Arithmetic and Logic in Computer Systems
Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples.
No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
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Addition and Subtraction
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2's complement addition addition/subtraction area complexity array multiplier binary number bit position Bj+i carry lookahead adder carry propagation carry-in carry-lookahead carry-out Carry-Save Adder cell circuit Cj+i Comp complement number complement system Computer Arithmetic cycles delay dividend division algorithm divisor Equation example exponent floating point floating-point number fraction full adder gate Hence hexadecimal IEEE IEEE Trans implemented input integer iteration logarithm logic mantissa moduli set multiplicand multiply modules n-bit negation negative number non-restoring division number multiplication number of bits number representation number represented number system octal odd number One's Complement operands output overflow parity partial product partial remainder performed positive number procedure qj+i quotient digit radix point recoding redundancy Residue Number Residue Number System result scan shown in Figure sign-magnitude signed number Signed-Digit Number signed-digit representation step subtraction summands Table Two's Complement unsigned vector Wallace tree wmax