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

2. A Simple Boolean Model A = A’ InputsOutput s TiTi+1 0 1 InputsOutput s TiTi+1 0 1 1 InputsOutput s TiTi+1 0 1 1 0 A’

3. 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

4. Consider the Following Boolean Model With 4 Input Variables A =(BCD) B=(D+C) C=(AD) D=B’

5. Number of Inputs: 4 2 x =2 4 =16 Rows

6. 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

7. 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

8. 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

9. 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

10. 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

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