,-l rn-' + dn-2 T ~ +- + d l , ~ since do < r and other terms on the right-hand side are integer times of r If we divide the above quotient again by T , we will obtain the remainder d l , and so forth After performing the division n - 1 times, d,-l will become the quotient If we divide it by r again, we will have quotient 0, since any di < r and the last remainder d,-l... the integer digit in parentheses after each multiplication and it won't participate in the next multiplication except the fraction part 0 S625 x 2 (1) 1250 6 COMPUTER NUMBER SYSTEMS x 2 (0).2500 x 2 (0)SOOO x 2 (l).OOOO As to the conversion between binary numbers and octal numbers, or between binary and hexadecimal numbers, the following has been observed In octal numbers r = 8 and digit 0 5 di 5 7 In. .. binary numbers r = 2 and 8 = Z3 3 bits in binary are necessary and sufficient to represent the value of one digit in octal For example, (5)s = (101)2 and (7)8 = (111)2 Hence, to convert an octal number to a binary number, represent each digit in octal with 3 bits in binary, and concatenate all the bits together For example, 4 7 2 6 AAAA = 100 111 010 110 1s 0012 On the other hand, to convert a binary... starting from the radix point For the integer part, group from right to left, and add O(s) on the left if the last group contains less than 3 bits For the fraction part, group from left to right, and add O(s) on the right if the last group contains less than 3 bits Find the value for each group applying Equation (1.3) In hexadecimal numbers r = 16 and digit 0 5 di 5 15 In binary numbers T = 2 and 16 . h0" alt="" Arithmetic and Logic in Computer Systems This Page Intentionally Left Blank Arithmetic and Logic in Computer Systems Mi Lu Texas A&M University WILEY- INTERSCIENCE. practicing engineers and computer scientists involved in the design, application and development of computer arithmetic units. For the number systems covered in Sections 1.4, 1.6 and 1.7,. in DifSerent Number Finding Signed Digits 14 21 30 32 33 Systems 12 Resewed Representation in IEEE Standard Delay Time and Area of Logic Gates Logic Function of a Half-Adder Logic