Found 496 Articles for Computer Engineering

A multistation access unit (MSAU), also called a media access unit (MAU), is a central device that acts as Ethernet transceivers in local area networks. It is used to connect network stations or nodes in LANs and operates according to the principle of token ring. The multiple stations are connected in a star topology physically but are internally wired into a logical ring.The following figure shows a MSAU having 8 ports shown in black squares and numbered from 1 to 8, each of which can be connected to a device. Additionally, it has two ports ring-out (RO) and ring-in (RI) ... Read More

In computer networks, Gigabit Ethernet (GbE) is the family of Ethernet technologies that achieve theoretical data rates of 1 gigabit per second (1 Gbps). It was introduced in 1999 and was defined by the IEEE 802.3ab standard.Varieties of Gigabit EthernetThe popular varieties of fast Ethernet are 1000Base-SX, 1000Base-LX, 1000BASE-T and 1000Base-CX.1000BASE-CXDefined by IEEE 802.3z standardThe initial standard for Gigabit EthernetUses shielded twisted pair cables with DE-9 or 8P8C connectorMaximum segment length is 25 metresUses NRZ line encoding and 8B/6B block encoding1000BASE-SXDefined by IEEE 802.3z standardUses a pair of fibre optic cables of a shorter wavelength having 770 – 860 nm ... Read More

A covering graph is a subgraph that contains either all the vertices or all the edges corresponding to some other graph. A subgraph that contains all the vertices is called a line/edge covering. A subgraph that contains all the edges is called a vertex covering.Let 'G' = (V, E) be a graph. A subset K of V is called a vertex covering of 'G', if every edge of 'G' is incident with or covered by a vertex in 'K'.ExampleTake a look at the following graph −The subgraphs that can be derived from the above graph are as follows −K1 = ... Read More

Sets can be classified into many types. Some of which are finite, infinite, subset, universal, proper, singleton set, etc.Finite SetA set which contains a definite number of elements is called a finite set.Example − S = { x | x ∈ N and 70 > x > 50 }Infinite SetA set which contains infinite number of elements is called an infinite set.Example − S = { x | x ∈ N and x > 10 }SubsetA set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.Example ... Read More

The Empty Relation between sets X and Y, or on E, is the empty set ∅The Full Relation between sets X and Y is the set X × YThe Identity Relation on set X is the set { (x, x) | x ∈ X }The Inverse Relation R' of a relation R is defined as − R' = { (b, a) | (a, b) ∈ R }Example − If R = { (1, 2), (2, 3) } then R' will be { (2, 1), (3, 2) }A relation R on set A is called Reflexive if ∀ a ∈ A ... Read More

To deduce new statements from the statements whose truth that we already know, Rules of Inference are used.What are Rules of Inference for?Mathematical logic is often used for logical proofs. Proofs are valid arguments that determine the truth values of mathematical statements.An argument is a sequence of statements. The last statement is the conclusion and all its preceding statements are called premises (or hypothesis). The symbol “$\therefore$”, (read therefore) is placed before the conclusion. A valid argument is one where the conclusion follows from the truth values of the premises.Rules of Inference provide the templates or guidelines for constructing valid ... Read More

If G = (V, E) be a non-directed graph with vertices V = {V1, V2, …Vn} thenn ∑ i=1 deg(Vi) = 2|E|Corollary 1If G = (V, E) be a directed graph with vertices V = {V1, V2, …Vn}, thenn ∑ i=1 deg+(Vi) = |E| = n ∑ i=1 deg−(Vi)Corollary 2In any non-directed graph, the number of vertices with Odd degree is Even.Corollary 3In a non-directed graph, if the degree of each vertex is k, thenk|V| = 2|E|Corollary 4In a non-directed graph, if the degree of each vertex is at least k, thenk|V| = 2|E|Corollary 5In a non-directed graph, if the ... Read More

German mathematician G. Cantor introduced the concept of sets. He had defined a set as a collection of definite and distinguishable objects selected by the means of certain rules or descriptions.Set theory forms the basis of several other fields of study like counting theory, relations, graph theory, and finite state machines. In this chapter, we will cover the different aspects of Set Theory.Set - DefinitionA set is an unordered collection of different elements. A set can be written explicitly by listing its elements using a set bracket. If the order of the elements is changed or any element of a ... Read More

Venn diagram, invented in 1880 by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.ExamplesSet OperationsSet Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product.Set UnionThe union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.Example − If A = { 10, 11, 12, 13 } and B = { 13, 14, 15 }, ... Read More

To deduce new statements from the statements whose truth that we already know, Rules of Inference are used.What are Rules of Inference for?Mathematical logic is often used for logical proofs. Proofs are valid arguments that determine the truth values of mathematical statements.An argument is a sequence of statements. The last statement is the conclusion and all its preceding statements are called premises (or hypothesis). The symbol “∴”, (read therefore) is placed before the conclusion. A valid argument is one where the conclusion follows from the truth values of the premises.Rules of Inference provide the templates or guidelines for constructing valid ... Read More