In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (hardware) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called complements. Thus subtraction of any number is implemented by adding its complement. Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the radix complement (as described below) is also valuable in number theory, such as in Midy's theorem. The nines' complement of a number given in decimal representation is formed by replacing each digit with nine minus that digit. To subtract a decimal number y (the subtrahend) from another number x (the minuend) two methods may be used: In the first method the nines' complement of x is added to y. Then the nines' complement of the result obtained is formed to produce the desired result. In the second method the nines' complement of y is added to x and one is added to the sum. The leftmost digit '1' of the result is then discarded. Discarding the leftmost '1' is especially convenient on calculators or computers that use a fixed number of digits: there is nowhere for it to go so it is simply lost during the calculation. The nines' complement plus one is known as the ten's complement. The method of complements can be extended to other number bases (radices); in particular, it is used on most digital computers to perform subtraction, represent negative numbers in base 2 or binary arithmetic and test underflow and overflow in calculation. (Wikipedia).
Double Complement of a Set | Set Theory
What is the complement of the complement of a set? In today's set theory lesson we'll discuss double complements with respect to "absolute complements - being complements taken with respect to a universal set as opposed to relative complements. When we consider a universal set, every oth
From playlist Set Theory
Math 060 Fall 2017 103017C Orthogonal Complements
Orthogonal subspaces; examples; nonexample. Orthogonal complements. Trivial observations about orthogonal subspaces and orthogonal complements. Fundamental Subspaces Theorem. More facts about orthogonal complements: the dimension of an orthogonal complement is complementary to the dime
From playlist Course 4: Linear Algebra (Fall 2017)
Adding And Subtracting Fractions - Quick Method
Adding and subtracting fractions by cross-multiplying or the upside down picnic table!
From playlist QTS Numeracy Skills
How to subtract two vectors with scalars
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
How to subtract two vectors with scalars
Learn how to determine the resultant vector by adding, subtracting and multiplying vectors by a scalar. We will also learn how to graph the resultant vectors to show the operations. Vectors can be added, subtracted and multiplied. To add or subtract two or more vectors, we add each of the
From playlist Vectors
How to multiply two decimals by each other
👉 You will learn how to multiply numbers in decimal form. We will work with decimals that are greater and less than one. When multiplying decimals it is important to line up the decimal point so that you keep the place values of the numbers. We will apply multi digit multiplication to f
From playlist How to multiply and divide decimals
Learn how to multiply a three digit decimal to a two digit decimal
👉 You will learn how to multiply numbers in decimal form. We will work with decimals that are greater and less than one. When multiplying decimals it is important to line up the decimal point so that you keep the place values of the numbers. We will apply multi digit multiplication to f
From playlist How to multiply and divide decimals
How to multiply a two digit decimal from a three digit decimal
👉 You will learn how to multiply numbers in decimal form. We will work with decimals that are greater and less than one. When multiplying decimals it is important to line up the decimal point so that you keep the place values of the numbers. We will apply multi digit multiplication to f
From playlist How to multiply and divide decimals
Orthogonal complements. The direct sum of a subspace and its orthogonal complement. Dimension of the orthogonal complement. The orthogonal complement of the orthogonal complement.
From playlist Linear Algebra Done Right
Binary Addition and Subtraction With Negative Numbers, 2's Complements & Signed Magnitude
This video tutorial explains how to perform binary addition and subtraction with negative numbers. It also explains how to express numbers in binary form using two methods - the 2's complement and the signed magnitude method. My E-Book: https://amzn.to/3B9c08z Video Playlists: https://
From playlist Number Systems
Binary 2 - Two's Complement Representation of Negative Numbers
This is the second in a series of computer science videos about the binary number system which is fundamental to the operation of a digital electronic computer. It covers the two's complement system of representing positive and negative integers in binary. It demonstrates how two's comple
From playlist Binary
ELEC2141 Digital Circuit Design - Lecture 25
ELEC2141 Week 9 Lecture 3: Arithmetic Circuits
From playlist ELEC2141 Digital Circuit Design
Excel Busn Math 44: Series Trade Discounts
Download Excel File: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/135ch06.xls Download pdf file: https://people.highline.edu/mgirvin/YouTubeExcelIsFun/BusnMathCh06.pdf Learn about: 1)Series Trade Discounts a.Discounts separately method b.Complement method Net Cost Equivalent
From playlist Excel Business Math Formulas, Functions, Solving Problems
Using the Element Method to prove a Set Containment w/ Modus Tollens
We use the element method to show that B^c is a subset of A^c if A is a subset of B. The element method works by taking one generic element in the first set and demonstrating that it is necessarily in the other. In this video we will use modus tollens and the idea of contrapositives to for
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Showed that natural numbers and real n
From playlist MIT 18.404J Theory of Computation, Fall 2020
Hierarchical Interpolative Factorization
At the 2013 SIAM Annual Meeting, Lexing Ying of Stanford University discussed some recent results on developing new factorizations for matrices obtained from discretizing differential and integral operators. A common ingredient of these new factorizations is the interpolative decomposition
From playlist Complete lectures and talks: slides and audio
Factorization-based Sparse Solvers and Preconditions, Lecture 5
Xiaoye Sherry Li's (from Lawrence Berkeley National Laboratory) lecture number five on Factorization-based sparse solves and preconditioners
From playlist Gene Golub SIAM Summer School Videos
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Discussed the reducibility method to p
From playlist MIT 18.404J Theory of Computation, Fall 2020
Adding, subtracting, multiplying and dividing two functions
👉 Learn how to apply operations to functions such as adding, subtracting, multiplying, and dividing to two functions. To add/subtract/multiply or divide two functions, we algebraically add/subtract/multiply or add the rules (contents) of the two functions. We will then simplify the sum, d
From playlist Add Subtract Multiply Divide Functions
Yang Liu: Fully Dynamic Electrical Flows: Sparse Maxflow Faster than Goldberg-Rao
We give an algorithm for computing exact maximum flows on graphs with m edges and integer capacities in the range [1,U] in ̃O(m^((3/2) −(1/328)) log U) time. For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the ̃O(m^(1.5) log U) time bou
From playlist Workshop: Continuous approaches to discrete optimization