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


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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 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


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)

C=(AD)

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


Now It’s Your Turn…

The output columns have been left for personal practice


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