company logo dkt 122/3 digital system 1 week #7 combinational logic analysis
TRANSCRIPT
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
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)
Basic Combinational Logic Ccts
AND-OR LOGIC
Represents SOP implementation – AND gate for product term, OR gate for summing the product terms
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.
Basic Combinational Logic Ccts
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 ( ).
Implementing Combinational Logic
Example: Logic circuit for X = AB + CDE
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.
Implement logic circuit from Boolean Expression
Implementing Combinational Logic
First, write the SOP expression from the Truth Table. Then, implement the logic circuit.
INPUT OUTPUT
A B C X
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0
QUESTION:What is the SOP
expression?
QUESTION:What is the SOP
expression?
Implementing Combinational Logic
Implement logic circuit from Truth-table
Universal Property - NAND & NOR
NAND gate is a universal gate because it can be used to produce the NOT, AND, OR and NOR functions.
NAND 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.
Universal Property - NAND & NOR
NOR GATE AS A UNIVERSAL LOGIC ELEMENT
Combinational Logic - NAND & NOR
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.
NAND 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.
Combinational Logic - NAND & NOR
NOR LOGIC
Example:Using appropriate dual symbols, redraw the logic diagram and develop the output expression for the following circuit:
Combinational Logic - NAND & NOR