SUBBLOCK OCCURRENCES IN SIGNED DIGIT REPRESENTATIONS
نویسندگان
چکیده
منابع مشابه
Subblock Occurrences in Signed Digit Representations
Abstract. Signed digit representations with base q and digits − q 2 , . . . , q 2 (and uniqueness being enforced by applying a special rule which decides whether −q/2 or q/2 should be taken) are considered with respect to counting the occurrences of a given (contiguous) subblock of length r. The average number of occurrences amongst the numbers 0, . . . , n−1 turns out to be const · log q n + δ...
متن کاملCarry propagation in signed digit representations
Abstract. Von Neumann’s addition method adds two numbers given in q-ary representation by forming a number consisting of the added digits, reduced modulo q, and another number, representing the carries and repeating this until the string of carries consists only of zeros. The average number of iterations was studied by Knuth. We extend these results by considering the (q, d) system, with base q...
متن کاملOn binary signed digit representations of integers
Applications of signed digit representations of an integer include computer arithmetic, cryptography, and digital signal processing. An integer of length n bits can have several binary signed digit (BSD) representations and their number depends on its value and varies with its length. In this paper, we present an algorithm that calculates the exact number of BSD representations of an integer of...
متن کاملArithmetic Circuits Combining Residue and Signed-Digit Representations
This paper discusses the use of signed-digit representations in the implementation of fast and efficient residue-arithmetic units. Improvements to existing signed-digit modulo adders and multipliers are suggested and new converters for the residue signed-digit number system are described for the moduli . By extending an existing efficient signed-digit adder design to handle modulo operations, w...
متن کاملFractional Windows Revisited: Improved Signed-Digit Representations for Efficient Exponentiation
This paper extends results concerning efficient exponentiation in groups where inversion is easy (e.g. in elliptic curve cryptography). It examines the right-to-left and left-to-right signed fractional window (RL-SFW and LR-SFW) techniques and shows that both RL-SFW and LR-SFW representations have minimal weight among all signed-digit representations with digit set {±1,±3, . . .,±m, 0}. (Fracti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2003
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089503001368