Found 468 Articles for Mathematics

Adjacency MatrixAdjacency Matrix is used to represent a graph. We can represent directed as well as undirected graphs using adjacency matrices. Following are the key properties of an Adjacency matrix.PropertiesAn Adjacency Matrix A[V][V] is a 2D array of size V × V where V is the number of vertices in a undirected graph.If there is an edge between Vx to Vy then the value of A[Vx][Vy] = 1 and A[Vy][Vx]=1, otherwise the value will be zero.For a directed graph, if there is an edge between Vx to Vy, then the value of A[Vx][Vy]=1, otherwise the value will be zero.Adjacency Matrix ... Read More

To reach on a conclusion on quantified statements, there are four rules of inference which are collectively called as Inference Theory of the Predicate Calculus.Table of Rules of InferenceRule of InferenceName$$\begin{matrix} \forall x P(x) \ \hline \therefore P(y) \end{matrix}$$Rule US: Universal Specification$$\begin{matrix} P(c) \text { for any c} \ \hline \therefore \forall x P(x) \end{matrix}$$Rule UG: Universal Generalization$$\begin{matrix} \exists x P(x) \ \hline \therefore P(c) \text { for any c} \ \end{matrix}$$Rule ES: Existential Specification$$\begin{matrix} P(c) \text { for any c} \ \therefore \exists x P(x) \end{matrix}$$Rule EG: Existential GeneralizationRule US: Universal Specification - From $(x)P(x)$, one can conclude $P(y)$.Rule ... Read More

Measuring things and distances is one of the important concepts to learn when we are studying maths. For maximum uses, measuring scales do the work quite well and everyone is aware of it how to use one. But the measuring scale only provides a specific level of correctness and once you need exact measurements which lie between two spots on the scale it becomes difficult to get a correct reading without a bit of counterpart.Also measuring scales are very vulnerable to parallax mistakes which can cause a huge portion of the difference in readings from person to person which is ... Read More

The reflected binary code or Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers.Conversion of Gray to Binary CodeGray codes are used in rotary and optical encoders, Karnaugh maps, and error detection. The ... Read More

The reflected binary code or Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers.Conversion of Binary to Gray CodeGray codes are used in rotary and optical encoders, Karnaugh maps, and error detection. The ... Read More

The reflected binary code or Gray code is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). Gray codes are very useful in the normal sequence of binary numbers generated by the hardware that may cause an error or ambiguity during the transition from one number to the next. So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers.Gray code is not weighted that means it does not depends on positional value of digit. This cyclic variable code ... Read More

The excess-3 code (or XS3) is a non-weighted code used to express code used to express decimal numbers. It is a self-complementary binary coded decimal (BCD) code and numerical system which has biased representation. It is particularly significant for arithmetic operations as it overcomes shortcoming encountered while using 8421 BCD code to add two decimal digits whose sum exceeds 9. Excess-3 arithmetic uses different algorithm than normal non-biased BCD or binary positional number system.Representation of Excess-3 CodeExcess-3 codes are unweighted and can be obtained by adding 3 to each decimal digit then it can be represented by using 4 bit ... Read More

Digital Computers use Binary number system to represent all types of information inside the computers. Alphanumeric characters are represented using binary bits (i.e., 0 and 1). Digital representations are easier to design, storage is easy, accuracy and precision are greater.There are various types of number representation techniques for digital number representation, for example: Binary number system, octal number system, decimal number system, and hexadecimal number system etc. But Binary number system is most relevant and popular for representing numbers in digital computer system.Storing Real NumberThese are structures as following below −There are two major approaches to store real numbers (i.e., ... Read More

Complements are used in digital computers in order to simply the subtraction operation and for the logical manipulations. For the Binary number (base-2) system, there are two types of complements: 1’s complement and 2’s complement.1’s Complement of a Binary NumberThere is a simple algorithm to convert a binary number into 1’s complement. To get 1’s complement of a binary number, simply invert the given number.2’s Complement of a Binary NumberThere is a simple algorithm to convert a binary number into 2’s complement. To get 2’s complement of a binary number, simply invert the given number and add 1 to the ... Read More

Binary Number System is one the type of most popular Number Representation techniques that used in digital systems. In the Binary System, there are only two symbols or possible digit values, i.e., 0 (off) and 1 (on). Represented by any device that only 2 operating states or possible conditions. Generally, there are two types of complement of Binary number: 1's complement and 2’s complement. To get 1’s complement of a binary number, simply invert the given number. For example, 1’s complement of binary number 110010 is 001101. To get 2’s complement of binary number is 1’s complement of given number ... Read More