Computer Architecture CST 250

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Computer ArchitectureCST 250

• K-Map
• Prepared byOmar Hirzallah

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Contents

• K-Map
• Two Variables K-Map
• Three Variables K-Map
• Rules for Representation of
• 3-Variables K-Map
• Four Variables K-Map
• Rules for Representation of
• 4-Variables K-Map

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Karnaugh Map
The traditional way for the simplification of
Boolean expressions is awkward as it lacks
specific rules to predict each succeeding step in
the process. The MAP method provides a simple
straightforward procedure for minimizing Boolean
functions. This map method is also known as
Karnaugh Map or K-Map. There are different
representations of K-maps depending on the no. of
variables
Two Variable Map
m1 m0
m3 m2
y
y
1
0
xy xy
xy xy
x
0
x
1
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Representation of functions in the Map
y
y
y
y
1
0
1
0
1
1 1

1
0
x
x
0
1
x
1
x
(b) x y
(a) xy
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Representation of three variables k-map
BC
B C B C B C B C
1 0 1 1 0 1 0 0
ABC 0 1 0 ABC 0 1 1 ABC 0 0 1 ABC 0 0 0 0
ABC 1 1 0 ABC 1 1 1 ABC 1 0 1 ABC 1 0 0 1
BC
A

m2 m3 m1 m0
m6 m7 m5 m4
A
A A

• The Rules (For 3-Variables Representation of
  K-map)
• One square represents one term of 3-variables.
• Two adjacent squares represent a term of two
  variables.
• Four adjacent squares represent a term of one
  variable.
• Eight adjacent squares represent a function that
  is always equal to 1.

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Representation of four variables k-map
CD

m2 m3 m1 m0
m6 m7 m5 m4
m14 m15 m13 m12
m10 m11 m9 m8
AB
C D C D C D C D
CD
1 0 1 1 0 1 0 0
ABCD 0 0 1 0 ABCD 0 0 1 1 ABCD 0 0 0 1 ABCD 0 0 0 0 00
ABCD 0 1 1 0 ABCD 0 1 1 1 ABCD 0 1 0 1 ABCD 0 1 0 0 01
ABCD 1 1 1 0 ABCD 1 1 1 1 ABCD 1 1 0 1 ABCD 1 1 0 0 11
ABCD 1 0 1 0 ABCD 1 0 1 1 ABCD 1 0 0 1 ABCD 1 0 0 0 10
AB
AB AB AB AB
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• The Rules (For 4-Variables Representation of
  K-map)
• One square represents one term of 4-variables.
• Two adjacent squares represent a term of three
  variables.
• Four adjacent squares represent a term of two
  variables.
• Eight adjacent squares represent a term of one
  variable.
• Sixteen adjacent squares represent a function
  that is always equal to 1.