The central executive component of working memory has been argued to play an important role in the performance of span tasks, particularly backward span. Age-related decline in central executive function has also been reported, and yet there have been inconsistent findings to indicate that with increasing age, the discrepancy between forward and backward span increases. A secondary analysis of ...

Participants switched frequently between high/low and odd/even classification of a digit. The interval between a task cue and the next digit varied between blocks. In Experiment 1, the task switched predictably every two, four, or eight trials. In Experiment 2, switching predictably every four trials was compared with random switching. With predictable switching, the cost was limited to the fir...

This paper presents an investigation into using a combination of two alternative digital number representations; the residue number system (RNS) and the signed-digit (SD) number representation in digital arithmetic circuits. The combined number system is called RNS/SD for short. Since the performance of RNS/SD arithmetic circuits depends on the choice of the moduli set (a set of pairwise prime ...

We propose an asymmetric high-radix signed-digit (AHSD) number system for fast binary addition, and show that the AHSD number system supports carry-free (CF) addition. The CF additions in AHSD, to be classified as quasi-closed and subclosed additions, use only one redundant digit for any radix r ≥ 2. Novel algorithms for constructing the three-stage CF adder (CFA) based on the AHSD number syste...

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...

The number 6174 arises in a semifamous problem in recreational mathematics: take any 4-digit number which uses more than one digit and find the difference between the numbers formed by writing the digits in descending order and ascending order (e.g., starting with 4083 yields 8430− 0348= 8082). Iterate this process using the difference as the new 4-digit number. It was first discovered by the I...

Benford’s Law gives the expected frequencies of the digits in tabulated data and asserts that the lower digits (1, 2, and 3) are expected to occur more frequently than the higher digits. This study tested whether the law applied to two large earth science data sets. The first test analyzed streamflow statistics and the finding was a close conformity to Benford’s Law. The second test analyzed th...

where a, b, c, d are multi-digit integers. Since the product of two n-digit integers becomes 2n-digit, every multiplication operation doubles number of digits of the numerator and the denominator. Rational number computation divides them by their GCD to get irreducible form after every operation. We develop a computing environment in which multi-digit integer such as a, b, c, d in above express...

Personal Identification Numbers (PINs) are ubiquitously used in computer systems where user input interfaces are constrained, such as ATMs, POS terminals, electronic doors and mobile devices. Yet, so far little attention has been paid to this important kind of authentication credentials, especially for 6-digit PINs which dominate in Asian countries and are gaining popularity worldwide. Unsurpri...