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Five Karnaugh Maps : Five Karnaugh Maps : “mirror”“mirror”• 3 variables 3 variables are laid out horizontallyare laid out horizontally• 2 variables2 variables are laid out vertically are laid out vertically
Completely specifiedCompletely specified Output value is known for every possible combination of Output value is known for every possible combination of inputinput
Incompletely specifiedIncompletely specified
Truth table does not generate an output value for every Truth table does not generate an output value for every possible combination of input variablespossible combination of input variables
Don’t Care termDon’t Care term
Minterm or Maxterms that are not used as part of Minterm or Maxterms that are not used as part of output output functionfunction
Don’t Care Don’t Care TermsTermsProcedureProcedure
Develop the truth table that describes the Develop the truth table that describes the input/output relationshipinput/output relationship
Determine if all of the input combinations are used to Determine if all of the input combinations are used to generate output(s)generate output(s) If so, then If so, then no don’t care terms existno don’t care terms exist If not, then If not, then those combinations of input variables not usedthose combinations of input variables not used
to determine output values are to determine output values are don’t care termsdon’t care terms
Once the don’t care terms have been identified, use a Once the don’t care terms have been identified, use a separate symbol, in the K-map squares, so they will not separate symbol, in the K-map squares, so they will not be confused with normal Minterms or Maxterms input be confused with normal Minterms or Maxterms input variables never occursvariables never occurs
Create as large an EPI grouping as possible, including Create as large an EPI grouping as possible, including don’t care terms that have been combined with normal don’t care terms that have been combined with normal MintermsMinterms
Do not group don’t care term by themselvesDo not group don’t care term by themselves
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Karnaugh Karnaugh MapsMapsDon’t Care TermsDon’t Care Terms
Don’t care terms are the same for each output Don’t care terms are the same for each output variable in the problem, because the same set variable in the problem, because the same set of input combinations are usedof input combinations are used
Don’t care terms are distinguished from Don’t care terms are distinguished from regular minterms in that it does not matter regular minterms in that it does not matter whether we assign “0” or “1”whether we assign “0” or “1”
These combinations of input variables never These combinations of input variables never occursoccurs
Distinct advantage when simplifying the output Distinct advantage when simplifying the output eq.eq.
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Don’t Care TermsDon’t Care Terms
A=W+XY+XZA=W+XY+XZ B=X’Y+X’Z+XY’Z’B=X’Y+X’Z+XY’Z’
C=Y’Z’+YZC=Y’Z’+YZ D=Z’D=Z’
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Karnaugh Karnaugh MapsMapsBCD to EX-3 Code Conversion CircuitsBCD to EX-3 Code Conversion Circuits