DKT 122/3 DIGITAL SYSTEM 1

1. DKT 122/3DIGITAL SYSTEM 1 WEEK #7 COMBINATIONAL LOGIC ANALYSIS

2. Topic Outlines • Basic Combinational Logic Circuits • Implementing Combinational Logic • Implement Logic Circuit from Boolean Expression • Implement Logic Circuit from Truth Table • The Universal Property of NAND and NOR Gates • NAND Gate as a Universal Logic Element • NOR Gate as a Universal Logic Element • Combinational Logic Using NAND and NOR Gates • Logic Circuits Operations with Pulse Waveform Inputs

3. Basic Combinational Logic Ccts DEFINITION OF COMBINATIONAL LOGIC • Combination of basic gates to form circuits that can carry out a desired application. • In combinational logic, the output level is at all times dependent on the combination of input levels • Combinational logic circuits contain no memory (no ability to store information)

4. Basic Combinational Logic Ccts AND-OR LOGIC Represents SOP implementation – AND gate for product term, OR gate for summing the product terms

5. Basic Combinational Logic Ccts AND-OR-INVERT LOGIC Represents POS implementation – AND gate for product term, OR gate for summing the product terms, NOT gate to complement the AND-OR circuit.

6. Basic Combinational Logic Ccts XOR LOGIC Combination of 2 AND gates, 1 OR gate, & 2 NOT gates. Considered a type of logic with own unique symbol ( ).

7. Basic Combinational Logic Ccts XNOR LOGIC The complement of XOR logic.

8. Implementing Combinational Logic Implement logic circuit fromBoolean Expression Example: Logic circuit for X = AB + CDE

9. Implementing Combinational Logic Implement logic circuit fromBoolean Expression Example: Logic circuit for X = AB(CD + EF) It is usually best to reduce a circuit to SOP form to reduce the overall propagation delay time.

10. Implementing Combinational Logic Implement logic circuit fromTruth-table First, write the SOP expression from the Truth Table. Then, implement the logic circuit. QUESTION: What is the SOP expression?

11. Universal Property - NAND & NOR NAND GATE AS A UNIVERSAL LOGIC ELEMENT NAND gate is a universal gate because it can be used to produce the NOT, AND, OR and NOR functions.

12. Universal Property - NAND & NOR NAND GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

13. Universal Property - NAND & NOR NOR GATE AS A UNIVERSAL LOGIC ELEMENT NOR gate is also a universal gate because it can be used to produce the NOT, AND, OR and NAND functions.

14. Universal Property - NAND & NOR NOR GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

15. Combinational Logic - NAND & NOR NAND LOGIC NAND Gate can function as either a NAND or a negative-OR because by DeMorgan’s Theorem: AB = A + B NAND Negative-OR The NAND symbol and the negative-OR symbol are called dual-symbol.

16. Combinational Logic - NAND & NOR NOR LOGIC NOR Gate can function as either a NOR or a negative-AND because by DeMorgan’s Theorem: A+ B = A B NOR Negative-AND The NOR symbol and the negative-AND symbol are called dual-symbol.

17. Combinational Logic - NAND & NOR Example: Using appropriate dual symbols, redraw the logic diagram and develop the output expression for the following circuit:

18. Combinational Logic - NAND & NOR

19. Pulse Waveform Inputs Operation The output of a logic circuit at any given time depends on the input at that particular time. Example: Determine the final output waveform X for the circuit in figure below, with input waveforms A,B and C as shown. END