A complex-number multiplier using radix-4 digits

Wei, B.W.Y.; Du, Hejun; Chen, Honglu

doi:10.1109/arith.1995.465373

Cited by 17 publications

(8 citation statements)

References 16 publications

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“…The following base, digit-set combinations are examples of the large number of possible number systems that can be constructed combining two integer digit-sets: These number systems are constructed such that the real and imaginary parts of a number are written using, respectively, the real and imaginary parts of the digit-set. This has some obvious advantages since arithmetic can be based on the conventional integer arithmetic algorithms [19]. Furthermore, converting from a conventional representation to a complex representation and computing the complex conjugate are fairly simple tasks.…”

Section: Complex Number Systems With An Integer Radixmentioning

confidence: 99%

Redundant radix representations of rings

Nielsen¹,

Kornerup²

1999

IEEE Trans. Comput.

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ÐThis paper presents an analysis of radix representations of elements from general rings; in particular, we study the questions of redundancy and completeness in such representations. Mappings into radix representations, as well as conversions between such, are discussed, in particular where the target system is redundant. Results are shown valid for normed rings containing only a finite number of elements with a bounded distance from zero, essentially assuring that the ring is ªdiscrete.º With only brief references to the more usual representations of integers, the emphasis is on various complex number systems, including the ªclassicalº complex number systems for the Gaussian integers, as well as the Eisenstein integers, concluding with a summary on properties of some low-radix representations of such systems. Index TermsÐRadix representation of rings, integer and computer radix number systems, redundancy, number system conversion, computer arithmetic.

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Section: Complex Number Systems With An Integer Radixmentioning

confidence: 99%

Redundant radix representations of rings

Nielsen¹,

Kornerup²

1999

IEEE Trans. Comput.

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“…Unlike for complex multipliers [10], [12], its implementation has been commonly provided in software. To improve its performance, a hardware implementation is considered.…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of a Radix-4 Complex Division Unit with Prescaling

Dormiani

Ercegovac

Muller

2009

2009 20th IEEE International Conference on Application-Specific Systems, Architectures and Processors

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Abstract-We present a design and implementation of a radix-4 complex division unit with prescaling of the operands. Specifically, we extend the treatment of the residual bound and errors due to the use of truncated redundant representation. The requirements for prescaling tables are simplified and a detailed specification of the table design is given. All principal components used in the design are described and the proposed optimizations are explained. The target platform for implementation was an Altera Stratix II FPGA [15] for which we report timing and area requirements. For a precision of 36 bits, the implementation uses 1185 ALUTs, achieving a latency of 157 ns. The maximum clock frequency is 173.49 MHz.

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“…For multiplication, two conventional approaches were considered, including the standard four-multiplications and two additions (4M2A) approach, and the threemultiplications and five additions (3M5A) approach presented in [12]. For division, four real on-line multipliers, two real on-line dividers, two square units, and three real on-line adders were used.…”

Section: Discussionmentioning

confidence: 99%

On-line algorithms for complex number arithmetic

McIlhenny

Ercegovac

Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284)

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A class of on-line algorithms for complex number arithmetic is presented. These algorithms adopt a redundant complex number system (RCNS) to represent complex numbers as a single number. Such a scheme simplifies the specification of the design, and has the additionaleffect that singleprecision complex arithmetic can be easily reconfigured for double-precision real arithmetic. We present cost delay comparisons with the more conventional approach to show a significant improvement, demonstrating that the presented algorithms are attractive for VLSI systems demanding complex number operations.

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A complex-number multiplier using radix-4 digits

Cited by 17 publications

References 16 publications

Redundant radix representations of rings

Redundant radix representations of rings

Design and Implementation of a Radix-4 Complex Division Unit with Prescaling

On-line algorithms for complex number arithmetic

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