This paper introduces the class of reflected number systems. Members of this class have the adjacency property, i.e. representations for consecutive numbers differ in only one digit and the magnitude of this difference is one. It shows that every number system based on a positional weighting scheme has a reflected analogue. It presents procedures to convert a number system to its reflected anal...

The noise robustness of automatic speech recognition systems can be increased by transforming the signal to make the cumulative density functions of the signal’s values in recognition match the ones that where estimated on the training data. This paper describes a real–time online algorithm to approximate the cumulative density functions, after Mel scaled filtering, using a small number of quan...

New cyclic n-digit Gray codes are constructed over {0, 1, . . . , R − 1} for all R,n ≥ 2. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For every n ≥ 2, the number of occurrences of each digit in the n-digit codes is within R-1 of the average Rn/n, and for the 2-digit codes every transition count is either bR2/2c or dR2/2e.

We introduce a new number system that we call the strictlyregular system, which efficiently supports the operations: digit-increment, digit-decrement, cut, concatenate, and add. Compared to other number systems, the strictly-regular system has distinguishable properties. It is superior to the regular system for its efficient support to decrements, and superior to the extended-regular system for...

In this paper, we present a new approach to designing optical digital arithmetic systems. We present new arithmetic algorithms based on a modified signed -digit number representation. New Signed -digit symbolic substitution rules are introduced to implement them. These signed -digit arithmetic algorithms are well suited for optical implementation because, of the confined carry propagation withi...

A normal number is one whose decimal expansion (or expansion to some base other than 10) contains all possible finite configurations of digits roughly with their expected frequencies. More formally, let N(α; b, a, x) = #{1 ≤ n ≤ x : the nth digit in the base-b expansion of α is a} (1) denote the counting function of the occurrences of the digit a (0 ≤ a < b) in the b-ary expansion of the real n...

We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit is 2−1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees...

The Natwest and Royal Bank of Scotland (RBS) online banking systems are vulnerable to a remote attack which allows an adversary to steal money from a customer’s account. The vulnerability has arisen as a result of poor software engineering practice which neglected security. More precisely, the authentication mechanisms used by Natwest and RBS are dependent on six pieces of customer data, namely...

This study measured changes in adult performance following prolonged exposure (90 minutes) to nitrous oxide at psychosedative levels. Using a repeated-measures randomized blind design, experimenters exposed 12 subjects to four treatment combinations. These included: room air for 90 minutes (baseline); 100% oxygen for 90 minutes; nitrous oxide-oxygen sedation for 90 minutes followed by 100% oxyg...