07/ago/2017 digital fundamentals - inf.pucrs.br · pdf filefigure 3-1standard logic symbols...

Digital Fundamentals

CHAPTER

ELEVENTH EDITION

Digital Fundamentals, Eleventh EditionThomas L. Floyd

Copyright © 2015 by Pearson Education, Inc.All Rights Reserved

Introductory Concepts

1

07/ago/2017



FIGURE 1-1 Graph of an analog quantity (temperature versus time).

Most natural quantities that we see are analog and vary continuously. Analog systems can generally handle higher power than digital systems.



FIGURE 1-2 Sampled-value representation (quantization) of the analog quantity in Figure 1–1. Each value represented by a dot can be digitized by representing it as a digital code that consists of a series of 1s and 0s.

Digital systems can process, store, and transmit data more efficiently but can only assign discrete values to each point.



FIGURE 1-4 Basic block diagram of a CD player. Only one channel is shown.

Many systems use a mix of analog and digital electronics to take advantage of each technology. A typical CD player accepts digital data from the CD drive and converts it to an analog signal for amplification.



FIGURE 1-6 Logic level ranges of voltage for a digital circuit.

Digital electronics uses circuits that have two states, which are represented by two different voltage levels called HIGH and LOW. The voltages represent numbers in the binary system.

In binary, a single number is called a bit (for binary digit). A bit can have the value of either a 0 or a 1, depending on if the voltage is HIGH or LOW.



FIGURE 1-7 Ideal pulses.

• Digital waveforms change between the LOW and HIGH levels.

• A positive going pulse is one that goes from a normally LOW logic level to a HIGH level and then back again.

• Digital waveforms are made up of a series of pulses.



FIGURE 1-8 Nonideal pulse characteristics.

Actual pulses are not ideal but are described by the rise time, fall time, amplitude, and other characteristics.



FIGURE 1-9 Examples of digital waveforms.

In addition to frequency and period, repetitive pulse waveforms are described by the amplitude (A), pulse width (tW) and duty cycle. Duty cycle is the ratio of tW to T.

Volts

Time

Amplitude (A)

Pulse width (tW)

Period, T



Periodic pulse waveforms are composed of pulses that repeats in a fixed interval called the period. The frequency is the rate it repeats and is measured in hertz.

Tf 1= f

T 1=

The clock is a basic timing signal that is an example of a periodic wave.

What is the period of a repetitive wave if f = 3.2 GHz?

===GHz 2.311

fT 313 ns

Digital Fundamentals

CHAPTER

ELEVENTH EDITION



Logic Gates

3



FIGURE 3-1 Standard logic symbols for the inverter (ANSI/IEEE Std. 91-1984/Std. 91a-1991).

The Inverter



The inverter performs the Boolean NOT operation. When the input is LOW, the output is HIGH; when the input is HIGH, the output is LOW.

The InverterA X

InputA X

Output

LOW (0) HIGH (1)HIGH (1) LOW(0)

The NOT operation (complement) is shown with an overbar. Thus, the Boolean expression for an inverter is X = A.



Example waveforms:

A

X

A group of inverters can be used to form the 1’s complement of a binary number:

Binary number

1’s complement

1 0 0 0 1 1 0 1

0 1 1 1 0 0 1 0

The InverterA X



FIGURE 3-8 Standard logic symbols for the AND gate showing two inputs (ANSI/IEEE Std. 91-1984/Std. 91a-1991).

The AND gate



The AND gate produces a HIGH output when all inputs are HIGH; otherwise, the output is LOW. For a 2-input gate, the truth table is

The AND operation is usually shown with a dot between the variables but it may be implied (no dot). Thus, the AND operation is written as X = A . B or X = AB

InputsA B X

Output

0 00 11 01 1

00 01

A

BX

The AND gate



FIGURE 3-10 Example of AND gate operation with a timing diagram showing input and output relationships.

The AND gate



Example waveforms:

A

X

The AND operation is used in computer programming as a selective mask. If you want to retain certain bits of a binary number but reset the other bits to 0, you could set a mask with 1’s in the position of the retained bits.

A

BX

B

00000011If the binary number 10100011 is ANDed with the mask00001111, what is the result?

The AND gate



FIGURE 3-13

X

Waveform for X ?

The AND gate



FIGURE 3-15 Boolean expressions for AND gates with two, three, and four inputs.

The AND gate



The OR gate produces a HIGH output if any input is HIGH; if all inputs are LOW, the output is LOW. For a 2-input gate, the truth table is

The OR operation is shown with a plus sign (+) between the variables. Thus, the OR operation is written as X = A + B.

InputsA B X

Output

0 00 11 01 1

01 11

AB

X AB

X≥ 1

The OR gate



Example waveforms:

A

X

The OR operation can be used in computer programming to set certain bits of a binary number to 1.

B

AB

X

ASCII letters have a 1 in the bit 5 position for lower case letters and a 0 in this position for capitals. (Bit positions are numbered from right to left starting with 0.) What will be the result if you OR an ASCII letter with the 8-bit mask 00100000?

The resulting letter will be lower case.

The OR gate



FIGURE 3-23

The OR gate



FIGURE 3-24 Boolean expressions for OR gates with two, three, and four inputs.

The OR gate



The NAND gate produces a LOW output when all inputs are HIGH; otherwise, the output is HIGH. For a 2-input gate, the truth table is

InputsA B X

Output

0 00 11 01 1

11 10

A

BX A

BX&

The NAND operation is shown with a dot between the variables and an overbar covering them. Thus, the NAND operation is written as X = A .B (alternatively, X = AB)

The NAND gate



Example waveforms:

A

X

The NAND gate is particularly useful because it is a “universal” gate – all other basic gates can be constructed from NAND gates.

B

A 2-input NAND gate with both inputs connected together is equivalent to which gate ?

A

BThe NAND gate



FIGURE 3-29

The output waveform X is LOW only when all three input waveforms are HIGH as shown in the timing diagram.

The NAND gate



The NOR gate produces a LOW output if any input is HIGH; if all inputs are HIGH, the output is LOW. For a 2-input gate, the truth table is

InputsA B X

Output

0 00 11 01 1

10 00

AB

X AB

X≥1

The NOR operation is shown with a plus sign (+) between the variables and an overbar covering them. Thus, the NOR operation is written as X = A + B.

The NOR gate



Example waveforms:

A

X

The NOR operation will produce a LOW if any input is HIGH.

B

When is the LED is ON for the circuit shown?

The LED will be on when any of the four inputs are HIGH.

ACBD

X

330 W

+5.0 V

AB

XThe NOR gate



FIGURE 3-37

The NOR gate



FIGURE 3-38 Standard symbols representing the two equivalent operations of a NOR gate.

De Morgan’s Theorem

FIGURE 3-30 ANSI/IEEE standard symbols representing the two equivalent operations of a NAND gate.



The XOR gate produces a HIGH output only when both inputs are at opposite logic levels. The truth table is

InputsA B X

Output

0 00 11 01 1

01 10

AB

X AB

X= 1

The XOR operation is written as X = AB + AB. Alternatively, it can be written with a circled plus sign between the variables as X = A + B.

The XOR gate



Example waveforms:

A

X

Notice that the XOR gate will produce a HIGH only when exactly one input is HIGH.

B

If the A and B waveforms are both inverted for the above waveforms, how is the output affected?

There is no change in the output.

AB

XThe XOR gate



The XNOR gate produces a HIGH output only when both inputs are at the same logic level. The truth table is

The XNOR Gate

InputsA B X

Output

0 00 11 01 1

10 01

AB

X AB

X

The XNOR operation shown as X = AB + AB. Alternatively, the XNOR operation can be shown with a circled dot between the variables. Thus, it can be shown as X = A . B.

= 1



FIGURE 3-48



TABLE 3–13 An XOR gate used to add two bits.



FIGURE 3-75



Transformações entre Representações Lógicas



Transformações entre Representações Lógicas



[John_R._Gregg]_Ones_and_Zeros_Understanding_Bool(BookZZ.org)



[John_R._Gregg]_Ones_and_Zeros_Understanding_Bool(BookZZ.org)



Examine the conditions indicated in Figure 3–92, and identify the faulty gates.



Simplificação Lógica

• Lógica simplificada == hardware mais eficiente§ Menor área de hardware§ Menor o atraso da lógica

• Próximo conteúdo: simplificação lógica.

07/ago/2017 digital fundamentals - inf.pucrs.br · pdf filefigure 3-1standard logic symbols...

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