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Chapter 20
Digital Circuits
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Objectives
• Explain the difference between analog and digital systems.
• Convert decimal numbers to their binary equivalents and binary numbers to their decimal equivalents.
• Name seven types of logic gates.
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Objectives
• Explain the operation of various types of logic gates.
• Use truth tables to determine the output of a logic gate.
• Discuss two types of logic families.
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Objectives
• Explain the digital encoders and decoders.
• Explain analog-to-digital and digital-to-analog devices.
• List three types of flip-flops and explain their truth tables.
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ICs
• Include transistors, diodes, resistors, and capacitors
• Major advantage is size• Linear circuits
– Used as amplifiers and have variable outputs
• Digital circuits– Used as switches and work in the on or off
state
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Digital Fundamentals
• Binary numbering system
• Voltage logic levels
• Bits, nibbles, and bytes
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Digital Advantages
• Inexpensive, compared to analog systems
• Easier information storage
• Speed is greater than in analog systems
• Compatibility with computers
• Less effect from temperature changes
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Digital Characteristics
• Capable of replacing analog systems
• Cannot be distinguished from analog systems in most cases
• Information is handled using switching circuits
• Combination of logic gate and flip-flop circuits
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Binary Numbering System
• Digital circuits act in on or off states
• Comparable to a single-pole single-throw (SPST) switch– Switch in “on” position
represents a 1
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Basic Counting Rules
• Digits must be recorded one after the other for each counting unit
• When count exceeds total number of available digits, a second column begins
• Decimal system’s first column ends at 9, and second column begins at 10
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Binary System
• 2 is comparable to decimal system’s 10
• 2 moves to second column, becomes a 0 or 1
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Decimal to Binary Conversion Table
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Binary Numbers
• Count binary numbers on your fingers
• Number the fingers on your left hand as shown
• Fingers pointing up are 1s, fingers folded down are 0s
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Large Binary Numbers and Addition
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Voltage Logic Levels in Digital Circuits
• Type of logic circuitry or family affects operating voltages needed in a circuit
• Valid logic high range
• Valid logic low range
• Invalid value range, or intermediate range
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Bits, Nibbles, and Bytes
• Bit comes from joining binary and digit
• Bit is smallest unit of information
• Computer memory– Kilobytes– Megabytes– Gigabytes
• Computer storage abilities are growing
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Review
What is the primary difference between the decimal numbering system and the binary numbering system?
The decimal system has numbers 0–9, and the binary system has 0 and 1
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Review
What is the smallest unit of information in binary code?
A bit
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Logic Gates
• AND gates
• OR gates
• NOT gates
• NAND gates
• NOR gates
• XOR gates
• XNOR gates
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AND Gates
• Accepts high and low inputs (1 and 0)
• High and low outputs• Output of 1 if all
inputs are 1• If only one gate is on,
circuit will not work• Truth tables
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AND Gates (Cont.)
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AND Gates (Cont.)
• Valid logic highs and lows
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OR Gates
• Output signal of 1 if either or both inputs is 1
• When all inputs are 0, output is 0
• Acts similar to two switches in parallel
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OR Gates (Cont.)
• Valid logic highs and lows
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NOT Gates
• Used to invert polarity of input signal– Also called inverters
• If input is 1, output is 0• If input is 0, output is 1
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NOT Gates (Cont.)
• Valid logic highs and lows
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NAND Gates
• Made of an AND gate and a NOT gate
• Reverse of AND application
• Also called NOT AND gates
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NAND Gates (Cont.)
• Valid logic highs and lows
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NOR Gates
• Opposite of OR gate• Made of OR and NOT
gates• Used to test for any
kind of input• No input will have
output of 1
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NOR Gates (Cont.)
• Valid logic highs and lows
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XOR Gates
• Also called exclusive OR gates
• Provide high output if any, but not all, inputs are logic high
• Provide low output if all inputs are logic high
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XOR Gates (Cont.)
• Valid logic highs and lows
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XNOR Gates
• Also called exclusive NOR gates
• XOR gate with inverted output
• High output only when all inputs are logic high or logic low
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Review
Which gate has an output signal of 1 if either or both inputs is 1?
OR gate
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Review
Which gate provides high output if any, but not all, inputs are logic high, but provides a low output if all inputs are logic high?
XOR gate
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Review
Which gate is made of an AND and a NOT gate?
NAND gate
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Review
Which gate has an inverted output so it has a high output only when all inputs are logic high or logic low?
XNOR
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Logic Families
• Traits of one logic family must match traits of another family when many digital ICs are used in one device
• Complementary metal-oxide semiconductor logic (CMOS)
• Transistor-transistor logic (TTL)
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CMOS Logic
• Circuits have good resistance to noise
• Use FETs
• Require small amounts of power
• Can be damaged by static electricity
• Worker and work surface must be grounded through high-resistance resistor
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TTL
• Circuits work quickly
• Function from 20 megahertz to 60 megahertz
• Faster than CMOS ICs
• Require high power dissipation and high current
• Many gates can be placed in one TTL IC
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Review
If many digital circuits are used in one device, how should logic families be treated?
Traits of one logic family must match traits of another family
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Review
Which of the two types of logic families can be easily damaged by static electricity?
CMOS
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Digital Applications
• Logic probes
• Digital encoders and decoders
• Digitized analog signals
• Flip-flops
• Counters
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Logic Probes
• Indicate a high or low signal using LEDs
• Connect to power supply of circuit being tested
• Equipped with a slide switch to select the logic family
• If both LEDs light, there is an invalid logic level voltage
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Digital Encoders and Decoders
• Electronic systems translate binary system into decimal system
• Analog-to-digital converters can change analog numbers to a digital number equivalent– Digital multimeter as example
• Can convert electrical pulses into binary numbers
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Digitized Analog Signals
• Digital signals representing sound waves or linear voltage
• Analog-to-digital encoders are used
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Flip-Flops
• Set-reset (R-S) flip-flops
• J-K flip-flops
• D flip-flops
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R-S Flip-Flops
• When S is high, Q is high• Output represents last input setting if both inputs are low• Outputs are complementary• Clocked R-S flip-flops
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J-K Flip-Flops
• Clock driven• Retain output status
when two inputs are low
• When both inputs are high, outputs toggle on and off
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D Flip-Flops
• Do not require two inputs
• Q outputs toggle when input signal is received if clock signal is applied
• Output state of Q will not change without clock signal
• Output Qs are always complementary
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Counters
• Can carry and borrow• Fabricated from individual flip-flops• Available as integrated chips
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Decade Counters
• Can count based on ten• Can be used to divide by ten• Used as frequency dividers for oscilloscopes or
in digital clocks
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Computerized Tomography (CT)
• Uses photomultiplier tubes, computer scans, and X-rays to produce digitized images of the body
• Photocathodes
• Dynodes
• Anode grid
• Gantry
• Contrast agent
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Review
How can binary numbers be translated into the decimal system?
Digital decoders
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Review
What is a flip-flop?
A semiconductor device that can assume one of two stable states
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Review
What kind of flip-flop does not require two inputs?
D flip-flop
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Review
What does it mean if two outputs are complementary?
When one output is high, the other is low
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For Discussion
• Give examples of advantages integrated circuits have over transistors.
• What are the differences among the logic gates?
• Give examples of possible advances that will be made in the computer field in the next 25 years, based on what you have learned in this chapter.