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EEC 18 Lecture 4 Bevan M. Baas
Digital Systems I EEC 18 Lecture 4 Bevan M. Baas
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Minterm Example m0 m1 This circuit schematic shows all 8 minterms “present” for a 3-input combinational logic function In practice, all possible minterms would never all be present in a circuit (do you see why?) There is one possible minterm for each row in the truth table m2 m3 Z m4 m5 m6 m7
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Minterm Example m0 1 m1 By construction, one and only one minterm is active (equals 1) at any point in time m2 m3 1 Z m4 m5 m6 m7
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Minterm Example m0 1 m1 1 By construction, one and only one minterm is active (equals 1) at any point in time m2 m3 1 Z m4 m5 m6 m7
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Minterm Example m0 1 m1 By construction, one and only one minterm is active (equals 1) at any point in time m2 1 m3 1 Z m4 m5 m6 m7
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Minterm Example m0 1 1 m1 By construction, one and only one minterm is active (equals 1) at any point in time m2 m3 1 1 Z m4 m5 m6 m7
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Minterm Example m0 1 m1 By construction, one and only one minterm is active (equals 1) at any point in time m2 m3 1 Z m4 1 m5 m6 m7
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Minterm Example m0 1 1 m1 By construction, one and only one minterm is active (equals 1) at any point in time m2 m3 1 Z m4 m5 1 m6 m7
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Minterm Example m0 1 1 m1 Z = m0 + m1 + m7
1 m1 Z = m0 + m1 + m7 To implement an expression, a circuit is built with only the present minterm(s) The output can be 1 only when one of the present minterms forces the output to 1 m2 Z nothing is here m7
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Minterm Example m0 1 1 1 m1 Z = m0 + m1 + m7
1 1 m1 Z = m0 + m1 + m7 To implement an expression, a circuit is built with only the present minterm(s) The output can be 1 only when one of the present minterms forces the output to 1 m2 1 Z m7 1
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Minterm Example m0 1 1 1 m1 Z = m0 + m1 + m7
1 1 m1 Z = m0 + m1 + m7 Of course gate inputs can not be left unconnected (unspecified). There are two solutions: Tie unused inputs to a value that disables those inputs. For an OR gate, inputs would be tied to 0 (or False or Gnd) The best solution is to simplify the gate. In this example, the 8-input OR gate is simplified to a 3-input OR gate 1 Z m7 1
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