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04-612-307 ระบบคอมพวิเตอร์และการเช่ือมโยง Computer Systems and Interfacing

บทที ่1 พืน้ฐานดจิติอล

สาขาวชิาวศิวกรรมคอมพวิเตอร์คณะวศิวกรรมศาสตร์ มหาวิทยาลยัเทคโนโลยรีาชมงคลพระนคร

Digital and Analog Quantities


Analog quantities have continuous valuesDigital quantities have discrete sets of values


Analog quantities have

continuous valuesDigital quantities have

discrete sets of values


Types of electronic devices or instruments:AnalogDigitalCombination analog and digital

Binary Digits, Logic Levels, and Digital Waveforms


The conventional numbering system uses ten digits: 0,1,2,3,4,5,6,7,8, and 9.

The binary numbering system uses just two digits: 0 and 1.


The two binary digits are designated 0 and 1

They can also be called LOW and HIGH, where LOW = 0 and HIGH = 1


Binary values are also

represented by voltage levels


Major parts of a digital pulseBase lineAmplitudeRise time (tr)Pulse width (tw)Fall time (tf)


T

1f

tw = pulse widthT = period of the waveform f = frequency of the waveform


%100T

tcycle Duty w

The duty cycle of a binary waveform is

defined as:

Basic Logic Operations


There are only three basic logic operations:


When the input is LOW, the output is HIGHWhen the input is HIGH, the output is LOW

The NOT operation

The output logic level is

always opposite the input

logic level.


The AND operation When any input is LOW, the output is LOW When both inputs are HIGH, the output is HIGH

Switch S1 AND Switch S2 must be

closed to light the lamp


The OR operation

When any input is HIGH, the output is HIGH When both inputs are LOW, the output is

LOW

Switch S1 OR Switch S2 (or both of

them) must be closed to light the

lamp

Introduction

Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-NOR.

Switch S1 OR Switch S2 (or both of

them) must be closed to light the

lamp

Switch S1 AND Switch S2 must be

closed to light the lamp

Three basic logic gates

Common logic gates

NAND and NOR gates are logically equivalent to AND and OR gates followed by inverters. Since NAND is actually easier to build, ANDs are often constructed as inverted NAND gates.

Example: logic diagram for a + b’c

More complicated expression

The logic diagram above depicts ((ab + bc’)a)’For a parenthesized expression, construct parenthesized portion first

Note the connectors () used to indicate a continuation of the same input (for a and b)

Same expression, abbreviated

Two inverters eliminated: first by including c’ as an input (instead of c) and second by making the third AND gate a NAND gate

In this version, inputs a and b are shown multiple times – use same symbols, so we know they’re the same inputs

One more example

To translate logic diagram to Boolean expression: label output of each gate (starting from left) with appropriate sub-

expression output of last gate is full expression

Fixed-Function Integrated Circuits


IC package stylesDual in-line package (DIP)Small-outline IC (SOIC)Flat pack (FP)Plastic-leaded chip carrier (PLCC)Leadless-ceramic chip carrier (LCCC)


Dual in-line package (DIP)


Small-outline IC (SOIC)


Flat pack (FP)


Plastic-leaded chip carrier (PLCC)


Leadless-ceramic chip carrier (LCCC)

Introduction to Programmable Logic


SPLD—Simple programmable logic devicesCPLD—Complex programmable logic devicesFPGA—Field-programmable gate arrays


SPLD PAL (programmable array logic) GAL (generic array logic) PLA (programmable logic array) PROM (programmable read-only memory)

Test and Measurement Instruments

Analog OscilloscopeDigital OscilloscopeLogic AnalyzerLogic Probe, Pulser, and Current ProbeDC Power SupplyFunction GeneratorDigital Multimeter

Number Systems

Decimal Numbers

The decimal number system has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

The decimal numbering system has a base of 10 with each position weighted by a factor of 10:

Binary Numbers

The binary number system has two digits: 0 and 1

The binary numbering system has a base of 2 with each position weighted by a factor of 2:

Decimal-to-Binary Conversion

Decimal-to-Binary Conversion

Sum-of-weights methodRepeated division-by-2 methodConversion of decimal fractions to binary

Binary Arithmetic

Binary Arithmetic

Binary additionBinary subtractionBinary multiplicationBinary division

Complements of Binary Numbers


1’s complements2’s complements


1’s complement


2’s complement

Signed Numbers

Signed Numbers

Signed-magnitude form1’s and 2’s complement formDecimal value of signed numbersRange of valuesFloating-point numbers

Signed Numbers

Signed-magnitude form The sign bit is the left-most bit in a signed binary number A 0 sign bit indicates a positive magnitude A 1 sign bit indicates a negative magnitude

Signed Numbers

1’s complement form A negative value is the 1’s complement of the corresponding positive

value

2’s complement form A negative value is the 2’s complement of the corresponding positive

value

Signed Numbers

Decimal value of signed numbers Sign-magnitude 1’s complement 2’s complement

Signed Numbers

Range of Values2’s complement form:

– (2n – 1) to + (2n – 1 – 1)

Hexadecimal Numbers

Hexadecimal Numbers

Decimal, binary, and hexadecimal numbers

Hexadecimal Numbers

Binary-to-hexadecimal conversionHexadecimal-to-decimal conversionDecimal-to-hexadecimal conversion

Hexadecimal Numbers

Binary-to-hexadecimal conversion1. Break the binary number into 4-bit groups2. Replace each group with the hexadecimal equivalent

Hexadecimal Numbers

Hexadecimal-to-decimal conversion1. Convert the hexadecimal to groups of 4-bit binary2. Convert the binary to decimal

Hexadecimal Numbers

Decimal-to-hexadecimal conversion Repeated division by 16

Binary Coded Decimal (BCD)

Binary Coded Decimal (BCD)

Decimal and BCD digits

Digital Codes

Digital Codes

Gray codeASCII code

Digital Codes

Gray code

Digital Codes

ASCII code (control characters)

Digital Codes

ASCII code (graphic symbols 20h – 3Fh)

Digital Codes


Digital Codes

Extended ASCII code (80h – FFh)Non-English alphabetic charactersCurrency symbolsGreek lettersMath symbolsDrawing charactersBar graphing charactersShading characters

Decoders

Decoders

Binary decoder4-bit decoderBCD-to-decimal decoderBCD-to-7-segement decoder

Decoders

Binary decoderThe output is 1 only when:

A0 = 1A2 = 0A3 = 0A4 = 1

This is only one of an infinite

number of examples

Encoder/Decoder Vocabulary

ENCODER- a digital circuit that produces a binary output code depending on which of its inputs are activated.

DECODER- a digital circuit that converts an input binary code into a single numeric output.

ENCODERS AND DECODERS

A0

A1

A2

A3

A4

A5

A6

A7

ENCODER

O0

O1

O2

A0

A1

A2

O0

O1

O2

O3

O4

O5

O6

O7

DECODER

ONLY ONE INPUT

ACTIVATED AT A TIME

BINARY CODE OUTPUT

BINARY CODE INPUT

ONLY ONE OUTPUT

ACTIVATED AT A TIME

THE 8421 BCD CODE

BCD stands for Binary-Coded Decimal.

A BCD number is a four-bit binary group that represents one of the ten decimal digits 0 through 9.

Example:

Decimal number 4926 4 9 2 6

8421 BCD coded number 0100 1001 0010 0110

ELECTRONIC ENCODER -

DECIMAL TO BCD

0

Decimal

to

BCD

Encoder

BCD output

Decimal input0 0 0 0

5

0 1 0 1

7

0 1 1 1

3

0 0 1 1

• Encoders are available in IC form.

• This encoder translates from decimal

input to BCD output.

10 line to 4 line Encoder

ENCODER

1248

DECIMAL BINARY (BCD)

9 5V

8 5V

7 5V

6 5V

5 5V

4 5V

3 5V

2 5V

1 5V

74147I9I8I7I6I5I4I3I2I1

A0A1A2A3

10 line to 4 line Encoder

0

1

2

3

4

5

6

7

8

9

DECODER

BINARY (BCD)

DECIMAL

1 0V

2 0V

4 0V

8 0V

74LS42

A3A2A1A0

9876543210

4 line to 10 line Decoder

BCD-to-

7-Segment

Decoder/

Driver

DECODERS: BCD TO

7-SEGMENT DECODER/DRIVER

BCD input

0 0 0 0

Decimal outputLED

0 0 0 10 0 1 00 0 1 10 1 0 0

• Electronic decoders are available in IC form.

• This decoder translates from BCD to decimal.

• Decimals are shown on an 7-segment LED display.

• This IC also drives the 7-segment LED display.

7-segment display

There are two types of 7segment LED displays; common - anode common - cathode

81

In commonanode, the anode of all of the LEDs are tied together to positive of the power supply (Vcc) as shown

82

Common Anode

Common Cathode

In commoncathode, the cathode of all of the LEDs are tied together to ground as shown.

83

GND

BCD-to-

7-Segment

Decoder/

Driver

BCD inputDecimal output

0 0 1 1

?

Q #1- What is the decimal output from the decoder that appears on the 7-segment display?

Answer: 3


0 0 0 0

Answer: 0


1 0 0 1

Answer: 9


Answer: 7

0 1 1 1


Answer: 6

0 1 1 0

TEST

BCD-TO-SEVEN SEGMENT DECODER DRIVER

5V

abcdef g .

V+

74LS47A3A2A1A0

testRBI

gfedcba

RBO

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