Fast Fourier transform (FFT) coprocessor, having a significant impact on the performance of communication systems, has been a hot topic of research for many years. The FFT function consists of consecutive multiply add operations over complex numbers, dubbed as butterfly units. Applying floating-point (FP) arithmetic to FFT architectures, specifically butterfly units, has become more popular recently. It offloads compute-intensive tasks from general-purpose processors by dismissing FP concerns (e.g., scaling and overflow/underflow). However, the major downside of FP butterfly is its slowness in comparison with its fixed-point counterpart. This reveals the incentive to develop a high-speed FP butterfly architecture to mitigate FP slowness. This brief proposes a fast FP butterfly unit using a devised FP fused-dot-product-add (FDPA) unit, to compute AB ± CD ± E, based on binary-signed-digit (BSD) representation. The FP three-operand BSD adder and the FP BSD constant multiplier are the constituents of the proposed FDPA unit. A carry-limited BSD adder is proposed and used in the three-operand adder and the parallel BSD multiplier so as to improve the speed of the FDPA unit. Moreover, modified Booth encoding is used to accelerate the BSD multiplier. The synthesis results show that the proposed FP butterfly architecture is much faster than previous counterparts but at the cost of more area.

Fast Fourier Transform (FFT) processors, having a significant impact on the performance of communication systems, have been a hot topic of research for many years. FFT function consists of consecutive multiply-add operations over complex numbers, dubbed as butterfly units. Use of redundant number systems is a way of increasing the speed of FFT coprocessors. It eliminates carry-propagation and hence permits latency reduction of each stage of the pipelined FFT architecture. This paper proposes a high-speed FFT processor using the devised fused-dot-product-add (FDPA) unit, to compute AB ± CD ± E, based on Binary-Signed-Digit (BSD) representation. Three-operand BSD adder and BSD constant multiplier are the constituents of the proposed FDPA unit. A carry-limited BSD adder is proposed and used in the three-operand adder and in the parallel BSD multiplier, so as to improve the speed of the FDPA unit. Moreover, modified-booth encoding is used to accelerate the BSD multiplier. Synthesis results show that the proposed design is about two times faster than the best previous work; but at cost of more area/power consumption.

Multiplication, as one of the four basic operations embedded in arithmetic processors, is nowadays experiencing being spotlighted by the hardware designers involved in the revived decimal arithmetic. The decimal hardware units usually employ the sequential implementation for this operation, due to the high area cost of the parallel decimal multipliers. However, the main drawback of this iterative method is in regard to its high latency. This paper, with the intention of ameliorating this problem, proposes a high-frequency sequential decimal multiplier. The cycle time of the proposed multiplier is determined by a decimal carry-save adder which is about 22% less than that of the fastest previous design.

Hardware implementation of decimal floating-point arithmetic is a topic of great interest among the researchers in computer arithmetic and also the digital processor industry. Software packages for decimal arithmetic are actually being challenged by decimal hardware units. This spreading trend seems to include hardware implementation of elementary functions. The (Coordinate Rotation Digital Computer) CORDIC algorithm, due to its simplicity, is one of the most efficient methods for computing elementary functions. In this work, we develop a decimal CORDIC scheme with almost half number of equally long cycles with respect to the best previous design. This is achieved via retiming of the conventional CORDIC architecture and selection of the microrotation factors by rounding. However, the proposed design does not lead to a predetermined constant scaling factor. The solution that we use is to iteratively compute the logarithm of the scaling factor followed by a decimal exponentiation. The same CORDIC hardware is reused for performing the latter. The proposed CORDIC method requires 2n + 3 cycles for n-digit decimal operands vs. 4n cycles of the previous methods. Evaluations with 16-digit operands based on logical effort analysis conclude that the proposed architecture shows 82% speed advantage, at the cost of 60% more area and 2.5 KB more ROM.

Hardware support for decimal computer arithmetic is regaining popularity. One reason is the recent growth of decimal computations in commercial, scientific, financial, and Internet-based computer applications. Newly commercialized decimal arithmetic hardware units use radix-10 sequential multipliers that are rather slow for multiplication-intensive applications. Therefore, the future relevant processors are likely to host fast parallel decimal multiplication circuits. The corresponding hardware algorithms are normally composed of three steps: partial product generation (PPG), partial product reduction (PPR), and final carry-propagating addition. The state of the art is represented by two recent full solutions with alternative designs for all the three aforementioned steps. In addition, PPR by itself has been the focus of other recent studies. In this paper, we examine both of the full solutions and the impact of a PPR-only design on the appropriate one. In order to improve the speed of parallel decimal multiplication, we present a new PPG method, fine-tune the PPR method of one of the full solutions and the final addition scheme of the other; thus, assembling a new full solution. Logical Effort analysis and 0.13 mum synthesis show at least 13 percent speed advantage, but at a cost of at most 36 percent additional area consumption.

Data shifting is required in many key computer operations from address decoding to computer arithmetic. Full barrel shifters are often on the critical path, which has led most research to be directed toward speed optimizations. With the advent of quantum computer and reversible logic, design and implementation of all devices in this logic has received more attention. This paper proposes a reversible implementation of a barrel shifter, and also evaluation of its quantum cost is presented.