1. WEEK #7 COMBINATIONAL LOGIC ANALYSIS
DKT 122/3 DIGITAL 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 from Boolean Expression
Example: Logic circuit for X = AB + CDE

9. Implementing Combinational Logic
Implement logic circuit from Boolean 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 from Truth-table
First, write the SOP expression from the Truth Table. Then, implement
the logic circuit.
INPUT
OUTPUT A B C X 1
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.
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