Related papers: Comparing quaternary and binary multipliers
The data transfer between a processor and memory has become a design bottleneck in data-intensive applications. Processing-In-Memory (PIM) is a practical approach to overcome the memory wall bottleneck. The 4:2 compressor is suitable for…
Deep Convolutional Neural Networks (CNNs) have become state-of-the art for computer vision and other signal processing tasks due to their superior accuracy. In recent years, large efforts have been made to reduce the computational costs of…
Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the…
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
Binary neural networks have attracted tremendous attention due to the efficiency for deploying them on mobile devices. Since the weak expression ability of binary weights and features, their accuracy is usually much lower than that of…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
Two multiplierless algorithms are proposed for 4x4 approximate-DCT for transform coding in digital video. Computational architectures for 1-D/2-D realisations are implemented using Xilinx FPGA devices. CMOS synthesis at the 45 nm node…
Binary addition is one of the most primitive and most commonly used applications in computer arithmetic. A large variety of algorithms and implementations have been proposed for binary addition. Huey Ling proposed a simpler form of CLA…
This paper explores the possibilities of using a computing methodology --hardware and software-- that employs technology other than binary. I refer to this as "supra - binary" computing. Software constructs that use more than binary…
Since compiler optimization is the most common source contributing to binary code differences in syntax, testing the resilience against the changes caused by different compiler optimization settings has become a standard evaluation step for…
A new variant of bit interleaved coded modulation (BICM) is proposed. In the new scheme, called Parallel BICM, L identical binary codes are used in parallel using a mapper, a newly proposed finite-length interleaver and a binary dither…
The $N$th power of a polynomial matrix of fixed size and degree can be computed by binary powering as fast as multiplying two polynomials of linear degree in~$N$. When Fast Fourier Transform (FFT) is available, the resulting complexity is…
Geometric objects are primarily represented using curves and surfaces and the subdivision schemes are the basic tools for these representations. This study is based on a new thought that there is a special relation between the binary and…
This paper explores whether or not a complete ternary full adder, whose input variables can independently be '0', '1', or '2', is indispensable in the arithmetic blocks of adder, subtractor, and multiplier. Our investigations show that none…
In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A1, A2,... Ak…
The finite field multiplier is mainly used in many of today's state of the art digital systems and its hardware implementation for bit parallel operation may require millions of logic gates. Natural causes or soft errors in digital design…
Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This…