1. ECE 331 – Digital System Design
Basic Logic Operations
and
Standard Logic Gates
(Lecture #1)

2. What is an analog signal?
Spring 2011
ECE Digital Electronics

3. ECE 301 - Digital Electronics
Analog Signal
An analog signal is a signal that can take on a continuous range of values.
Spring 2011
ECE Digital Electronics

4. ECE 301 - Digital Electronics
Analog Signal
Most, if not all, physical (naturally occurring) quantities are analog values.
Time
Temperature
Pressure
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5. What is an digital signal?
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6. ECE 301 - Digital Electronics
Digital Signal
An digital signal is a signal that can take on only discrete (specific) values.
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7. What is an binary signal?
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8. ECE 301 - Digital Electronics
Binary Signal
An binary signal is a signal that can take on only two values.
Typically represented by 0 and 1.
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9. Can a binary number be used to represent an analog value?
What about accuracy (or is it precision)?
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10. Can a binary number be used to represent an digital value?
How many bits are required?
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ECE Digital Electronics

11. Processing Physical Quantities
The analog signal (representing the physical quantity) must be sampled at specific instances in time.
The sampled values must be digitized.
The digital value must be encoded in binary.
Sample
and
Hold
ADC
Binary
Encoder
analog
sampled
digital
binary
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12. Basic Logic Operations
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13. Definition: the output is true (1) iff both inputs are true (1).
AND
Definition: the output is true (1) iff both inputs are true (1).
logical operator
F = A.B = AB = “A and B” A B
A . B 1
Boolean expression F
Truth table
Symbol (aka. logic gate)
Spring 2011
ECE Digital Electronics

14. ECE 301 - Digital ElectronicsOR
Definition: the output is true (1) if either or both inputs are true (1).
logical operator
F = A+B = “A or B” A B
A + B 1
Boolean expression F
Truth table
Symbol
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ECE Digital Electronics

15. Definition: the output is true (1) if the input is false (0).
NOT
Definition: the output is true (1) if the input is false (0).
logical operator
F = A' = “ not A” A A' 1
Boolean expression
Truth table A
F = A'
Symbol
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16. ECE 301 - Digital Electronics
Order of Precedence
The order of precedence of the basic logic operations is defined as follows:
NOT
AND OR
The order of precedence can be modified by using parenthesis.
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17. Functionally Complete
The AND, OR, and NOT operations comprise a functionally complete set.
All logic functions can be expressed in terms of these logic operations.
All logic circuits can be realized using the associated logic gates.
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ECE Digital Electronics

18. Definition: the output is false (0) iff both inputs are true (1).
NAND
Definition: the output is false (0) iff both inputs are true (1).
F = (A.B)' = “not (A and B)” A B
(A . B)' 1
Boolean expression
F = (A.B)'
Truth table
Symbol
shorthand for inversion
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ECE Digital Electronics

19. ECE 301 - Digital Electronics
NOR
Definition: the output is false (0) if either or both inputs are true (1).
F = (A+B)' = “not (A or B)” A B
(A+B)' 1
Boolean expression F
F = (A+B)' F
Truth table
Symbol
shorthand for inversion
Spring 2011
ECE Digital Electronics

20. ECE 301 - Digital Electronics
XOR
Definition: the output is true (1) if either but not both inputs are true (1).
F = A xor B A B
A xor B 1
Boolean expression
logical operator
Truth table
Symbol
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ECE Digital Electronics

21. XNOR (aka. Equivalence)
Definition: the output is false (0) if either but not both inputs are true (1).
F = A xnor B A B
A xnor B 1
Boolean expression
logical operator
Symbol
Truth table
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ECE Digital Electronics

22. ECE 301 - Digital Electronics
Logic Circuits
Logic circuits are realized through the interconnection of logic gates.
Each logic gate represents a logical operation.
This can be done using
discrete components
Standard Logic Gates
programmable devices
Read-only Memories (ROM)
Programmable Logic Devices (PLD)
Field Programmable Gate Arrays (FPGA)
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23. ECE 301 - Digital Electronics
Standard Logic Gates
Spring 2011
ECE Digital Electronics

24. ECE 301 - Digital Electronics
Standard Logic Gates
Device
Logic Gate
74xx08
Quad 2-input AND gate
74xx32
Quad 2-input OR gate
74xx04
Hex Inverter (NOT gate)
74xx00
Quad 2-input NAND gate
74xx02
Quad 2-input NOR gate
74xx86
Quad 2-input XOR gate
Note: “xx” refers to the logic family
Spring 2011
ECE Digital Electronics

25. ECE 301 - Digital Electronics
Standard Logic Gates
Data sheets provide essential information:
Logic Function
Truth Table
Pin-out
Electrical Characteristics
Timing Characteristics
Package Description(s)
This information is necessary when building logic circuits from discrete components.
Each logic family has a unique set of characteristics.
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26. Standard Logic Gates: 74xx08
pin-out
Truth table
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27. Standard Logic Gates: 74xx32
pin-out
Truth table
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28. Standard Logic Gates: 74xx04
pin-out
Truth table
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29. Building a Logic Circuit
Diagram B C A F
inputs
output
74xx08
74xx04
74xx32
74xx08
Boolean
Expression
F = B'.C + A.B
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ECE Digital Electronics

30. Building a Logic CircuitV DD
7404
7408
7432 A B C F
Wiring
Diagram
components
wires
inputs
output
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ECE Digital Electronics

31. ECE 301 - Digital Electronics
Example
Draw the circuit diagram and wiring diagram for the following Boolean expression:
F = A'.B + A.B'
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ECE Digital Electronics

32. ECE 301 - Digital Electronics
Example
(circuit diagram)
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ECE Digital Electronics

33. ECE 301 - Digital Electronics
Example
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34. ECE 301 - Digital Electronics
Questions?
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ECE Digital Electronics