Division in a binary representation for complex numbers

David C. Blest*, Tariq Jamil

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةArticleمراجعة النظراء

7 اقتباسات (Scopus)

ملخص

Computer operations involving complex numbers, essential in such applications as Fourier transforms or image processing, are normally performed in a ‘divide-and-conquer’ approach dealing separately with real and imaginary parts. A number of proposals have treated complex numbers as a single unit but all have foundered on the problem of the division process without which it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single ‘binary’ representation, reviews basic complex arithmetic and is able to provide a fail-safe procedure for obtaining the quotient of two complex numbers expressed in the representation. Thus, while an outstanding problem is solved, recourse is made only to readily accessible methods. A variety of extensions to the work requiring similar basic techniques are also identified. An interesting side-line is the occurrence of fractal structures, and the power of the ‘binary’ representation in analysing the structure is briefly discussed.

اللغة الأصليةEnglish
الصفحات (من إلى)561-574
عدد الصفحات14
دوريةInternational Journal of Mathematical Education in Science and Technology
مستوى الصوت34
رقم الإصدار4
المعرِّفات الرقمية للأشياء
حالة النشرPublished - 2003
منشور خارجيًانعم

ASJC Scopus subject areas

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