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Boolean Models A Mechanism for Constructing Truth Tables By Alex Efta Kelly Martin Lance DehnePowerPoint Presentation

Boolean Models A Mechanism for Constructing Truth Tables By Alex Efta Kelly Martin Lance Dehne

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### Boolean ModelsA Mechanism for ConstructingTruth TablesByAlex EftaKelly MartinLance Dehne

Algorithm for Constructing Any Size

Truth Table

- If there are X input variables there will be 2X possible input combinations and therefore 2X rows will be required
2. For the Yth column, begin the column with 2(Y-1) 0s follwed by 2(Y-1) 1s. Repeat the resultant pattern until entire column is filled

2x=24=16 Rows

For the Yth column, begin the column with 2(Y-1) 0s follwed by 2(Y-1) 1s. Repeat the resultant pattern until entire column is filled

Number of Zeros: 2(Y-1)=2(1-1)=2(0)=1

Number of Ones: 2(Y-1)=2(1-1)=2(0)=1

Resultant Pattern= 0 1

Number of Zeros: 2(Y-1)=2(2-1)=2(1)=2

Number of Ones: 2(Y-1)=2(2-1)=2(1)=2

Resultant Pattern= 0 0 1 1

Number of Zeros: 2(Y-1)=2(3-1)=2(2)=4

Number of Ones: 2(Y-1)=2(3-1)=2(2)=4

Resultant Pattern= 0 0 0 0 1 11 1

Number of Zeros: 2(Y-1)=2(4-1)=2(3)=8

Number of Ones: 2(Y-1)=2(4-1)=2(3)=8

Resultant Pattern= 0 0 0 0 0 0 0 0 1 1 1 1 1 11 1

Now It’s Your Turn…

The output columns have been left for personal practice

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