1. Basic Digital Design Discussion D5.4 Appendix F

2. Basic Digital Design Sum-of-Products Design Product-of-Sums Design

3. Sum of Products Design Exclusive-OR Gate z = x ^ y x y z 0 0 0 0 1 1 1 0 1 1 1 0 XOR x y z

4. Sum of Products Design x y minterms 0 0 m0 = ~x & ~y 0 1 m1 = ~x & y 1 0 m2 = x & ~y 1 1 m3 = x & y

5. Sum of Products Design x y z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate m1 = ~x & y m2 = x & ~y z = m1 | m2 = (~x & y) | (x & ~y)

6. Sum of Products: Exclusive-OR

7. Precedence of Logical Operators All ~ operations are done first All & operations are done next All | operations are done last z = (~x & y) | (x & ~y) = ~x & y | x & ~y

8. Basic Digital Design Sum-of-Products Design Product-of-Sums Design

9. Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = ~m0 = ~(~x & ~y) = ~~(~~x | ~~y) = x | y

10. Product of Sums Design x y minterms maxterms 0 0 m0 = ~x & ~y M0 = ~m0 = x | y 0 1 m1 = ~x & y M1 = ~m1 = x | ~y 1 0 m2 = x & ~y M2 = ~m2 = ~x | y 1 1 m3 = x & y M3 = ~m3 = ~x | ~y

11. Product of Sums Design x y z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate z is NOT minterm m0 AND it is NOT minterm m3

12. Product of Sums Design x y z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate M0 = x | y M3 = ~x | ~y z = M0 & M3 = (x | y) & (~x | ~y)

13. Product of Sums: Exclusive-OR