Analysis of carries in signed digit expansions
نویسندگان
چکیده
منابع مشابه
Multiplication of Signed-digit Numbers
A recently proposed technique for common-multiplicand multiplication of binary numbers is shown to be applicable to signed-digit numbers. We prove that multiplication of a single k-bit multiplicand by n k-bit multipliers can be performed using 0:306nk additions for canonically recoded signed-digit numbers, while the binary case requires 0:375nk additions.
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In this work novel-efficient implementations to convert a two’s complement binary number into its canonic signed digit (CSD) representation are presented. In these CSD recoding circuits two signals, H and K, functionally equivalent to two carries are described. They are computed in parallel reducing the critical path and they possess some properties that lead to a simplification of the algebrai...
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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...
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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...
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اندیشمندان و صاحب نظران علوم اجتماعی بر این باورند که مرحله تازه ای در تاریخ جوامع بشری اغاز شده است. ویژگیهای این جامعه نو را می توان پدیده هایی از جمله اقتصاد اطلاعاتی جهانی ، هندسه متغیر شبکه ای، فرهنگ مجاز واقعی ، توسعه حیرت انگیز فناوری های دیجیتال، خدمات پیوسته و نیز فشردگی زمان و مکان برشمرد. از سوی دیگر قدرت به عنوان موضوع اصلی علم سیاست جایگاه مهمی در روابط انسانی دارد، قدرت و بازتولید...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2016
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-016-0917-x