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

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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 Simple Boolean Model

A = A’

A’

A’

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

Consider the Following Boolean Model

With 4 Input Variables

A =(BCD)

B=(D+C)

D=B’

Number of Inputs: 4

2x=24=16 Rows

Rule for Filling Columns

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

Column 1: Input for A

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

Column 2: Input for B

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

Column 3: Input for C

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

Column 4: Input for D

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