# Boolean Algebra Examples

May 29th, 2015
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Example No1 -Construct a Truth Table for the logical functions at points C, D and Q in the following circuit and identify a single logic gate that can be used to replace the whole circuit. First observations tell us that the circuit consists of a

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Boolean Algebra ExamplesExample No1Construct a Truth Table for the logical functions at pointsC,DandQin the following circuit and identify a single logic gate that can be used to replace the whole circuit.First observations tell us that the circuit consists of a 2-inputNANDgate, a 2-inputEX-ORgate and finally a 2-inputEX-NORgate at the output. As there are only 2 inputs to the circuit labelledAandB, there can only be 4 possible combinations of the input (22) and these are:0-0,0-1,1-0and finally1-1. Plotting the logical functions from each gate in tabular form will give us the following truth table for the whole of the logic circuit below.InputsOutput atABCDQ00100011111011111001From the truth table above, columnCrepresents the output function from theNANDgate and columnDrepresents the output function from theEx-ORgate. Both of these two output expressions then become the input condition for theEx-NORgate at the output. It can be seen from the truth table that an output atQis present when any of the two inputsAorBare at logic1. The only truth table that satisfies this condition is that of anORGate. Therefore, the whole of the above circuit can be replaced by just one single2-inputORGate.Example No2Find the Boolean algebra expression for the following system.The system consists of anANDGate, aNORGate and finally anORGate. The expression for theANDga

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