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  ../images/main/bulllet_4dots_orange.gif 4-Variable K-Map

There are 16 cells in a 4-variable (W, X, Y, Z); K-map as shown in the figure below.

   

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../images/digital/kmaps_4vars1.gif
   

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There are 2 wrap-around: a horizontal wrap-around and a vertical wrap-around. Every cell thus has 4 neighbours. For example, the cell corresponding to minterm m0 has neighbours m1, m2, m4 and m8.

   

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../images/digital/kmaps_4vars2.gif
   

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  ../images/main/bullet_star_pink.gif Example

F(W,X,Y,Z) = (1,5,12,13)

   

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F = WY'Z + W'Y'Z

   

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  ../images/main/bullet_star_pink.gif Example

F(W,X,Y,Z) = (4, 5, 10, 11, 14, 15)

   

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F = W'XY' + WY

   

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  ../images/main/bulllet_4dots_orange.gif 5-Variable K-Map

There are 32 cells in a 5-variable (V, W, X, Y, Z); K-map as shown in the figure below.

   

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../images/digital/kmaps_5vars.gif
   

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  ../images/main/bulllet_4dots_orange.gif Inverse Function
   

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  • The 0's on a K-map indicate when the function is 0.
  • We can minimize the inverse function by grouping the 0's (and any suitable don't cares) instead of the 1's.
  • This technique leads to an expression which is not logically equivalent to that obtained by grouping the 1's (i.e., the inverse of X != X').
  • Minimizing for the inverse function may be particularly advantageous if there are many more 0's than 1's on the map.
  • We can also apply De Morgan's theorem to obtain a product-of-sum expression.
   

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Deepak Kumar Tala - All rights reserved

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