Binary arithmetic | Floating point types | Computer arithmetic
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.4028235 × 1038. All integers with 7 or fewer decimal digits, and any 2n for a whole number −149 ≤ n ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754-2008 standard, the 32-bit base-2 format is officially referred to as binary32; it was called single in IEEE 754-1985. IEEE 754 specifies additional floating-point types, such as 64-bit base-2 double precision and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language designers. E.g., GW-BASIC's single-precision data type was the 32-bit MBF floating-point format. Single precision is termed REAL in Fortran, SINGLE-FLOAT in Common Lisp, float in C, C++, C#, Java, Float in Haskell and Swift, and Single in Object Pascal (Delphi), Visual Basic, and MATLAB. However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers. In most implementations of PostScript, and some embedded systems, the only supported precision is single. (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
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 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
Chapter 01.05: Lesson: IEEE-754 Single Precision Representation: Part 2 of 2
Learn how the IEEE-754 standard represents a floating point in single precision. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/floatingpoint_representation.html
From playlist Scientific Computing
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
Decimal Notation: Writing Decimals in Words
This video explains how to write numbers in decimal notation in words. http://mathispower4u.com
From playlist Introduction to Decimals
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
Go to https://www.youtube.com/watch?v=ICJ5dtBUc1M for replacement. Floating Pt Repre Ex Pt 1 of 2.
Learn via example how to represent a number in floating point. For more videos and resources on this topic, please visit http://nm.mathforcollege.com/topics/floatingpoint_representation.html
From playlist Scientific Computing
Performant, scalable models in TensorFlow 2 with tf.data, tf.function & tf.distribute (TF World '19)
TensorFlow’s tf.distribute library helps you scale your model from a single GPU to multiple GPUs and finally to multiple machines using simple APIs that require very few changes to your existing code. Come learn about how you can use tf.distribute to scale your machine learning model on a
From playlist TensorFlow World 2019
[1] - Introduction to C/C++ - Basic starting points
This is my very first video introducing basic concepts of programming in C/C++. See the notebook page here: https://tinyurl.com/y88xv3kl Please comment and give me feedback. Was it too basic, too slow, too fast? What should I cover in the next video? Did I skip over something or do s
From playlist One-off Tutorials
Introducing MATLAB Fundamental Classes (Data Types)
Get a Free Trial: https://goo.gl/C2Y9A5 Get Pricing Info: https://goo.gl/kDvGHt Ready to Buy: https://goo.gl/vsIeA5 Work with numerical, textual, and logical data types. For more videos, visit http://www.mathworks.com/products/matlab/examples.html
From playlist MATLAB Tutorials: Getting Started with MATLAB
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
Python Quick Tip: F-Strings - How to Use Them and Advanced String Formatting
In this Python Programming Tutorial, we will be learning how to use f-strings to format strings. F-strings are new to Python3.6+ and are extremely useful once you learn how to use them. Viewers have likely seen me use f-strings in previous videos so this video will go into detail exactly h
From playlist Python Tutorials
Ultimate Guide To Scaling ML Models - Megatron-LM | ZeRO | DeepSpeed | Mixed Precision
🚀 Sign up for AssemblyAI's speech API using my link 🚀 https://www.assemblyai.com/?utm_source=youtube&utm_medium=social&utm_campaign=theaiepiphany 👨👩👧👦 Join our Discord community 👨👩👧👦 https://discord.gg/peBrCpheKE In this video I show you what it takes to scale ML models up to tril
From playlist Miscellaneous
Decimal Notation: Saying Decimals and Writing Decimals as Fractions
This video explains how to say numbers written in decimal notation using place value. Decimals are also writing in fraction form. http://mathispower4u.com
From playlist Introduction to Decimals