1. TUTORIAL CHAPTER 3 GATE_LEVEL MINIMIZATION PART 2 TA. Arwa Al Saad. 9 November 2013

2. NAND and NOR Implementation - Digital circuits are frequently constructed with NAND or NOR gates rather than with AND and OR gates.

3. NAND Circuits  NAND gate: a universal gate – Any digital system can be implemented with it including AND, OR and complement

4. Steps of Implementation two levels NAND gates 1. Express simplified function in sum of products. 2. Change every AND in first level to AND-invert. 3. Change OR in second level to AND-invert or invert-OR 4. Invert any single literal in the first level.

5. Two-Level Implementation with NAND  sum of product expression and its equivalent NAND implementation F = AB + CD = [(AB)’*(CD)’]’

6. Question#1  Draw a NAND diagram that implements the following function: F(A,B,C)=∑(5,6,7): F= AC+AB

7. Diagram with AND,OR: Diagram with AND-invert and invert-OR:Diagram with two AND-invert: Question#1 F=((AC)’(AB)’)’ F= AC+AB

8. Steps of implementing Multilevel NAND Circuits 1. Convert all AND gates to NAND gates with AND-invert graphic symbols. 2. Convert all OR gates to NAND gates with only invert-OR graphic symbols. 3. Check all the bubbles in the diagrams. For a single bubble, invert an inverter (one-input NAND gate) or complement the input literal.

10. NOR Circuite  The NOR gate is anothar universal gate to implement any Boolean Function.

11. Steps of Implementation two levels NOR gates 1. Express simplified function in product of sum. 2. Change every OR in first level to OR-invert. 3. Change AND in second level to OR-invert or invert-AND. 4. Invert any single literal in the first level.

12. Questions #2  Draw a NOR diagram that implements the following function: F= (A+B)(C+D)E

13. Questions #2 Diagram with OR-invert and invert-AND:

14. Steps of implementing Multilevel NOR Circuits 1. Convert all OR gates to NOR gates with OR-invert graphic symbols. 2. Convert all AND gates to NOR gates with only invert-AND graphic symbols. 3. Check all the bubbles in the diagrams. For a single bubble, invert an inverter (one-input NOR gate) or complement the input literal.

15.  Draw logic diagram with NOR gate for the following function: F=(AB’ + A’B) (C+D’)

16. Evolution 4  Draw a NAND logic diagram that implements the following function: F(A,B,C,D)=∑(0,4,8,9,10,11,12,14)

18. Q3.28  Derive the circuits for a three-bit parity generator and four-bit checker using an odd parity bit  0 means a correct transmission.

19.  Three-bit parity generator (odd)  F=(X Y Z)’

21.  Four-bit parity checker(odd)  F=(X Y Z)’

23. DONE