Karnaugh Map is the method used to minimize and simplify the Boolean functions.
It works on the basis of complement laws: X +X’ = 1 and X.X’ =0.
Thereby, to cancel a variable in K-Map, we need pairs of variables and their complements which is done by grouping. K-Map uses some rules for grouping of adjacent cells.
In this video, we will check out simple explanation for these rules, one by one.
Karnaugh Map Introduction: https://youtu.be/a1Zwqjw_sp0
Boolean Simplification using Boolean laws: https://youtu.be/j7Qkrm1YJ0c
Rule 1: For minterms, groups may include only 1s; zeros are never allowed. Similarly, for maxterms, groups may include only 0s and 1s are never allowed.
Rule 2: Groups may be horizontal or vertical; Diagonal groups not allowed.
Rule 3: Groups must contain 1, 2, 4, 8, etc terms (that is the total terms of the group must be in powers of 2). Groups made up of 3, 5 terms are not allowed.
Rule 4: All the ones in K-Map must be covered by at least one group.
Rule 5: Groups should always be fewer in number and larger in size.
Rule 6: Overlapping groups are permitted.
Rule 7: Groups may wrap around the table (K-Map).
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