1. Computer Architecture CST 250 K-Map Prepared by:Omar Hirzallah

2. 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

3. Karnaugh Map m1m1 m0m0 m3m3 m2m2 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: x’yx’y’ xyxy’ 0 10 1 x’ y’ x y

4. Representation of functions in the Map: 1 1 11 (a) xy (b) x + y 0 0 0 0 1 1 1 1 x’ x x y’ y y

5. Representation of three variables k-map: m2m2 m3m3 m1m1 m0m0 m6m6 m7m7 m5m5 m4m4 1 0 1 1 0 10 A’BC’ 0 1 0 A’BC 0 1 1 A’B’C 0 0 1 A’B’C’ 0 0 0 0 ABC’ 1 1 0 ABC 1 1 1 AB’C 1 0 1 AB’C’ 1 0 0 1 BC A A B’ C’ B’ C B C B C’ 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.

6. Representation of four variables k-map: m2m2 m3m3 m1m1 m0m0 m6m6 m7m7 m5m5 m4m4 m 14 m 15 m 13 m12m12 m 10 m 11 m9m9 m8m8 1 01 0 10 A’B’CD’ 0 0 1 0 A’B’CD 0 0 1 1 A’B’C’D 0 0 0 1 A’B’C’D’ 0 0 A’BCD’ 0 1 1 0 A’BCD 0 1 1 1 A’BC’D 0 1 A’BC’D’ 0 1 0 0 01 ABCD’ 1 1 1 0 ABCD 1 1 ABC’D 1 1 0 1 ABC’D’ 1 1 0 0 11 AB’CD’ 1 0 AB’CD 1 0 1 1 AB’C’D 1 0 0 1 AB’C’D’ 1 0 0 0 10 CD AB C’ D’ C’ D C D C D’ A’B’ A’B AB AB’ CD AB

7. 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.