Digital Logic Tutorial and Design

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Digital Logic Tutorial and Design
http://www.electronicsteacher.com
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2. Digital Logic Lab (A mini-lab experience)

• We are going to build both a combination lock and a
flashing railroad crossing signal using digital logic devices
• To build these circuits we will draw upon knowledge or
resources developed by several areas of electrical
engineering
• First, we will need to learn a little about digital logic
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3. Some Definitions

• Definition: Discrete System - a system with a finite
number of sizes or measures
– Shoes, Dresses, Pants, Bolts, Pencils
• Definition: Digital System - a Discrete System with only
two values of system variables: 1 and 0
– True/False; Yes/No; Male/Female; On/Off
• Let’s compare digital and continuous (analog) systems
– Digital signals are binary; analog signals are real-valued numbers
– Digital is less susceptible to noise
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4.

Analog Waveform
Voltage (V)
5
Time
0
Digital Waveform
5
1
Voltage (V)
1
0
Time
0
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5. AND Operator

• Let’s look at the relationship between the semantic and
logical operator known as the AND operator
• Consider:
If the car is fueled AND the engine works,
then the engine will start
AND Operator
Truth Table
• AND means that both conditions
A B Output
must be true in order for the
0 0 0
conclusion to be true
0 1 0
1 0 0
1 1 1
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6. Digital AND

• We can build an electrical device that performs the logical
AND operation on voltage equivalents of logic values
• An AND gate has the
electrical schematic:
A
Inputs
Output
B
For digital logic:
True = 1 is 5 volts
False = 0 is 0 volts
• Practice with the Excel spreadsheet
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7. OR Operator

• Another basic operator is the OR
• Consider:
If I have cash OR a credit card,
then I can pay the bill
• OR works such that the output is true,
if either of the two inputs is true
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OR Operator
Truth Table
A B Output
0 0 0
0 1 1
1 0 1
1 1 1
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8. NOT Operator/Inverter Gate

• The NOT gate reverses the input
A
B
NOT Operator
Truth Table
• All digital computers are
built using only three gate
types: AND, OR, and NOT
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A B
0 1
1 0
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9. XOR (Exclusive OR) Operator

• Let’s look at the relationship between the semantic and
logical operator known as the XOR operator
• Consider a biological example:
If gender A XOR gender B,
then reproduction is possible
• XOR works such that output is activated (equal to one) if
both inputs are of a different value
• Try the Excel spreadsheet exercise
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10. Digital XOR

• We can build an electrical device that performs the logical
XOR operation on voltage equivalents of logic values
• An XOR gate has the
electrical schematic:
A
Inputs
B
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Output
XOR Operator
Truth Table
A B Output
0 0 0
0 1 1
1 0 1
1 1 0
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11. Digital Combination Lock

Design and Software Simulation
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12. Multi-Input AND Gate

• AND gates can be built with any number of inputs
• Consider the symbol for the 4-input AND gate
A
B
C
D
F
• F is true only when all the inputs are true (1’s)
• Using the Excel workbook “EE-WISE-DigitalLab”, open
the “Digital Locks” worksheet, and test this circuit
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13. Digital Combination Lock

• Using 3 two-input AND gates, we could build a combination
lock that requires a four-digit code, specifically: 1 1 1 1
1
AND
1
1
AND
1
1
AND
1
1
• The number of inputs could be increased by using more and
more AND gates
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14. Digital Combination Lock

• We could build a combination lock that only uses the AND
gate, but that would be of little use since everyone would
know our combination, namely 1 1 1 1
• To build a more interesting combination lock, we will
utilize the NOT (inverter) gate
0
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15. Digital Combination Lock

• Let’s build a combination lock whose input (key code)
combination is 0 1 1 0
0
1
AND
1
1
AND
1
1
AND
0
1
1
• Is there any other combination that works?
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16. “Picking” a Digital Lock

• Use the truth table below to record the lock outputs for
the different lock combinations in the “Pick the Locks”
Input
worksheet
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Combination
A B C D
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
Lock #1
Lock Output
Lock #2 Lock #3 Lock #4
Lock #5
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17. Digital Railroad Crossing Signal

Design and Software Simulation
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18. Digital Railroad Crossing Signal

• Now, let’s develop a digital circuit whose output changes
over time
• We are all familiar with a railroad crossing signal that
alternates flashing red lights
• In addition to constructing the digital combination lock, we
will build the railroad crossing signal in the lab, so let’s
begin by designing the circuit
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19. Railroad Crossing Signal Design

• Here we will need some type of timing signal that will tell
the lights when to turn on and off
• The problem is that we seemingly need two timing signals
since one light is on while the other is off, and vice versa
• A digital logic implementation can allow us to save cost by
using only a single timing signal
• The design effort is then one of considering which gate(s)
need to be used to achieve the alternating signal patterns
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20. Railroad Crossing Signal

Turn-on voltage puts
out a constant +5 volts
1 AND 0 outputs 0
1 AND 1 outputs 1
0/1
1
AND
Square wave is
being repeatedly
turned on then off
0/1
XOR
1/0
1 XOR 0 outputs 1
1 XOR 1 outputs 0
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21. Railroad Crossing Signal Simulation

• The “Railroad Xing Simulation” worksheet may be used
in Excel to view (over time) the activation of the RR
crossing lights
• Note that this Excel simulation uses some advanced
features of Excel such as iteration and conditional
formatting to achieve the software simulation
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