Computer arithmetic

Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols. The four best-known methods of extending the binary numeral system to represent signed numbers are: , , , and . Some of the alternative methods use implicit instead of explicit signs, such as negative binary, using the . Corresponding methods can be devised for other bases, whether positive, negative, fractional, or other elaborations on such themes. There is no definitive criterion by which any of the representations is universally superior. For integers, the representation used in most current computing devices is two's complement, although the Unisys ClearPath Dorado series mainframes use ones' complement. (Wikipedia).

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1. Unsigned Binary Numbers - How to Convert From Unsigned Binary Numbers to Whole Numbers

This tutorial shows how to convert from an unsigned binary number to a whole number. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Binary Numbers

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Representation theory: Introduction

This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr

From playlist Representation theory

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Prealgebra 2.01b - Integers and the Number Line

Integers on the number line, a quick intro to set notation, and recognizing which numbers are integers are which are not. From the Prealgebra course by Derek Owens. This course is available online at http://www.LucidEducation.com.

From playlist Prealgebra Chapter 2 (Complete chapter)

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Identifying Sets of Real Numbers

This video provides several examples of identifying the sets a real number belongs to. Complete Video Library: http://www.mathispower4u.com Search by Topic: http://www.mathispower4u.wordpress.com

From playlist Number Sense - Properties of Real Numbers

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Imaginary Numbers, Functions of Complex Variables: 3D animations.

Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.

From playlist Physics

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Signed Number Operations (L1.4)

This video reviews the absolute value, addition, subtraction, multiplication, and division of signed numbers. Video content created Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)

From playlist Multiplying and Dividing Integers

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Ex 2: Multiplying Signed Mixed Number

This video provides two examples of multiplying signed mixed numbers. Search Video Library at http://www.mathispower4u.wordpress.com

From playlist Multiplying and Dividing Mixed Numbers

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2. Unsigned Binary Numbers - How to Convert From Whole Numbers to Unsigned Binary Numbers

This tutorial shows how to convert from a whole number to an unsigned binary number. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)

From playlist Binary Numbers

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Floating Point Representation

Floating Point Representation

From playlist Scientific Computing

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The local Gan-Gross-Prasad conjecture for real unitary groups - Hang Xue

Joint IAS/Princeton University Number Theory Seminar Topic: The local Gan-Gross-Prasad conjecture for real unitary groups Speaker: Hang Xue Affiliation: The University of Arizona Date: March 25, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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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

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Jessica Fintzen - 1/2 Supercuspidal Representations: Construction, Classification, and Characters

We have seen in the first week of the summer school that the buildings blocks for irreducible representations of p-adic groups are the supercuspidal representations. In these talks we will explore explicit exhaustive constructions of these supercuspidal representations and their character

From playlist 2022 Summer School on the Langlands program

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Different Types of Numbers on the number line, lesson 1 #shorts

Watch the full playlist: https://www.youtube.com/watch?v=kcxK3_sROZA&list=PL14bv5vXK2WWuODhGbpPQA0GamV5ohOVb&index=1 Natural Numbers (N), (also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …} Whole Numbers (W). This is the set of na

From playlist Celebrities Teach Math: The Number System

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Talk by Hang Xue (University of Arizona, USA)

Local Gan–Gross–Prasad Conjecture for Real Unitary Groups

From playlist Seminars: Representation Theory and Number Theory

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Binary 6 – Normalised Floating Point Binary Fractions

This is the sixth 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 conversion of real numbers, both positive and negative, from denary into normalised floating point binary. It

From playlist Binary

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Molecular Structure & Statistical Mechanics 131B. Lecture 03. Transformation Matrices.

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 03. Molecular Structure & Statistical Mechanics -- Transformation Matrices. View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html Instructor: R

From playlist Chem 131B: Molecular Structure & Statistical Mechanics

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Discrete Structures: Floating-Point Representation and IEEE-754

In this session we'll learn how computers store floating-point numbers using a standard called IEEE-754. However, because the number of bits in the real standard is unwieldy, we will use a modified representation that uses fewer bits.

From playlist Discrete Structures, Spring 2022

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Blocks and Defect Groups of SLn - Nate Harman

SL2 Seminar Topic: Blocks and Defect Groups of SLn Speaker: Nate Harman Affiliation: Member, School of Mathematics Date: November 10, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

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Wee Teck Gan: Theta lifts of tempered representations and Langlands parameter

Abstract: In joint work with Hiraku Atobe, we determine the theta lifting of irreducible tempered representations for symplectic-metaplectic­orthogonal and unitary dual pairs in terms of the local Langlands correspondence. The main new tool for proving our result is the recently establishe

From playlist Jean-Morlet Chair - Research Talks - Prasad/Heiermann

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Complex Numbers as Matrices

In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im

From playlist Complex Numbers

Related pages

IEEE 754 | Absolute value | Significand | Numerical digit | Two's complement | Negation | Signedness | Carry flag | Byte | Integer overflow | Balanced ternary | Signed zero | Congruence relation | Negative number | Power of two | Signed-digit representation | Most significant bit | Floating-point arithmetic | Exponential-Golomb coding | Method of complements | Exponent bias | Sign bit | Mathematics | Variable-length quantity | Ring (mathematics) | Least significant bit | Bit | Excess-127 | Excess-3 | Radix | Computer number format | Excess-1023 | Positional notation | Binary-coded decimal | Modular arithmetic