Combinational Logic - Digital Principles and Computer Organization
Subject and UNIT: Digital Principles and Computer Organization: Unit I: Combinational Logic
During the process of simplification of Boolean expression we have to predict each successive step. We can never be absolutely certain that an expression simplified by Boolean algebra alone is the simplest possible expression.
Combinational Logic - Digital Principles and Computer Organization
Subject and UNIT: Digital Principles and Computer Organization: Unit I: Combinational Logic
When logic gates are connected together to produce a specified output for certain specified combinations of input variables, with no storage involved, the resulting circuit is calledcombinational logic circuit.
Lattices and Boolean Algebra - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit V: Lattices and Boolean Algebra
A Boolean algebra is a complemented, distributive lattice.Electronic circuites and switching matchings are working with the rules of Boolean algebra.
Lattices and Boolean Algebra - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit V: Lattices and Boolean Algebra
In order to emphasize the role of an ordering relation, a lattice is first introduced as a partially ordered set. Both lattices and Boolean algebra have important applications in the theory and design of computers.
Lattices and Boolean Algebra - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit V: Lattices and Boolean Algebra
A binary relation R in a set P is called a partial order relation or a partial ordering in P iff R is reflexive, antisymmetric, and transitive.
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
An algebraic system (S, +, .) is called a ring if the binary operations + and on S satisfy some properties
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
Let (H, *) be a subgroup of (G, *). For any a Є G, the set a H defined by a H = {a * h/ h Є H} is called the left coset of H in G determined by the element a Є G.
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
The necessary and sufficient condition that a non-empty subset H of a group G be a subgroup is a Є H, b Є H ⇒ a*b-1€ H.
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
If a and b are any two elements of a group (G, *), then show that G is an abelian group
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
A homomorphism of a semi-group into itself is called a semi-group endomorphism.
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
A non-empty set S, together with a binary operation * is called a semi-group
Algebraic Structures - Discrete Mathematics
Subject and UNIT: Discrete Mathematics: Unit IV: Algebraic Structures
A system consisting of a set and one or more n-ary operations on the set will be be called an algebraic system or simply an algebra.