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

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

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