Arithmetic and Logic in Computer Systems (Wiley Series in by Mi Lu

By Mi Lu

Mathematics and good judgment in desktops offers an invaluable consultant to a primary topic of machine technological know-how and engineering. Algorithms for appearing operations like addition, subtraction, multiplication, and department in electronic desktops are offered, with the aim of explaining the innovations at the back of the algorithms, instead of addressing any direct purposes. replacement equipment are tested, and reasons are provided of the basic fabrics and reasoning at the back of theories and examples.

No different present books take care of this topic, and the writer is a number one authority within the box of laptop mathematics. The textual content introduces the normal Radix quantity procedure and the Signed-Digit quantity method, in addition to Residue quantity approach and Logarithmic quantity procedure. This e-book serves as a necessary, up to date consultant for college kids of electric engineering and computing device and mathematical sciences, in addition to training engineers and computing device scientists fascinated about the layout, software, and improvement of machine mathematics devices.

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Extra resources for Arithmetic and Logic in Computer Systems (Wiley Series in Microwave and Optical Engineering, Book 169)

Example text

On the other hand, to convert a binary number to a hexadecimal, group each 4 bits together 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 4 bits. For the fraction part, group from left to right and add O(s) on the right if the last group contains less than 4 bits. For example, 10 101010011111 . 11002. vvvv = 2 A 9 F * ' C16 In the decimal to octal (hexadecimal, respectively) conversion, instead of the dividing by 8 (by 16) operation described earlier, one can first convert the decimal number to binary since dividing by 2 is easier, and then convert the binary number to octal (hexadecimal).

2, IEEE Computer Society Press, Los Alamitos, CA, 1990. 28. N. S. Szabo and R. I. Tanaka, Residue ArithmeticandltsApplications to Computer Technology, McGraw-Hill, NY, 1967. 29. C. Tung, “Arithmetic,” in Computer Science, A. F. , WileyInterscience, New York, 1972, Chap. 3. 30. S. Waser and M. J. Flynn, “Introduction to Arithmetic for Digital System Designers,” Holt, Rinehart, Winston, New York, 1982. 4, what decimal value does it represent if (a) It is an octal number? (b) It is a hexadecimal number?

Let a borrow request made to bit position i be a borrow-in signal denoted as li implying a loan from position i. The borrow-out bit li+l is a borrow request made to bit position i + 1, or a loan from bit position i + 1. 4. The logic expression of the difference bit in terms of the three input bits is similar to that of the sum bit in a full-adder. Namely, di = ai @ bi @ li. The borrow-out bit can be found by li+l = Cibi + bili + Cili. 5 shows a a single-bit subtractor with three inputs and two outputs.

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