lunes 25 de agosto de 2008
articulo
PROCEDURE OF A MAP KARNAUGH
A map of Karnaugh (also well-known as chart of Karnaugh or diagram of Veitch, abbreviated as K-map or Kw-map) it is a diagram used for the minimization of functions algebraic booleanas. The map of Karnaugh was invented in 1950 by Maurice Karnaugh, a physique and mathematical of the laboratories Bell.
The maps K takes advantage of the capacity of the human brain to work better with patterns that with equations and other forms of analytic expression. Externally, a map of Karnaugh consists of a series of squares, each one of which it really represents a line of the chart. Since the chart really of a function of N variables it possesses 2N lines, the map corresponding K should also possess 2N squares. Each square harbors a 0 or a 1, depending on the value that he/she takes the function in each line. The charts of Karnaugh can be used for functions of up to 6 variables -
METHOD OF REDUCTION OF MAPS DE KARNAUGH:
The Algebra of Boole, solves problems that depending on the number of terms that had the canonical function, being the number of used logical floodgates similar to the number of obtained terms MORE ONE; therefore, the obtained circuits are of two commutation levels with a minimum time of retard, but that in no way it is the simplest neither the most economic.
The way to simplify functions is representing them in maps of Karnaugh. This is equivalent to solve the simplifications for theorems. However, a lot of people consider that you/he/she is easier to visualize the simplifications if they are presented graphically.
The maps of Karnaugh can be applied at two, three, four five variables. For more variable, the simplification is so complicated that it suits in that case to use theorems better. For class effects, we will see the simplifications of two, three four variables.
Example 1: It simplifies the function of two variable f = a'b + ab' + ab
The first thing that I should make is to represent it in a map of two variables. It is represented like a chart. To fill the chart, I put an one where you intersecte the value of the function. For example, for the first term of the function f = a'b + ab' + ab, it has been marked in red where he/she put on the 1 in the chart.
Once fact the map, we should mark the contiguous regions that manage it Simplifies the function of three variable f = a'b + ab'c + c'
The first thing that I should make is to represent it in a map of three variables to fill the chart, I put an one where he/she crosses the value of the function. For example, for the terms of the function f = a'b +ab'c + c', it has been marked where he/she put on the 1 in the chart.
Now we should look for the regions that indicate us the simplified function. The first thing that we should observe is that the regions can group of the ends of the map.
This region represents c'. Now, we see that it is a bit in a'bc, but it always suits to contain it the most possible thing, in regions whose cells are multiples of 2 (1, 2, 4, 8...) In this case, we contain it with the 1 contiguous, so that the region is as a'b. This way, the resulting function would be f = a'b + ab' + c.
It simplifies the function of four variable f = ac'd' + a'bd + abcd + ab'cd + a'bc'd' + a'b'c'd', again, the first thing that we make is to empty the function to the map. Notice you the form that he/she takes the map.
Now, the following thing is to contain the variables in regions. The first to region, the red one, it is contained of the corners. This grouping represents c', but it had meant to already contain a 1 contained, and to leave other 1 even not contained without containing. So he/she groups this way, and the green region represents to a'bd. The 1s that are until this free moment can group together
2.2 procedure to MINIMIZE a FUNCTION for MAPS K
In definitive form, the map that will be used for the minimization of functions booleanas with three variables, will be the one that is shown in the Figure 2.9.(d). next we will explain the form like it will be used in this map. The steps to continue will be the same ones for any map, it doesn't care which is the number of variables.
1. of the definition of the problem and of the functional chart the canonical function is obtained.
2. the minitérminos or maxitérminos of the canonical function move to the map K. a 1 it is placed if it is minitérmino and 0 if it is maxitérmino.
3. they are carried out the connections embracing the biggest low number of terms the following approaches:
to) The number of terms that you/they are linked (they contain) they should follow the rule of binary formation, that is to say, of 1 in 1, of 2 in 2, of 4 in 4, of 8 in 8, etc.
b) When containing the terms, he/she should take care the symmetry with the central and secondary axes.
4. the fact that he/she has taken a term for a connection he/she doesn't mean that this same it cannot be used for other connections.
5. the reduced function will have as many terms as connections they have been carried out.
6. to obtain the reduced term they are carried out two movements on the map, one vertical that sweeps to the horizontal more significant and more other variables that it sweeps to the less significant variables.
7. the following postulates are applied:
A . A' = 0
A . A = A
Publicado por javier lewonardo en 18:44 0 comentarios
miércoles 20 de agosto de 2008
ensayo
ANALISIS DE TEMATICAS TRABAJADAS
Encontraremos un gran planteamiento en las primeras clases para seguir los conceptos ya trabajados con lógica matemática y podremos utilizar todo ese conocimiento conceptual a la practica también empezaremos a recordar muchos elementos utilizados como lo son las funciones lógicas
Combinacionales para utilizarla en un circuito.
La primera fase de la materia se busca hacer comprensión total de los conceptos trabajados y el entendimiento en el planteamiento de la construcción de un circuito utilizando herramientas que demuestre el funcionamiento de este y demostrarlo de acuerdo a una practica en donde se enmadera el funcionamiento como tal en un circuito y la practica que tiene este en un sistema guiado hacia la ingeniería de sistemas.
Reconociendo los conceptos podemos utilizar nuevas herramientas de trabajo para profundizar en el tema y utilizaremos nuevas funciones para el desarrollo avanzado en un circuito y la utilidad que le puede a uno generar creando la aplicabilidad de los temas conceptos trabajados en la anterior etapa.
Después tomaremos como referencia las secuencias entre un circuito y experimentaremos situaciones para comprender e identificar las diferencias que hay entre estos utilizando conceptos teóricos y conociendo las funciones que aquí experimentarlos y los elementos que utilizaremos para llevar acabo estos sistemas secuenciales-
Encontrando y comprendiendo los temas a utilizar podremos ya profundizar en las aplicaciones de estos encontrando y definiendo por medio de situaciones presentadas el comportamiento que se toman en este y podremos analizar y darle así una aplicabilidad total de un circuito digital.
El fin principal es poder manejar adecuadamente todos los comportamientos que se tiene de las partes que constituyen un circuito se puede decir de una forma que el fin de este programa académico es un programa llevado especialmente a la practica ya que es en esta en donde encontramos la viabilidad del programa.
En conclusión se puede tomar como un proceso de adquirir conocimiento para llevarla acabo en la practica y con esta encontrar el comportamiento de un circuito y todos estopara entender los pasos que corresponden a la construcción de un circuito.
