Most number systems use a single base – e.g., 10 or 2 – and represent each number as a combination of powers of the base. However, historically, there were two civilizations that used a more complex systems to represent numbers. They also used bases: Babylonians used 60 and Mayans used 20, but for each power, instead of a single digit, they used two. For example, a number 19 was represented by ...

A quasigroup (Q, ∗) is called totally anti-symmetric if (c ∗ x) ∗ y = (c ∗ y) ∗ x⇒ x = y and x∗y = y∗x⇒ x = y. A totally anti-symmetric quasigroup can be used for the definition of a check digit system. Ecker and Poch [9] conjectured that there are no totally anti-symmetric quasigroups of order 4k + 2. This article will completely disprove their conjecture (except for n = 2, 6) as we will give ...

If the digits of any multi-digit number are multiplied together, another number results. If this process is iterated, eventually a single digit number will be produced. The number of steps that this process takes, before a single digit number is obtained, is referred to as the persistence of the of the original number [5]. Neil Sloane conjectured that for any base b, there is a number c(b) such...

This paper presents a novel eld-programmable gate array logic block architecture which incorporates support for digit-serial DSP architectures on a digit wide basis, without diminishing the support for random and control logic applications. To eeciently realize a digit-serial DSP design on FPGAs, one must create an FPGA architecture optimized for those types of systems. Key to the suitability o...

This study provides a new perspective on both the cognitive processes actually implemented and the effect of a simple experimental control - the recall constraint - in Sternberg's memory scanning task. These findings were highlighted by adopting a new approach based on the comparison of qualitative and quantitative results. The analysis of individual processing, on 72 adults, each participating...

The purpose of the current investigation was to evaluate hand-digit mapping in finger counting in French children and adults and whether handedness might constraint hand-digit mapping. To this aim, hand-digit mapping used when counting from one to ten by means of fingers, together with performance-based and preference-based measures of handedness, were evaluated in French individuals of four di...