Abstract
This paper presents a comparative study of the performances of arithmetic units, based on different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) and Mixed Number System (MNS) for DSP applications. The performance analysis is carried out in terms of the hardware utilization, timing complexity and efficiency. The arithmetic units based on these number systems were employed in designing various modulation schemes like Binary Frequency Shift Keying (BFSK) modulator/demodulator. The analysis of the performance of the proposed modulator on above mentioned number systems indicates the superiority of other number systems over binary number system.
Highlights
With the advent of high speed Digital Signal Processing (DSP) applications where the basic requirement was high data rates and fast adders and multipliers, the binary adders and multipliers were limited because of its carry propagation chain
Binary system is special case of above representation. From these expression it is clear that when a binary number is converted into double base number system (DBNS), it is represented as number consisting of several (i, j) pairs
Arithmetic units of different number systems like Residue Number System (RNS), Double Base Number System (DBNS), Triple Base Number System (TBNS) and Mixed Number System (MNS) have been applied to a Binary Frequency Shift Keying (BFSK) modulator as well as demodulator and validated
Summary
With the advent of high speed DSP applications where the basic requirement was high data rates and fast adders and multipliers, the binary adders and multipliers were limited because of its carry propagation chain. Triple Base Number System (TBNS) [7] [8] is an improvement over DBNS, requiring smaller number of multipliers and adders for multiplication but at the cost of greater computational complexity. The conversion stages in TBNS are much more complex compared with DBNS, but execution time is greatly reduced, resulting in high speed multiplication. Mixed Number System (MNS) [9] [10] employs both residue and double base number systems It uses RNS adder and DBNS multiplier together to utilize both their advantages. It provides more speed of execution than any other number system but suffers from overheads like three conversion stages for being implemented
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