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COMBINATIONAL LOGIC ANALYSIS Lecture 6 Digital Design Dr. PO Kimtho Department of Computer Sciences Norton University (NU)

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COMBINATIONAL LOGIC ANALYSIS

Lecture 6

Digital Design

Dr. PO Kimtho

Department of Computer Sciences

Norton University (NU)

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 ( ).

B A BA BA

Basic Combinational Logic Ccts

XNOR LOGIC

The complement of XOR logic.

B A AB BA )B B)(A A( BA BA

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?

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

Universal Property - NAND & NOR

NAND GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

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

Universal Property - NAND & NOR

NOR GATE AS A UNIVERSAL LOGIC ELEMENT (Cont.)

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

Combinational Logic - NAND & NOR

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.