Low-area, pipelined conversion from signed-binary, to two's-complement, number representation

1996 ◽  
Vol 32 (20) ◽  
pp. 1866
Author(s):  
G.M. Blair
Keyword(s):  
Number Representation ◽  
Low Area ◽  
Complement Number

scholarly journals Digit Set Conversion from Redundant Number System into Complement Representation

1970 ◽  
Vol 3 (1) ◽  
pp. 39-44
Author(s):  
Veerasit Charoensiri ◽  
Athasit Surarerks
Keyword(s):  
Traditional Method ◽  
Number System ◽  
Propagation Problem ◽  
Number Representation ◽  
Generic Algorithm ◽  
Digit Set ◽  
Parallel Addition ◽  
Redundant Number System ◽  
Complement Number

Redundant number system was proposed in order to solve the carry-propagation problem. Although it provides a carry-free parallel addition, this representation requires a lot of space to store itself. Many conversions from the redundant number system into another number representation have been introduced to decrease the storage usage. This paper proposes a generic algorithm in order to convert the redundant number representation into the complement number representation. The proposed algorithm can perform the conversion of a number in any integer radix and eliminates the carry chain of the traditional method. The proofs of the proposed algorithm in term of correctness are also included in this paper.

An arithmetical-training regime improves number representation and broad mathematical performance

2010 ◽  
Author(s):  
Arava Y. Kallai ◽  
Andrea L. Ponting ◽  
Christian D. Schunn ◽  
Julie A. Fiez
Keyword(s):  
Number Representation ◽  
Mathematical Performance

Neural Underpinnings of Numerical and Spatial Cognition: An fMRI Meta-Analysis of Brain Regions Associated with Symbolic Number, Arithmetic, and Mental Rotation

2019 ◽  
Author(s):  
Zachary Hawes ◽  
H Moriah Sokolowski ◽  
Chuka Bosah Ononye ◽  
Daniel Ansari
Keyword(s):  
Mental Rotation ◽  
Parietal Lobe ◽  
Meta Analysis ◽  
Likelihood Estimation ◽  
Brain Regions ◽  
Angular Gyrus ◽  
Number Representation ◽  
Neural Underpinnings ◽  
The Right ◽  
Symbolic Number

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger
Keyword(s):  
Sixth Grade ◽  
Number Line ◽  
Number Representation ◽  
Large Numbers ◽  
Position Task ◽  
Sigmoidal Curve ◽  
Anchor Points ◽  
The Right ◽  
Line P ◽  
Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

A Low-Area and Low-Power Comma Detection and Word Alignment Circuits for JESD204B/C Controller

2021 ◽  
pp. 1-11
Author(s):  
Peng Yin ◽  
Zhou Shu ◽  
Yingjun Xia ◽  
Tianmei Shen ◽  
Xiao Guan ◽  
...  
Keyword(s):  
Low Power ◽  
Word Alignment ◽  
Low Area

Low-area and accurate inner product and digital filters based on stochastic computing

2021 ◽  
Vol 183 ◽  
pp. 108040
Author(s):  
Hamdan Abdellatef ◽  
Mohamed Khalil-Hani ◽  
Nasir Shaikh-Husin ◽  
Sayed Omid Ayat
Keyword(s):  
Digital Filters ◽  
Inner Product ◽  
Low Area ◽  
Stochastic Computing
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