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Boolean Models A Mechanism for Constructing Truth Tables By Alex Efta Kelly Martin Lance Dehne - PowerPoint PPT Presentation

Boolean Models A Mechanism for Constructing Truth Tables By Alex Efta Kelly Martin Lance Dehne. A Simple Boolean Model A = A’. A’. A’. Algorithm for Constructing Any Size Truth Table

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Boolean ModelsA Mechanism for ConstructingTruth TablesByAlex EftaKelly MartinLance Dehne

A = A’

A’

A’

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

With 4 Input Variables

A =(BCD)

B=(D+C)

D=B’

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

The output columns have been left for personal practice