Binary multiplierA binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of techniques can be used to implement a digital multiplier. Most techniques involve computing the set of partial products, which are then summed together using binary adders. This process is similar to long multiplication, except that it uses a base-2 (binary) numeral system. Between 1947 and 1949 Arthur Alec Robinson worked for English Electric Ltd, as a student apprentice, and then as a development engineer.
Euler methodIn mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).
Accumulator (computing)In a computer's central processing unit (CPU), the accumulator is a register in which intermediate arithmetic logic unit results are stored. Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to main memory, perhaps only to be read right back again for use in the next operation. Access to main memory is slower than access to a register like an accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register.
Instruction pipeliningIn computer engineering, instruction pipelining is a technique for implementing instruction-level parallelism within a single processor. Pipelining attempts to keep every part of the processor busy with some instruction by dividing incoming instructions into a series of sequential steps (the eponymous "pipeline") performed by different processor units with different parts of instructions processed in parallel. In a pipelined computer, instructions flow through the central processing unit (CPU) in stages.
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
Control unitThe control unit (CU) is a component of a computer's central processing unit (CPU) that directs the operation of the processor. A CU typically uses a binary decoder to convert coded instructions into timing and control signals that direct the operation of the other units (memory, arithmetic logic unit and input and output devices, etc.). Most computer resources are managed by the CU. It directs the flow of data between the CPU and the other devices. John von Neumann included the control unit as part of the Von Neumann architecture.
Execution unitIn computer engineering, an execution unit (E-unit or EU) is a part of the central processing unit (CPU) or graphics processing unit (GPU) that performs the operations and calculations forwarded from the instruction unit. It may have its own internal control sequence unit (not to be confused with the CPU's main control unit), some registers, and other internal units such as an arithmetic logic unit, address generation unit, floating-point unit, load–store unit, branch execution unit or some smaller and more specific components.
Central processing unitA central processing unit (CPU)—also called a central processor or main processor—is the most important processor in a given computer. Its electronic circuitry executes instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts with that of external components, such as main memory and I/O circuitry, and specialized coprocessors such as graphics processing units (GPUs). The form, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged.
Split-complex numberIn algebra, a split complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying A split-complex number has two real number components x and y, and is written The conjugate of z is Since the product of a number z with its conjugate is an isotropic quadratic form. The collection D of all split complex numbers for x,y \in \R forms an algebra over the field of real numbers. Two split-complex numbers w and z have a product wz that satisfies This composition of N over the algebra product makes (D, +, ×, *) a composition algebra.
Multiply–accumulate operationIn computing, especially digital signal processing, the multiply–accumulate (MAC) or multiply-add (MAD) operation is a common step that computes the product of two numbers and adds that product to an accumulator. The hardware unit that performs the operation is known as a multiplier–accumulator (MAC unit); the operation itself is also often called a MAC or a MAD operation. The MAC operation modifies an accumulator a: When done with floating point numbers, it might be performed with two roundings (typical in many DSPs), or with a single rounding.
Modular multiplicative inverseIn mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. In the standard notation of modular arithmetic this congruence is written as which is the shorthand way of writing the statement that m divides (evenly) the quantity ax − 1, or, put another way, the remainder after dividing ax by the integer m is 1.
Floating-point unitA floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be very low, so that some systems prefer to compute these functions in software.
Pipeline (computing)In computing, a pipeline, also known as a data pipeline, is a set of data processing elements connected in series, where the output of one element is the input of the next one. The elements of a pipeline are often executed in parallel or in time-sliced fashion. Some amount of buffer storage is often inserted between elements. Computer-related pipelines include: Instruction pipelines, such as the classic RISC pipeline, which are used in central processing units (CPUs) and other microprocessors to allow overlapping execution of multiple instructions with the same circuitry.
Split-octonionIn mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers. Unlike the standard octonions, they contain non-zero elements which are non-invertible. Also the signatures of their quadratic forms differ: the split-octonions have a split signature (4,4) whereas the octonions have a positive-definite signature (8,0). Up to isomorphism, the octonions and the split-octonions are the only two 8-dimensional composition algebras over the real numbers.
Modular arithmeticIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00.
ImplementationImplementation is the realization of an application, execution of a plan, idea, model, design, specification, standard, algorithm, policy, or the administration or management of a process or objective. In computer science, an implementation is a realization of a technical specification or algorithm as a program, software component, or other computer system through computer programming and deployment. Many implementations may exist for a given specification or standard.
Exponentiation by squaringIn mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For semigroups for which additive notation is commonly used, like elliptic curves used in cryptography, this method is also referred to as double-and-add.
Instruction set architectureIn computer science, an instruction set architecture (ISA), also called computer architecture, is an abstract model of a computer. A device that executes instructions described by that ISA, such as a central processing unit (CPU), is called an implementation. In general, an ISA defines the supported instructions, data types, registers, the hardware support for managing main memory, fundamental features (such as the memory consistency, addressing modes, virtual memory), and the input/output model of a family of implementations of the ISA.
Heun's methodIn mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.
Split-biquaternionIn mathematics, a split-biquaternion is a hypercomplex number of the form where w, x, y, and z are split-complex numbers and i, j, and k multiply as in the quaternion group. Since each coefficient w, x, y, z spans two real dimensions, the split-biquaternion is an element of an eight-dimensional vector space. Considering that it carries a multiplication, this vector space is an algebra over the real field, or an algebra over a ring where the split-complex numbers form the ring.
