This paper describes an attempt to combine advantages of the signed digit number representation, applied at the word-level, and the residue number system applied at the digit-level, to achieve arithmetic decomposition of high-radix systems. Also introduced is a new decomposition algorithm for multiple-output Boolean functions based on partition products. Analysis of the proposed new method of a...

The right-most digit of N is 5. Thus, N is composite, and if we replace any digit of N , other than the right-most digit, with a different digit, then the new number obtained will be divisible by 5 and, hence, be composite. On the other hand, if we replace the right-most digit of N by a different digit, then we obtain one of N ± j where j ∈ {1, 2, 3, 4, 5} and each of these is easily seen to be...

Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the base-b representation. Further let q be a positive integer. In this paper we study the length k of arithmetic progressions n, n+ q, . . . , n+ q(k − 1) such that sb(n), sb(n+ q), . . . , sb(n+ q(k − 1)) are (pairwise) distinct. More specifically, let Lb,q denote the supremum of k as n varies in ...

A noninvasive strain-gauge method of measuring blood flow in the digit was used to assess the influence of the sympathetic system in the digit. The sympathetic system was stimulated by the sudden application of ice to the neck, thus avoiding in the hand local reflexes and responses to cold. Seventeen normal subjects responded in similar fashion. Maximum flow reduction ranged from 26% to 92%, wi...

In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for solution of problem at hand. Significant proportions these performance improvements stem from ability to infer existence identical most-significant digits b...

Individuals are more likely to remember emotional than neutral information, but this benefit does not always extend to the surrounding background information. This memory narrowing is theorised to be linked to the availability of attentional resources at encoding. In contrast to the predictions of this theoretical account, altering participants' attentional resources at encoding by dividing att...

Understanding fractions and decimals is difficult because whole numbers are the most frequently and earliest experienced type of number, and learners must avoid conceptualizing fractions and decimals in terms of their whole-number components (the "whole-number bias"). We explored the understanding of fractions, decimals, two-digit integers, and money in adults and 10-year-olds using two number ...