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Showing posts with label Untai Digital. Show all posts
Showing posts with label Untai Digital. Show all posts

Monday, 21 October 2013

Teorema – teorema Aljabar Boolean

01:37

1.    X+0 = X                                               1.D. X.1 = X
2.    X+1 = 1                                               2.D. X.0 = 0
3.    X+X = X                                              3.D. X.X = X
4.    (X’)’ = X
5.    X+X’ = 1                                              5.D. X.X’ = 0
      Hukum komutatif
6.    X+Y = Y+X                                         6.D. XY = YX
      Hukum Asosiatif
7.    (X+Y)+Z = X+(Y+Z)                           7.D. (XY)Z    = X(YZ)
 = X+Y+Z                                                                   = XYZ
      Hukum Distributif
8.    X(Y+Z) = XY+XZ                               8.D. X+YZ = (X+Y)(X+Z)
      Hukum Absorptif
9.    XY+XY’ = X                                        9.D.  (X+Y)(X+Y’) = X
10. X+XY = X                                            10.D. X(X+Y) = X
11. (X+Y’)Y = XY                                     11.D. XY’+Y = X+Y
Hukum DeMorgan
12. (X+Y+Z+...)’ = X’Y’Z’...                      12.D.  (XYZ...)’ = X’+Y’+Z’+...
13. [f(X1,X2,...,Xn,0,1,+,.)]’ = f(X1’,X2’,...,Xn,1,0,.,+)

Dualitas
14. (X+Y+Z+...)D = XYZ ....                     14.D.  (XYZ ...)D = X+Y+Z+...
15. [f(X1,X2, ...,Xn,0,1,+,.)]D = f(X1,X2, ...,Xn,,1,0,.,+)

Teorema perkalian dan pemfaktoran
16. (X+Y)(X’+Z) = XZ + X’Y                    16.D.  XY + X’Z = (X+Z)(X’+Y)
Teorema Konsensus
17. XY+YZ+X’Z = XY+X’Z                     17.D. (X+Y)(Y+Z)(X’+Z) = (X+Y)(X’+Z)