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Basic Logic Operationsand
Standard Logic Gates
(Lecture #1)
ECE 331 – Digital System Design
Spring 2011 ECE 331 - Digital Systems Design 2
What is an analog signal?
Spring 2011 ECE 331 - Digital Systems Design 3
Analog Signal
An analog signal is a signal that can take on a continuous range of values.
Spring 2011 ECE 331 - Digital Systems Design 4
Analog Signal
Most, if not all, physical (naturally occurring) quantities are analog values.
Time Temperature Pressure
Spring 2011 ECE 331 - Digital Systems Design 5
What is an digital signal?
Spring 2011 ECE 331 - Digital Systems Design 6
Digital Signal
An digital signal is a signal that can take on only discrete (specific) values.
Spring 2011 ECE 331 - Digital Systems Design 7
What is an binary signal?
Spring 2011 ECE 331 - Digital Systems Design 8
Binary Signal
An binary signal is a signal that can take on only two values.
Typically represented by 0 and 1.
Spring 2011 ECE 331 - Digital Systems Design 9
Can a binary number be used to represent an analog value?
What about accuracy (or is it precision)?
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Can a binary number be used to represent an digital value?
How many bits are required?
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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.
SampleandHold
ADC BinaryEncoder
analog sampled digital binary
Spring 2011 ECE 331 - Digital Systems Design 12
Basic Logic Operations
Spring 2011 ECE 331 - Digital Systems Design 13
AND
Definition: the output is true (1) iff both inputs are true (1).
F = A.B = AB = “A and B”Boolean expression
logical operator
A B A . B
0 0 0
0 1 0
1 0 0
1 1 1
Truth tableF
Symbol (aka. logic gate)
Spring 2011 ECE 331 - Digital Systems Design 14
OR
Definition: the output is true (1) if either or both inputs are true (1).
F = A+B = “A or B”Boolean expression
logical operator
A B A + B
0 0 0
0 1 1
1 0 1
1 1 1
Truth table
Symbol
F F
Spring 2011 ECE 331 - Digital Systems Design 15
NOT
Definition: the output is true (1) if the input is false (0).
F = A' = “ not A”Boolean expression
logical operator
A A'
0 1
1 0
Truth table
Symbol
A F = A'
Spring 2011 ECE 331 - Digital Systems Design 16
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.
Spring 2011 ECE 331 - Digital Systems Design 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.
Spring 2011 ECE 331 - Digital Systems Design 18
NAND
Definition: the output is false (0) iff both inputs are true (1).
F = (A.B)' = “not (A and B)”Boolean expression
A B (A . B)'
0 0 1
0 1 1
1 0 1
1 1 0
Truth tableF = (A.B)'
Symbolshorthand for inversion
Spring 2011 ECE 331 - Digital Systems Design 19
NOR
Definition: the output is false (0) if either or both inputs are true (1).
F = (A+B)' = “not (A or B)”Boolean expression
A B (A+B)'
0 0 1
0 1 0
1 0 0
1 1 0
Truth table
Symbol
F FFF = (A+B)'
shorthand for inversion
Spring 2011 ECE 331 - Digital Systems Design 20
XOR
Definition: the output is true (1) if either but not both inputs are true (1).
F = A xor BBoolean expression
A B A xor B
0 0 0
0 1 1
1 0 1
1 1 0Truth table
Symbol
logical operator
Spring 2011 ECE 331 - Digital Systems Design 21
XNOR (aka. Equivalence)
Definition: the output is false (0) if either but not both inputs are true (1).
F = A xnor BBoolean expression
A B A xnor B
0 0 1
0 1 0
1 0 0
1 1 1
Truth tableSymbol
logical operator
Spring 2011 ECE 331 - Digital Systems Design 22
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)
Spring 2011 ECE 331 - Digital Systems Design 23
Standard Logic Gates
Spring 2011 ECE 331 - Digital Systems Design 24
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 331 - Digital Systems Design 25
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.
Spring 2011 ECE 331 - Digital Systems Design 26
Standard Logic Gates: 74xx08
pin-out
Truth table
Spring 2011 ECE 331 - Digital Systems Design 27
Standard Logic Gates: 74xx32
pin-out
Truth table
Spring 2011 ECE 331 - Digital Systems Design 28
Standard Logic Gates: 74xx04
pin-out
Truth table
Spring 2011 ECE 331 - Digital Systems Design 29
Building a Logic Circuit
CircuitDiagram
B
C
A
Finputs output
F = B'.C + A.BBoolean
Expression
74xx08
74xx08
74xx3274xx04
Spring 2011 ECE 331 - Digital Systems Design 30
Building a Logic CircuitV DD
7404
7408 7432
ABC F
components
wires
inputs
output
WiringDiagram
Spring 2011 ECE 331 - Digital Systems Design 31
Draw the circuit diagram and wiring diagram for the following Boolean expression:
F = A'.B + A.B'
Example
Spring 2011 ECE 331 - Digital Systems Design 32
Example
(circuit diagram)
Spring 2011 ECE 331 - Digital Systems Design 33
Example
Spring 2011 ECE 331 - Digital Systems Design 34
Questions?