Floating point | Computer arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term floating point refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times. The result of this dynamic range is that the numbers that can be represented are not uniformly spaced; the difference between two consecutive representable numbers varies with their exponent. Over the years, a variety of floating-point representations have been used in computers. In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, and since the 1990s, the most commonly encountered representations are those defined by the IEEE. The speed of floating-point operations, commonly measured in terms of FLOPS, is an important characteristic of a computer system, especially for applications that involve intensive mathematical calculations. A 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. (Wikipedia).
Binary 4 – Floating Point Binary Fractions 1
This is the fourth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers the representation of real numbers using floating point binary notation. It begins with a description of standard
From playlist Binary
Binary 5 – Floating Point Range versus Precision
This is the fifth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video elaborates on the representation of real numbers using floating point binary notation. It explains how the relative allo
From playlist Binary
Binary 7 – Floating Point Binary Addition
This is the seventh in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers adding together floating point binary numbers for a given sized mantissa and exponent, both in two’s complement.
From playlist Binary
Eva Darulova : Programming with numerical uncertainties
Abstract : Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. Finite-precision arithmetic, such as fixed-point or floating-point, is a common and efficient choice, but introd
From playlist Mathematical Aspects of Computer Science
IEEE 754 Standard for Floating Point Binary Arithmetic
This computer science video describes the IEEE 754 standard for floating point binary. The layouts of single precision, double precision and quadruple precision floating point binary numbers are described, including the sign bit, the biased exponent and the mantissa. Examples of how to con
From playlist Binary
Binary 8 – Floating Point Binary Subtraction
This is the eighth in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers subtraction of floating point binary numbers for a given sized mantissa and exponent, both in two’s complement.
From playlist Binary
Binary 3 – Fixed Point Binary Fractions
This is the third in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. It covers the representation of real numbers in binary using a fixed size, fixed point, register. It explains with examples how to convert both po
From playlist Binary
Optimizing Code in the Wolfram Compiler
In this talk, Mark Sofroniou gives an introductory overview of the design and current state of the Wolfram Compiler. He outlines the benefits of using an intermediary representation that maps to LLVM and describes how this has influenced recent improvements to the implementation. Examples
From playlist Wolfram Technology Conference 2020
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Mark Sofroniou Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, an
From playlist Wolfram Technology Conference 2018
Linear Algebra for the Standard C++ Library
Linear algebra is a mathematical discipline of ever-increasing importance in today's world, with direct application to a wide variety of problem domains, such as signal processing, computer graphics, medical imaging, machine learning, data science, financial modeling, and scientific simula
From playlist C++
Assembly Language Tutorial 4 Floats & Switch
Code & Transcript Here : http://goo.gl/Tl6GCN Support me on Patreon : https://www.patreon.com/derekbanas In this part of my Assembly Language Tutorial I will cover how to convert decimal values into floats, storing and loading floats, performing arithmetic on floats, comparing floats and
From playlist Assembly Language
Arithmetic in Python V3 || Python Tutorial || Learn Python Programming
Today we talk about the rules of arithmetic in Python Version 3. The key detail is when combining two numbers, Python will widen numbers to make sure they are all of the same type. (In Python v3, there are three numeric types: ints, floats and complex numbers.) And division has changed
From playlist Python Programming Tutorials (Computer Science)
Arithmetic in Python V2 || Python Tutorial || Learn Python Programming
Today we talk about the rules of arithmetic in Python Version 2. The key detail is when combining two numbers, Python will widen numbers to make sure they are all of the same type. (In Python v2, there are four numeric types: ints, longs, floats and complex numbers.) Also, when you divi
From playlist Python Programming Tutorials (Computer Science)
12/05/2019, Nicolas Brisebarre
Nicolas Brisebarre, École Normale Supérieure de Lyon Title: Correct rounding of transcendental functions: an approach via Euclidean lattices and approximation theory Abstract: On a computer, real numbers are usually represented by a finite set of numbers called floating-point numbers. Wh
From playlist Fall 2019 Symbolic-Numeric Computing Seminar
In this video, you’ll learn more about decimals. Visit https://www.gcflearnfree.org/decimals/ for our interactive text-based tutorial. This video includes information on: • Reading decimals • Comparing decimals We hope you enjoy!
From playlist Math Basics