Related papers: On Two Conversion Methods of Decimal-to-Binary
The paper proposes a new method to determine a binary control signal for an analog linear system such that the state, or some output, of the system follows a given target trajectory. The method can also be used for digital-to-analog…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
We introduce the concept of negative coefficients in various number-based systems, with a focus on decimal and binary systems. We demonstrate that every binary number can be transformed into a sparse form, significantly enhancing…
Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of…
This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…
When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing…
Binary stars are fundamental to astrophysics, providing critical insights into stellar evolution, galactic dynamics, and fundamental physics. However, the high dimensionality of orbital parameters and observational constraints present…
Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous…
The binary radix expansion of a real number can be used to code the outcome of any series of coin tosses, a fact that provides an intriguing link between number theory, measure theory and statistical physics. Inspired by this fact, a…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
A new application of a fast CCD drift scanning technique that allows us to perform speckle imaging of binary stars is presented. For each observation, an arbitrary number of speckle frames is periodically stored on a computer disk, each…
Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this work, we study the problem of data classification from binary data and…
Binary code similarity detection is to detect the similarity of code at binary (assembly) level without source code. Existing works have their limitations when dealing with mutated binary code generated by different compiling options. In…
Binary embedding of high-dimensional data aims to produce low-dimensional binary codes while preserving discriminative power. State-of-the-art methods often suffer from high computation and storage costs. We present a simple and fast…
We describe three algorithms for generating binary-valued holograms. Our methods are optimised for producing large arrays of tightly focussed optical tweezers for trapping particles. Binary-valued holograms allow us to use a digital mirror…
Binary linear block codes (BLBCs) are essential to modern communication, but their diverse structures often require tailor-made decoders, increasing complexity. This work introduces enhanced polar decoding ($\mathsf{PD}^+$), a universal…
This paper introduces the Adaptive Base Representation (ABR) Theorem and proposes a novel number system that offers a structured alternative to the binary number system for digital computers. The ABR number system enables each decimal…
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
Binary black hole simulations have traditionally been computationally very expensive: current simulations are performed in supercomputers involving dozens if not hundreds of processors, thus systematic studies of the parameter space of…