In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to N decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits. Be aware that roundoff errors can accumulate. If M decimal places are used in the intermediate calculation, we say there are MβN guard digits. Guard digits are also used in floating point operations in most computer systems. Given we have to line up the binary points. This means we must add an extra digit to the first operandβa guard digit. This gives us . Performing this operation gives us or . Without using a guard digit we have , yielding or . This gives us a relative error of 1. Therefore, we can see how important guard digits can be. An example of the error caused by floating point roundoff is illustrated in the following C code. int main{ double a; int i; a = 0.2; a += 0.1; a -= 0.3; for (i = 0; a < 1.0; i++) a += a; printf("i=%d, a=%f ", i, a); return 0;} It appears that the program should not terminate. Yet the output is : i=54, a=1.000000 Another example is: Take 2 numbers: and we bring the first number to the same power of as the second one: The addition of the 2 numbers is: 0.0256*10^2 2.3400*10^2 + ____________ 2.3656*10^2 After padding the second number (i.e., ) with two s, the bit after is the guard digit, and the bit after is the round digit. The result after rounding is as opposed to , without the extra bits (guard and round bits), i.e., by considering only . The error therefore is . (Wikipedia).
Quickly fill in the unit circle by understanding reference angles and quadrants
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
How to memorize the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Learn how to construct the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
How to quickly write out the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Watch me complete the unit circle
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Why the unit circle is so helpful for us to evaluate trig functions
π Learn about the unit circle. A unit circle is a circle which radius is 1 and is centered at the origin in the cartesian coordinate system. To construct the unit circle we take note of the points where the unit circle intersects the x- and the y- axis. The points of intersection are (1, 0
From playlist Trigonometric Functions and The Unit Circle
Math for Liberal Studies - Lecture 3.4.2 UPC Bar Codes
This is the second video lecture for Math for Liberal Studies Section 3.4: Bar Codes. In this video, we discuss the pattern of light and dark bars that is used to encode UPC numbers. We talk about the different parts of the UPC bar code and work through and example decoding parts of a UPC.
From playlist Math for Liberal Studies Lectures
Determine the point on the unit circle for an angle
π Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
EEVblog #1017 - Enter The World Of Atto Amps
Dave tears down the Keithley 617 Electrometer, capable of measuring sub-femtoamp (attoamps!) resolution. Low Level Measurement Handbook: http://www.tek.com/sites/tek.com/files/media/document/resources/LowLevelHandbook_7Ed.pdf Forum: http://www.eevblog.com/forum/blog/eevblog-1017-enter-the-
From playlist Teardown Tuesday
Math for Liberal Studies - Lecture 3.4.1 POSTNET Bar Codes
This is the first video for Math for Liberal Studies Section 3.4: Bar Codes. In this video, I discuss different kinds of bar codes, focusing on the POSTNET code, which was used on US mail until 2013. This code uses a pattern of tall and short bars that can be used to encode ZIP code inform
From playlist Math for Liberal Studies Lectures
EEVblog 1476 - Keithley 515A Wheatstone Bridge TEARDOWN & TUTORIAL
Teardown of the Keithley 515A Megohm Wheatstone bridge, plus a tutorial on how Wheatsone bridges work and their applications. Manual & Schematic: https://download.tek.com/manual/515A(Model515A).pdf 1960's Daven precision resistor and attenuator catalog: http://www.technicalaudio.com/pdf/Da
From playlist Product Reviews & Teardowns
DEFCON 15: The Next Wireless Frontier - TV White Spaces
Speaker: Doug Mohney Editor, VON Magazine More unlicensed bandwidth from TV!?! A long-term push to free up more wireless spectrum is expected to come to fruition this year as the FCC will open up unused TV channels - dubbed "white spaces" - for unlicensed broadband use this fall, with ful
From playlist DEFCON 15
Stanford Seminar - Crowds, Crisis & Convergence: Unpacking "Crowdsourcing" in Context of Disaster
Kate Starbird University of Washington This seminar series features dynamic professionals sharing their industry experience and cutting edge research within the human-computer interaction (HCI) field. Each week, a unique collection of technologists, artists, designers, and activists will
From playlist Stanford Seminars
Lec 1 - Motivation and Introduction
Lecture Series on Wireless Communications by Dr.Ranjan Bose, Department of Electrical Engineering, IIT Delhi. For more details on NPTEL, visit http://nptel.iitm.ac.in
From playlist Wireless Communication
Advanced Bitcoin Scripting -- Part 1: Transactions & Multisig
This is the first part of a more technical talk where Andreas explores Bitcoin script, with examples from the 2nd edition of Mastering Bitcoin, focusing on the use of conditional statements, flow control, guard clauses and time locks. The examples will include advanced multi-signature scri
From playlist Bitcoin Talks by Andreas M. Antonopoulos
How to find the point on the unit circle from the given real number
π Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
Barcodes In One Lesson. Barcodes have revolutionized modern life. Discover what happens every time you hear a beep at the checkout. I was inspired to make this video based upon an explanation of barcodes I found in a great book called Code: The Hidden Language of Computer Hardware and Sof
From playlist POS related videos
How to determine the point on the unit circle given an angle
π Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the a
From playlist Evaluate Trigonometric Functions With The Unit Circle (ALG2)
mod-25 lec-26 Introduction to Fluid Logic
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)