Computer arithmetic

Exponent bias

In IEEE 754 floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent.Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder. To solve this problem the exponent is stored as an unsigned value which is suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias. By arranging the fields such that the sign bit takes the most significant bit position, the biased exponent takes the middle position, then the significand will be the least significant bits and the resulting value will be ordered properly. This is the case whether or not it is interpreted as a floating-point or integer value. The purpose of this is to enable high speed comparisons between floating-point numbers using fixed-point hardware. To calculate the bias for an arbitrarily sized floating-point number apply the formula 2k−1 − 1 where k is the number of bits in the exponent. When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. * For a single-precision number, the exponent is stored in the range 1 .. 254 (0 and 255 have special meanings), and is interpreted by subtracting the bias for an 8-bit exponent (127) to get an exponent value in the range −126 .. +127. * For a double-precision number, the exponent is stored in the range 1 .. 2046 (0 and 2047 have special meanings), and is interpreted by subtracting the bias for an 11-bit exponent (1023) to get an exponent value in the range −1022 .. +1023. * For a quad-precision number, the exponent is stored in the range 1 .. 32766 (0 and 32767 have special meanings), and is interpreted by subtracting the bias for a 15-bit exponent (16383) to get an exponent value in the range −16382 .. +16383. (Wikipedia).

Video thumbnail

What are the rules of exponents and the most common mistakes with the rules

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

How Does the Rules of Exponents Allows to Multiply and Divide by Monomials

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What is the power of quotient property of exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Floating Point Representation

Floating Point Representation

From playlist Scientific Computing

Video thumbnail

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

Video thumbnail

Applying the rules of exponents to simplify an expression with numbers

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Teaching the Negative Exponent Rule without Talking

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What is an exponent - Teacher explains all

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Simplifying Expressions with Negative Exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What is the product of powers of exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Quotient rule of exponents without talking

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Dynamical fluctuations in classical and quantum systems by Carlos Perez Espigares

Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst

From playlist Large deviation theory in statistical physics: Recent advances and future challenges

Video thumbnail

L14.8 Inferring the Unknown Bias of a Coin and the Beta Distribution

MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

Video thumbnail

Stanford CS229: Machine Learning | Summer 2019 | Lecture 13-Statistical Learning Uniform Convergence

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3py8nGr Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html

From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)

Video thumbnail

MegaFavNumbers | The magic number and the legendary fast inverse square root hack.

Hi! I'm Rodrigo Aldana. This is my contribution to the #MegaFavNumbers project. This video is based on a presentation I gave some time ago about the fast inverse square root algorithm but now focused on the related magic number 1597463007. I want to make something clear: 1597463007 is not

From playlist MegaFavNumbers

Video thumbnail

Stanford CS229: Machine Learning | Summer 2019 | Lecture 22 - Practical Tips and Course Recap

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3jsA4Ng Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html

From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)

Video thumbnail

Can We Define Random Close Packing? by Dov Levin

DISCUSSION MEETING : STATISTICAL PHYSICS OF COMPLEX SYSTEMS ORGANIZERS : Sumedha (NISER, India), Abhishek Dhar (ICTS-TIFR, India), Satya Majumdar (University of Paris-Saclay, France), R Rajesh (IMSc, India), Sanjib Sabhapandit (RRI, India) and Tridib Sadhu (TIFR, India) DATE : 19 December

From playlist Statistical Physics of Complex Systems - 2022

Video thumbnail

Non-equilibrium Relaxation and Aging Scaling in Driven Systems by Uwe C Täuber

Bangalore School on Statistical Physics - VIII DATE: 28 June 2017 to 14 July 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru This advanced level school is the eighth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in s

From playlist Bangalore School on Statistical Physics - VIII

Video thumbnail

Topology of Norms Defined by Systems of Linear forms - Pooya Hatami

Pooya Hatami University of Chicago May 7, 2012 Gowers' uniformity norms are defined by average of a function over specific sets of linear forms. We study norms that are similarly defined by a system of linear forms. We prove that for bounded complex functions over FnpFpn, each such norm is

From playlist Mathematics

Video thumbnail

Learn how to apply the quotient rule of exponents with numbers

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Related pages

IEEE 754 | Offset binary | Significand | Two's complement | Floating-point arithmetic