simplificar funciones
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The document discusses techniques for minimizing Boolean functions including: 1. Algebraic methods such as identities, factorization, distribution, consensus theorem, and De Morgan's theorem. 2. Examples of four Boolean functions F1, F2, F3, and F4 that are minimized using these techniques. 3. Truth tables for AND and OR logic gates.
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Simplificar funciones.ppt
The document discusses methods for minimizing Boolean functions including algebraic methods. It defines four Boolean functions - F1(B,C), F2(D,C), F3(A,B), and F4(A,B,C) - and simplifies each using identities, factorization, distribution, consensus theorem, and De Morgan's laws. It also defines the truth tables for the AND and OR operations.
SIMPLIFICACION DE FUNCIONES BOOLEANAS
The document discusses methods for minimizing Boolean functions including algebraic methods. It defines four Boolean functions - F1(B,C), F2(D,C), F3(A,B), and F4(A,B,C) - and simplifies each using identities, factorization, distribution, consensus theorem, and De Morgan's laws. It also defines the truth tables for the AND and OR operations.
9. simplificar funciones
The document discusses methods for minimizing Boolean functions including algebraic methods. It defines four Boolean functions - F1(B,C), F2(D,C), F3(A,B), and F4(A,B,C) - and simplifies each using identities, factorization, distribution, consensus theorem, and De Morgan's laws. It also defines the truth tables for the AND and OR operations.
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Simplificar funciones.ppt
The document discusses methods for minimizing Boolean functions including algebraic methods. It defines four Boolean functions - F1(B,C), F2(D,C), F3(A,B), and F4(A,B,C) - and simplifies each using identities, factorization, distribution, consensus theorem, and De Morgan's laws. It also defines the truth tables for the AND and OR operations.
SIMPLIFICACION DE FUNCIONES BOOLEANAS
The document discusses methods for minimizing Boolean functions including algebraic methods. It defines four Boolean functions - F1(B,C), F2(D,C), F3(A,B), and F4(A,B,C) - and simplifies each using identities, factorization, distribution, consensus theorem, and De Morgan's laws. It also defines the truth tables for the AND and OR operations.
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This document discusses digital logic systems and Boolean algebra theory. It provides examples of simplifying logic functions using Boolean theorems like De Morgan's laws and the absorption law. Karnaugh maps are introduced as a method to simplify logic functions with up to 5 variables into their sum of products or product of sums forms. Practice problems are given involving using Karnaugh maps to minimize logic functions into canonical SOP and POS forms.
Answers homework2
This document provides answers to homework problems involving Boolean algebra expressions. For the first problem, it demonstrates how to prove the equality of two Boolean expressions by converting them to their canonical sum of products form. The second problem involves finding the complements of Boolean expressions. The third problem asks to convert expressions to canonical sum of products and canonical product of sums forms. The document shows the step-by-step work for several examples in each problem.
18. simpl met-algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for simplification of logic expressions into their simplest form.
3. An example is provided demonstrating the factorization of a Boolean function into its simplest form.
Métodos de simplificación
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for simplification of logic expressions into their simplest form.
3. An example is provided demonstrating the factorization of a Boolean function into its simplest form.
18. simpl met-algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, distribution property, and identities.
2. Karnaugh maps for simplifying functions with up to 4 variables into their simplest form.
3. An example is provided showing the step-by-step factorization of a Boolean function.
Simplificación funciones Booleanas
The document discusses techniques for minimizing Boolean functions including:
1) Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2) Karnaugh maps for simplification of logic expressions into their simplest form.
3) Examples are provided demonstrating factorization and simplification of logic expressions.
18. simpl met-algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for simplification of logic expressions into their simplest form.
3. An example is provided demonstrating the factorization of a Boolean function into its simplest form.
18. simpl met-algebraicos.ppt
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for factorization.
3. Examples are provided demonstrating factorization and simplification of Boolean functions using the described techniques.
11. simpl met-algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for simplification of logic expressions into their simplest form.
3. Examples are provided to demonstrate factorization and simplification of logic expressions.
11. simpl met algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for simplification of logic expressions into their simplest form.
3. Examples are provided to demonstrate factorization and simplification of logic expressions.
simplificacion sistemas algebraicos
The document discusses techniques for minimizing Boolean functions including:
1. Algebraic manipulation using factorization, duplicating terms, consensus theorem, and distributive property.
2. Karnaugh maps for factorization.
3. Examples are provided demonstrating factorization and simplification of Boolean functions using the discussed techniques.
Boolean algebra
This document discusses Boolean algebra and logic gates. It begins by defining Boolean variables and functions, and how they are represented using truth tables. It then covers basic identities and properties of Boolean algebra, including existence of 1 and 0 elements, complements, commutativity, associativity, distributivity, De Morgan's theorems, and examples of applying identities to minimize Boolean functions. Logic gates are also introduced as hardware implementations of Boolean operators.
Digital Electronics
Theorems of Boolean algebra:
THEOREMS (a) (b)
1 Idempotent x + x = x x . x = x
2 Involution (x’)’ = x
3 Absorption x+ xy = x x (x+ y) = x
DeMorgan’s Theorems state that the complement of a product is equal to the sum of the complements and the complement of a sum is equal to the product of the complements. Boolean expressions can be simplified using properties, laws, and theorems of Boolean algebra such as consensus theorem.
boolean algebra exercises
The document contains examples and solutions to problems involving boolean algebra, combinational logic circuits, binary number systems, and basic digital logic components like flip-flops. Some key points:
- It provides solutions to simplifying boolean expressions and designing combinational logic circuits from truth tables.
- Examples are given for binary coded decimal to seven segment decoding and frequency point calculations based on input frequency division.
- Conversions between binary, decimal, and hexadecimal number systems are demonstrated.
- The logic diagram, symbol, and truth table for an RS flip-flop implemented with NAND gates is illustrated.
Abdequipo1
The document shows 8 examples of algebraic expressions being simplified through the use of algebraic properties and identities. The expressions are factorized and like terms are combined. Through these steps, the expressions are reduced to their simplest forms in fewer steps.
Adbequipo2
The document contains 8 algebra of Boolean expressions problems with their step-by-step solutions. The expressions involve common Boolean algebra operations like complement, union, intersection and distributive laws to simplify the expressions into their minimal forms containing the least number of literals.
Boolean Algebra logic and De Morgan theorem
The document summarizes key concepts in Boolean algebra including:
1) It defines basic terminology like variables, constants, complements, literals, and Boolean functions.
2) It outlines Boolean postulates and laws including closure, identity elements, commutativity, distributivity, and complements.
3) It provides proofs for several Boolean laws and postulates using truth tables and shows how they are derived from a set of two elements.
Adbequipo3
The document contains algebraic expressions that are simplified step-by-step. Most of the expressions simplify down to single variables like X, Y, or Z. A few expressions simplify to sums of two variables like X + Y or W + Z. The simplification shows that regardless of the complexity of the initial expressions, they can be broken down into their fundamental parts.
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simplificar funciones
- 1. Minimización de funciones Booleanas • Métodos algebraicos
- 2. F1 (B,C)= 1+B’+C F1 (B,C)= 1 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1
- 3. F2 (D,C)= DC’(0) F2 (D,C)= 0 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1
- 4. F3 (A, B) = A’+B+A F3 (A, B) = 1 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1
- 5. F4 (A,,B,C) = A+A’BC F4 (A,,B,C)=(A+A’)(A+BC) F4 (A,,B,C)=A+BC 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1
- 6. F4 (A,,B,C) = A+A’BC F4 (A,,B,C)=(A+A’)(A+BC) F4 (A,,B,C)=A+BC 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1
- 7. 1.-Identidades 2.- Factorización AB’ + AB = A(B’+B)= A 3.- Propiedad Distributiva X+YZ = (X+Y) (X+Z) X (Y+Z) = XY +XZ 4.-Teorema del consenso AB+A’C+BC = AB+A’C 5.-Teorema de Dmorgan (AB)’=A’+ B’ (A+B)’=A’ B’ A+B =(A’ B’)’ AB =(A’+B’)’ AND OR A A=A A + A=A A 0 =0 A + 0 = A A 1 =A A + 1 =1 A A’ =0 A+A’ =1