Digital Logic Circuits - K-map for Product of Sums and DON’T-CARE Conditions

K-map for Product of Sums

• Covering logic-1 squares in K-map gives logic functions in sum of products form

• Covering logic-0 squares, will give logic functions in product of sums form, e.g.

• F’ = B’C + AC

• F = (B’C + AC)’

= (B’C)’ (AC)’

= (B+C’) (A’+C’)

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K-map for Product of Sums Example

DON’T-CARE Conditions

• In logic function, sometimes we do not have the specification for all the combinations

• We might define a logic function to be 1 for some combinations and 0 for some others but the rest is not define

• We do not care about the logic value of the function for these undefined combinations called as DON’T-CARE

conditions

• DON’T-CARE conditions are usually denoted by ‘x’, or ‘X’ or ‘d’

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Truth Table with DON’T-CARE Conditions

• f has unknown (or don’t care) values for combinations abc = 100 or 110

K-map with DON’T-CARE Conditions

• When constructing a K-map for a logic function with don’t-care conditions, we enter ‘x’ into the squares where the function is undefined

• When a K-map contains don’t-care conditions, we can treat the don’t-cares as either 1 or 0

• We make use of x=1for grouping them with adjacent 1’s to make the groups larger

• We don’t group x when it is treated as 0.