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Computer arithmetic- a new number system, mathematical methods, algorithms and its practices

حساب الحاسوب ـ نظام عد جديد طرق رياضية و خوارزميات و تطبيقاتها

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 Publication date 2007
and research's language is العربية
 Created by Shamra Editor




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The purpose of this research is to enhance fractional numbers precision according to the new representation of fractional numbers, adding some extra cost to the hardware so we suggest a new number system per representing of fractional numbers in computers, that depends on the series With mathematical, algorithmic study, and its hardware of our research, we consider the two principal formats of real numbers in computers: fixed- point, floating- point and the cost of the hardware required to store and process the numbers.


Artificial intelligence review:
Research summary
يهدف هذا البحث إلى تحسين دقة تمثيل الأعداد الكسرية في الحاسوب من خلال اقتراح نظام عد جديد يعتمد على السلسلة المتباعدة. يناقش البحث خوارزميات التمثيل الجديد للأعداد الكسرية في النظامين العشري والثنائي، ويقدم أمثلة متعددة لإثبات وحدانية هذا التمثيل. كما يتناول البحث العمليات الحسابية الأساسية مثل الجمع والطرح والضرب والقسمة وفقاً لهذا النظام الجديد، ويثبت وحدانية عملية الجمع. بالإضافة إلى ذلك، يقدم البحث خوارزميات لتحويل الأعداد بين النظام الجديد والنظم القياسية الأخرى. وأخيراً، يناقش البحث بعض العوامل التي تؤخذ في الاعتبار عند اختيار نظم العد في هذا التمثيل الجديد، مثل نوع الأعداد، مجال الأعداد القابلة للتمثيل، وحساب الدقة. يتم أيضاً تقديم برمجيات لخوارزمية التمثيل الجديد وخوارزمية الجمع بلغة البرمجة ++C لدراسة أدائها.
Critical review
دراسة نقدية: على الرغم من أن البحث يقدم حلاً مبتكراً لتحسين دقة تمثيل الأعداد الكسرية في الحاسوب، إلا أن هناك بعض النقاط التي تحتاج إلى مزيد من الدراسة والتوضيح. أولاً، لم يتم تقديم تحليل شامل لكلفة البنية الصلبة (Hardware) المطلوبة لتطبيق هذا النظام الجديد، وهو عامل مهم يجب أخذه في الاعتبار عند تقييم فعالية النظام. ثانياً، لم يتم تقديم مقارنة مفصلة بين أداء النظام الجديد والنظم القياسية الأخرى مثل نظام الفاصلة العائمة، مما يجعل من الصعب الحكم على مدى تفوق النظام الجديد. وأخيراً، يجب إجراء تجارب عملية أكثر لاختبار فعالية النظام الجديد في تطبيقات واقعية مختلفة لضمان أنه يمكن استخدامه بشكل فعال في الحواسيب الحديثة.
Questions related to the research
  1. ما هو الهدف الرئيسي من البحث؟

    الهدف الرئيسي هو تحسين دقة تمثيل الأعداد الكسرية في الحاسوب من خلال اقتراح نظام عد جديد يعتمد على السلسلة المتباعدة.

  2. ما هي الخوارزمية المقترحة لتمثيل الأعداد الكسرية؟

    الخوارزمية المقترحة تعتمد على السلسلة المتباعدة لتمثيل الأعداد الكسرية بطريقة جديدة تضمن وحدانية التمثيل.

  3. ما هي العمليات الحسابية التي تمت مناقشتها في البحث؟

    تمت مناقشة عمليات الجمع، الطرح، الضرب، والقسمة وفقاً للنظام الجديد للأعداد الكسرية.

  4. هل تم تقديم برمجيات لتطبيق الخوارزميات المقترحة؟

    نعم، تم تقديم برمجيات لخوارزمية التمثيل الجديد وخوارزمية الجمع بلغة البرمجة ++C لدراسة أدائها.


References used
Alexopoulos, A.G., and Swartz land, JR. E. E.(1975). “The Sign/ Logarithm Number System,” IEEE Trans. On computer, USA
Hayes, J. P. (1979). “Computer Architecture And Organization,” Mc Graw- Hill, USA
Hennessy, J.L., and Patterson, D.A. (1998). “Computer Organization And Design.” Morgan Kaufman Publishers, Inc.USA
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