301 ECE Digital Electronics
Basic logic operations,
Transistors, and CMOS
logic gates
(Lecture #4)
Learning Objectives
Logic operations
Transistors
BJT
MOSFET
CMOS logic gates and logic circuits
Standard logic gates and logic families
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Reading
Roth & Kinney
Sections 2.2, 3.2, 7.2
Appendix A
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Basic Logic Operations
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AND
Definition: the output is true (1) iff both inputs
are true (1).
logical operator
Boolean expression
F
A
B
A.B
0
0
0
0
1
0
1
F = A.B = AB = A and B
0
0
1
1
1
Truth table
Symbol (aka. logic gate)
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OR
Definition: the output is true (1) if either or both
inputs are true (1).
logical operator
FF
B
A+ B
0
0
0
1
1
1
Boolean expression
A
0
F = A+B = A or B
0
1
1
1
1
Truth table
Symbol
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NOT
Definition: the output is true (1) if the input is
false (0), and vice versa.
logical operator
F = A' = not A
A
A'
Boolean expression
0
1
1
0
Truth table
A
F = A'
Symbol
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Order of Precedence
The order of precedence of the basic logic
operations is defined as follows:
AND
NOT
OR
The order of precedence can be modified
by using parenthesis.
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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.
There are, however, additional (more
complex) logic gates.
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Additional Logic Gates
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NAND
Definition: the output is false (0) iff both inputs
are true (1).
F = (A.B)'
Symbol
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B
(A . B)'
0
0
1
1
1
1
Boolean expression
A
0
F = (A.B)' = not (A and B)
0
1
1
1
0
Truth table
shorthand for inversion
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NOR
Definition: the output is false (0) if either or both
inputs are true (1).
F
F
FF = (A+B)'
Symbol
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B
(A+B)'
0
0
1
1
0
1
Boolean expression
A
0
F = (A+B)' = not (A or B)
0
0
1
1
0
Truth table
shorthand for inversion
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XOR
Definition: the output is true (1) if either but not
both inputs are true (1).
A
Boolean expression
logical operator
B
A xor B
0
0
0
0
1
1
1
0
1
1
F = A xor B
1
0
Truth table
Symbol
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XNOR (aka. Equivalence)
Definition: the output is false (0) if either but not
both inputs are true (1).
F = A xnor B
A
Symbol
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0
0
1
0
1
0
0
0
1
logical operator
A xnor B
1
Boolean expression
B
1
1
Truth table
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Logic Gates
Logic gates are an abstraction.
They are electrical circuits that implement
the aforementioned logic operations.
They are the basic building blocks used in
the design (and realization) of digital logic
circuits.
Both combinational and sequential.
But how are they dDigital
realized?
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Transistors
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BJT
Bipolar Junction Transistor (BJT)
Three-terminal device
Fabricated from doped semiconductor
material
Two types of BJT's
Base, Collector, and Emitter
NPN and PNP
Used in
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Switching
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circuits and Amplifiers
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BJT
NPN
PNP
Wikipedia: http://en.wikipedia.org/wiki/Bjt
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TTL
Transistor Transistor Logic (TTL)
BJT's are used in the design of TTL gates.
Popular in the 1970's and 1980's
CMOS became the dominant technology
for the design of integrated circuits (IC).
TTL is now (mostly) obsolete.
Used in academic environments because
of its robustness.
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MOSFET
Metal Oxide Semiconductor Field Effect
Transistor (MOSFET)
Three-terminal device
Fabricated from doped semiconductor
material
Two types of MOSFET's
Gate, Drain, and Source
NMOS and PMOS
Used in
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MOSFET
NMOS
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PMOS
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MOSFET as an Amplifier
Used in analog integrated circuits.
Operates in the active (or saturation)
region.
Modeled as a voltage-dependent current
source.
Transistor amplifier circuits
are covered in extensive detail
in ECE 333 (Linear Electronics)
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MOSFET as a Switch
Used in digital integrated circuits.
Transistor is either on (closed) or off
(open).
Dependent upon the gate-to-source
voltage.
VGS > VTH : ON
VGS < VTH : OFF
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VSG > VTH : ON
VSG < VTH : OFF
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Digital Circuits
Digital circuits can only recognize and
operate on discrete signal levels.
Most use just two signal levels, one to
represent each of the Boolean logic
values.
VDD (supply voltage) true (logic 1)
GND (0 V) false (logic 0)
This simplifies the analysis of the behavior
o MOSFETsECE 301 - Digital as switches.
when used
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MOSFET a as Switch
N-channel MOSFET (NMOS)
VG = 0 V
(VS = 0 V)
looks like an open switch
VGS = 0 V
Operates in the cut-off region
VG = VDD
(VS = 0 V)
VGS = VDD
looks like a closed switch
Operates
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MOSFET as a Switch
P-channel MOSFET (PMOS)
VG = 0 V
(VS = VDD)
looks like a closed switch
VGS = VDD
Operates in the triode (or linear) region
VG = VDD
(VSG = VGS = VDD)
(VS = VDD)
VGS = 0 V
looks like an open switch
Operates
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ECE cutoff region.
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MOSFET as a Switch
NMOS
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PMOS
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CMOS Logic Gates
VDD = 5V
Inverter
VA
VF
GND = 0V
VA
Q2
VF
F
0
ON
OFF
VDD
1
VDD
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Q1
OFF
ON
0
0
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CMOS Logic Gates
VDD = 5V
VA
VB
VF
NAND
VA
VB
GND = 0V
VA
VB
Q1
Q2
Q3
Q4
VF
F
0
0
ON
OFF
ON
OFF
VDD
1
0
VDD
ON
OFF
OFF
ON
VDD
1
VDD
0
OFF
ON
ON
OFF
VDD
1
VDD
VDD
OFF
ON
OFF
ON
0
0
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CMOS Logic Gates
VDD = 5V
VA
NOR
VB
VF
VA
VB
GND = 0V
VA
VB
Q1
Q2
Q3
Q4
VF
F
0
0
ON
OFF
ON
OFF
VDD
1
0
VDD
ON
OFF
OFF
ON
0
0
VDD
0
OFF
ON
ON
OFF
0
0
VDD
VDD
OFF
ON
OFF
ON
0
0
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CMOS Logic Gates
How is an AND gate realized
using CMOS transistors?
How many transistors are required?
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CMOS Logic Gates
How is an OR gate realized
using CMOS transistors?
How many transistors are required?
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Foreshadowing
In terms of transistor count,
Is it more efficient to design
logic circuits using
AND and OR gates
or
NAND and NOR gates?
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CMOS Logic Circuits
In general, CMOS transistors can be used
to design and realize any logic function.
VDD
To output GND (logic 0):
P u ll-u p n e tw o rk
(P U N )
PMOS
Vf
VF
Vx
V1
1
V
x
Vnn
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P u ll-d o w n n e tw o rk
(P D N )
NMOS
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PUN must be off
PDN must be on
To output VDD (logic 1):
PUN must be on
PDN must be off
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Analysis of CMOS Circuits
The functional behavior of a
CMOS circuit can be
determined by analyzing the
behavior of the individual PMOS
and NMOS transistors, and,
thus, the behavior of the PUN
and PDN.
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Analysis of CMOS Circuits
1.
2.
3.
4.
Determine the state of each transistor for
each input combination.
Determine the output of the CMOS circuit
for each input combination.
Derive the corresponding truth table.
Determine the Boolean expression that
defines the functional behavior of the
CMOS circuit.
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CMOS Logic Circuits: Exercise
Given the CMOS Logic Circuit below,
fill in the table provided on the next slide.
V DD
VDD
Q1
Q5
Q3
Vf
VF
Vx
VC
1
Vx
VB
2
Q6
Q4
Q2
Vx
VA
3
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CMOS Logic Circuits: Exercise
VA
VB
VC
Q1
Q2
Q3
Q4
Q5
Q6
VF
F
0
0
0
ON
OFF
ON
OFF
ON
OFF
VDD
1
0
0
Vdd
ON
OFF
ON
OFF
OFF
ON
VDD
1
0
Vdd
0
ON
OFF
OFF
ON
ON
OFF
VDD
1
0
Vdd
Vdd
ON
OFF
OFF
ON
OFF
ON
0
0
Vdd
0
0
OFF
ON
ON
OFF
ON
OFF
VDD
1
Vdd
0
Vdd
OFF
ON
ON
OFF
OFF
ON
0
0
Vdd
Vdd
0
OFF
ON
OFF
ON
ON
OFF
VDD
1
Vdd
Vdd
Vdd
OFF
ON
OFF
ON
OFF
ON
0
0
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Logic Circuits
While logic circuits can be realized directly
from CMOS transistors, this course will
focus on the design of logic circuits using
logic gates as the basic building blocks.
We will, in general, not be concerned with
the underlying technology.
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Standard Logic Gates
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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
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Standard Logic Gates
Data sheets provide essential information:
Pinout
Electrical characteristics
Timing characteristics
Truth Table
Logic Function
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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74xx08
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74xx32
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74xx04
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Logic Families
Transistor
H
Schottky
S
Low Power Schottky
LS
Advanced Schottky
AS
Adv Low Power Schottky
ALS
Fast
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L
High Speed
CMOS
xx
Low Power
TTL
Logic Family
F
High Speed
HC
Advanced
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Comparison of Logic Families
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In the Lab
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Building a Logic Circuit
Discrete components can be
interconnected to build logic circuits.
Wiring Diagram
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Questions?
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