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

A Simple Boolean Model A = A’ InputsOutput s TiTi InputsOutput s TiTi InputsOutput s TiTi A’

Algorithm for Constructing Any Size Truth Table 1.If there are X input variables there will be 2 X possible input combinations and therefore 2 X 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 2 x =2 4 =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=

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=

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=

Now It’s Your Turn… The output columns have been left for personal practice