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- The Quine-McCluskey, or Tabular, method is an algorithmic method that
finds prime implicants, necessary prime implicants, and minimum
sum-of-products expressions for digital systems with any number of
variables
- The Quine-McCluskey method can be implemented as a computer program
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2
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- 1) Represent the minterms and the
dont cares by the values of the input variables
- -- For example, in a 5-variable
system minterm 7 would be represented by 00111
- Arrange the minterms and dont cares in groups according to the number
of 1s
- -- Group with no 1s
- -- Group with a single 1
- -- Group with two 1s
- --
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3
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- Compare each member of a group to each member of the adjacent group
- -- If two terms differ in a
single position, then record the reduced expression and mark the two
items as having been used
- For example
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4
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- As you compare minterms and dont cares, keep the reduced expressions in
groups
- For example
- Group from combining no 1s with a single 1
- --------------------------------
- Group from combining a single 1 with two 1s
- --------------------------------
- Group from combining two 1s with three 1s
-
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5
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- 5) Check each group of two expression against each expression in the
adjacent group
- Comparison is easier at this step and subsequent steps, because
simplification is only possible if the groups of two have eliminated the
same variable
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- Continue comparing group to adjacent group and separating the simpler
expressions that result until no
more simplifications can be achieved.
- This is the set of prime implicants
- Make a chart of which minterms are in which prime implicants
- The prime implicants define the rows
- The minterms define the columns
- The dont cares are excluded at this point
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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18
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- If all minterms are not covered after the removal of dominated rows and
choice of prime implicants that are the only way to cover the remaining
minterms, then
- Either chose a set to complete the expression by inspection, or
- Apply the Petrick algorithm, a structured method for making the choice
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19
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Notes
