Biography :

Dr. Tariq Jamil has been teaching and doing research in the areas of computer architecture, parallel processing, computer arithmetic, and cryptography, for the past 20 years and is currently associated with the Department of Electrical and Computer Engineering at Sultan Qaboos University (SQU, Oman). He holds a B.Sc. (Honors) degree in electrical engineering from the NWFP University of Engineering and Technology (Pakistan) and M.S./Ph.D. degrees in computer engineering from the Florida Institute of Technology (USA). He has authored three books (the latest one is on Complex Binary Number System published by Springer), co-authored a book on speech recognition for Arabic language, holds an Australian Innovation Patent on Complex Binary Associative Dataflow Processor, and has written over fifty research papers in refereed international conferences and journals. He has been a recipient of research grants from the Australian Research Council and SQU, and has given invited lectures in Finland, Thailand, Pakistan, and the United Kingdom. In acknowledgment of his internationally recognized academic and research excellence, Dr. Jamil was awarded a Certificate of Appreciation by H.E. The Vice-Chancellor of SQU, on 25 November 2012 during SQU Silver Jubilee Ceremony. On account of his outstanding academic achievements and for contributions to activities related to the computing discipline, he was awarded the IEEE Computer Society (USA)/Upsilon Pi Epsilon Honor Society (USA) Award for Academic Excellence in 1996. Dr. Jamil has served as a distinguished speaker in the IEEE Computer Society (USA) Distinguished Visitors Program (DVP) during 2005-2007 and his biography has been published in such renowned directories as Marquis's Who's Who in the World (USA), Who's Who in Science and Engineering (USA), and Dictionary of International Biography (UK). He is a senior member of IEEE (USA), member of the IET (UK), a Chartered Engineer (UK), and a registered Professional Engineer. 

Abstract :

Complex numbers play an important role in engineering applications such as digital signal processing and image processing. Arithmetic operations involving this type of numbers are usually carried out by the application of "divide-and-conquer" technique, whereby a complex number is broken-up into its real and imaginary parts and then operations are carried out on each part as if it was a part of the real arithmetic. Finally, the overall result of the complex operation is obtained by accumulation of the individual results. For instance, addition of two complex numbers requires two separate additions (one for the real parts and one for the imaginary parts) while multiplication of the same two complex numbers requires four multiplications, one subtraction, and one overall addition. This can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as single unit instead of two sub-units.