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2.1
Unit 2 – Digital Circuits (Logic)
2.2
ANALOG VS. DIGITAL
Moving from voltages to 1's and 0's…
2.3
Signal Types• Analog signal
– Continuous time signal where each voltage level has a unique meaning
– Most information types are inherently analog
• Digital signal
– Continuous signal where voltage levels are mapped into 2 ranges
meaning 0 or 1
– Possible to convert a single analog signal to a set of digital signals
0
1
0
1
0
vo
lts
vo
lts
timetime
Analog Digital
Threshold
2.4
Signals and Meaning
0.0 V
0.8 V
2.0 V
5.0 V
Each voltage value
has unique meaning
0.0 V
5.0 V
Lo
gic
1L
og
ic 0
Ille
gal
Analog Digital
Threshold Range
Each voltage maps to '0' or '1'
(There is a small illegal range where meaning is
undefined since threshold can vary based on
temperature, small variations in manufacturing, etc.)
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2.5
Analog vs. Digital
USC students used to program analog computers!
2.6
Analog vs. Digital
• Analog Advantages
– Can be easier to build simple systems
• AM Radio
• Digital Advantages
– Not affected by small changes (noise) in the signal
– Repeatable
– The above make it easier to build large, complex
systems
2.7
COMPUTERS AND SWITCHING
TECHNOLOGY
A Brief History
2.8
Mechanical Computers• Primarily gear-based
• Two prototypes designed and partially implemented by Charles Babbage
– Used mechanical levers, gears, and ball bearings, etc.
• ______________________
– prototype and not fully programmable
• ______________________
– Never completed
– To be programmed with punch cards
– Designed to perform4 basic arithmeticops. (add, sub, mul, div)
Charles Babbage and his Difference Engine
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2.9
Electronic Computers• 1945 - ENIAC was first, fully
electronic computer
• Used thousands of _______
______ as fundamental
switching (on/off) technology
• Weighed 30 tons, required
15,000 square feet, and
maximum size number was 10
decimal digits (i.e.
±9,999,999,999)
• Still required some patch panels
(wire plugs) to configure it
2.10
Vacuum Tube Technology• Digital, electronic computers use some sort of
voltage controlled switch (on/off)
• Looks like a light bulb
• Usually 3 nodes
– 1 node serves as the switch value allowing current to flow between the other 2 nodes (on) or preventing current flow between the other 2 nodes (off)
– Example: if the switch input voltage is 5V, then current is allowed to flow between the other nodes
Vacuum Tube
Switch Input
(Hi or Lo Voltage)
A
B
Current can flow based on voltage of input switch
2.11
Vacuum Tube Disadvantages
• ___________________________
– Especially when you need
_____________________________
• ___________________________
– Can
• ___________________________
2.12
Transistor• Another switching device
• Invented by Bell Labs in 1948
• Uses semiconductor materials (silicon)
• Much smaller, faster, more reliable (doesn't burn out), and dissipated less power
Individual Transistors (About the size of your fingertip)
Transistor is 'on'
Transistor is 'off'
Gate
+5V
Source Drain
- - - -
--
High voltage at gate allows current to flow from source to
drain
Gate0V
Drain
-
Low voltage at gate prevents current from flowing from
source to drain
-
Silicon
Silicon
Source
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2.13
Moore's Law & Transistors
• Moore's Law = Number of transistors able to
be fabricated on a chip will
_____________________________
• Transistors are the fundamental building block
of computer HW
– Switching devices: Can conduct [on = 1] or not-
conduct [off = 0] based on an input voltage
2.14
How Does a Transistor Work
• Transistor inner workings
– http://www.youtube.com/watch?v=IcrBqCFLHIY
2.15
NMOS Transistor Physics
• Transistor is started by implanting two n-type silicon
areas, separated by p-type
n-type silicon (extra negative charges)
p-type silicon ("extra" positive charges)
-
+
+
+
-
-
-Source Input
Drain Input
2.16
NMOS Transistor Physics
• A thin, insulator layer (silicon dioxide or just "oxide") is placed over the silicon between source and drain
n-type silicon (extra negative charges)
Insulator Layer (oxide)
p-type silicon ("extra" positive charges)
-
+
+
+
-
-
-
Source Input Drain Output
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2.17
NMOS Transistor Physics
• A thin, insulator layer (silicon dioxide or just "oxide") is placed over the silicon between source and drain
• Conductive polysilicon material is layered over the oxide to form the gate input
n-type silicon (extra negative charges)
Insulator Layer (oxide)
p-type silicon ("extra" positive charges)
conductive polysilicon
-
+
+
+
-
-
-
Gate InputSource Input Drain Output
2.18
NMOS Transistor Physics• Positive voltage
(charge) at the gate input _________
the extra positive charges in the p-type silicon
• Result is a negative-charge channel between the source input and drain
p-type
Gate Input
Source Input Drain Output
n-type
+
+
+
+
+
+ + + +
+ + + +
- - -
negatively-charge channel
--
positive charge "repelled"
2.19
NMOS Transistor Physics
• Electrons can flow through the negative channel from the source input to the drain output
• The transistor is "on"
p-type
Gate Input
Source Input Drain Output
n-type
+
+
+
+
+
+ + + +
+ + +
-
-
-
- - - --
-
-
+
- -
Negative channel between source and drain =
Current flow
- -
2.20
NMOS Transistor Physics
• If a low voltage (negative charge) is placed on the gate, no channel will develop and no current will flow
• The transistor is "off"
p-type
Gate Input
Source Input Drain Output
n-type
-
-
-
-
-
- - - -
+
+
+
No negative channel between source and drain
= No current flow
-
-
- --
-
-
+ + +
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2.21
View of a Transistor
• Cross-section of transistors
on an IC
• Moore's Law is founded on
our ability to keep
shrinking transistor sizes
– Gate/channel width shrinks
– Gate oxide shrinks
• Transistor feature size is
referred to as the
implementation
"technology node"Electron Microscope View of Transistor Cross-Section
2.22
DIGITAL LOGIC GATES
2.23
Transistors and Logic
• Transistors act as
switches (on or off)
• Logic operations (AND /
OR) formed by
connecting them in
specific patterns
– Series Connection
– Parallel Connection
Series Connection
S1 AND S2 must be
on for A to be
connected to B
Parallel Connection
S1 OR S2 must be
on for A to be
connected to B
A BS2S1
A BS1
S2
2.24
Digital Logic• Forms the basic processing circuits for digital signals (i.e. 1's and 0's)
• Digital Logic still abstracts many of the physical issues (voltage, current,
parasitics, etc.) dealt with in the study of integrated circuits
– An alarm should sound if the key is in the ignition AND your seatbelt is NOT
fastened
– If the voltage threshold sensor rises above 3 volts create a conductive
channel to excite the ignition sensor…
Integrated Circuits(Transistors)
Computer Architecture(Functional Blocks)
Digital LogicOR
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2.25
Gates
• Each logical operation (AND, OR, NOT) can be
implemented in circuit form using the
corresponding logic gate
AND Gate OR Gate NOT Gate
2.26
AND Gates• An AND gate outputs a '1' (true) if ALL inputs are '1' (true)
• Gates can have several inputs
• Behavior can be shown in a truth table (listing all possible input
combinations and the corresponding output)
Y
XF
X Y F
0 0 0
0 1 0
1 0 0
1 1 1
2-input AND
X Y Z F
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
3-input AND
F
X
Y
Z
F=X•Y F=X•Y•Z
2.27
OR Gates
• An OR gate outputs a '1' (true) if ANY input is '1' (true)
• Gates can also have several inputs
X Y F
0 0 0
0 1 1
1 0 1
1 1 1
2-input OR
X Y Z F
0 0 0 0
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 1
3-input OR
F
X
Y
Z
F=X+Y F=X+Y+Z
2.28
NOT Gate• A NOT gate outputs a '1' (true) if the input is '0' (false)
• Also called an "Inverter"
X F
1 0
0 1
F = X
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2.29
NAND and NOR Gates
NAND NOR
ZX
YZ
X Y Z
0 0 1
0 1 0
1 0 0
1 1 0
X
Y
X Y Z
0 0 1
0 1 1
1 0 1
1 1 0
YXZ ⋅= YXZ +=
X Y Z
0 0 0
0 1 0
1 0 0
1 1 1
X Y Z
0 0 0
0 1 1
1 0 1
1 1 1
AND NAND OR NOR
True if NOT ANY
input is true
True if NOT ALL
inputs are true
� Inverted versions of the AND and OR gate
2.30
XOR and XNOR Gates
XOR
ZX
Y
X Y Z
0 0 0
0 1 1
1 0 1
1 1 0
XNOR
ZX
Y
X Y Z
0 0 1
0 1 0
1 0 0
1 1 1
YXZ ⊕= YXZ ⊕=
True if an odd # of inputs are true
= True if inputs are different
True if an even # of inputs are true
= True if inputs are same
� Exclusive OR gate. Outputs a '1' if either input is a
'1', but not both.
2.31
Logic Example
0
0
1
0
2.32
Logic Example
0
1
0
0
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2.33
Delay Example
00
1
0
0 11
1
1
1 00
0
1
4 Levels of Logic
Change in D, C, or A must propagate
through 4 levels of gates
2.34
Logical Operations Summary
• All digital circuits can be described using AND, OR,
and NOT
– Note: You'll learn in future courses that digital circuits
can be described with any of the other sets:
• {AND, NOT}, {OR, NOT}, {NAND only}, or {NOR only}
• Normal convention: 1 = true / 0 = false
• A logic circuit takes some digital inputs and
transforms each possible input combination to a
desired output values
Logic
CircuitI0
I1
I2
O0
O1
Inputs Outputs
Trivia-of-the-day: The Apollo Guidance Computer that
controlled the lunar spacecraft in 1969 was built out of 8,400
3-input NOR gates.
2.35
Sequential Devices (Registers)
• AND, OR, NOT, NAND, and other gates are known as ____________
_____________________
– Outputs only depend on what the inputs are _________, not one second ago
– This implies they have no "memory" (can't remember a value)
• Sequential logic devices provide the ability to retain or
_______________ a value by itself (even after the input is changed
or removed)
– Outputs can depend on the current inputs, and previous states of the circuit
(stored values.)
– Usually have a controlling signal that indicates when the device should
update the value it is remembering vs. when it should simply remember that
value
– This controlling signal is usually the _________ signal
2.36
Registers
• Registers are the most common sequential
device
• Registers sample the data input (D) on the
edge of a clock pulse (CP) and stores that
value at the output (Q)
• Analogy: Taking a picture with your _____
____________ when you press a button
(clock pulse) the camera samples the scene
(input) and ______________________ it as
a snapshot (output)
Block Diagram of a Register
The clock pulse (positive edge)
here…
…causes q(t) to sample and hold the current d(t)
value
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2.37
Flip-Flops
• Flip-flops are the building blocks of ____________
– 1 Flip-flop PER ______ of input/output
– There are many kinds of flip-flops but the most common is the
D- (________) Flip-flop (a.k.a. D-FF)
• D Flip-flop triggers on the clock edge and captures the D-value at
that instant and causes Q to remember it until the next edge
– _____________ Edge: instant the clock transition from low to high (0 to 1)
Positive-Edge Triggered D-FF
D Q
CLK
D-FFClock Signal
d(t) q(t)
2.38
Registers and Flip-flops
• A register is simply a _____
of D flip-flops that all
trigger on a single clock
pulse
D Q
D Q
D Q
D Q
CP
D3
D2
D1
D0
Q3
Q2
Q1
Q0
D-FF
D-FF
D-FF
D-FF
4-bit Register
CLK Qt+1
0 Qt
1 Qt
↑ Dt
Steady level of 0 or 1
Positive Edge
2.39
Pulses and Clocks
• Registers need an edge to trigger
• We can generate pulses at specific times
(creating an ______________ pattern) when we
know the data we want has arrived
• Other registers in our hardware should trigger at
a ___________ interval
• For that we use a clock signal…
– Alternating high/low voltage pulse train
– Controls the ordering and timing of operations
performed in the processor
– 1 ________ is usually measured from
rising/positive edge to rising/positive edge
• Clock frequency (F) = # of cycles per second
• Clock Period (T) = ______________
Processor
Clock Signal
0 (0V)
1 (5V)
1 cycle
2.8 GHz = 2.8*109 cycles per second
= 0.357 ns/cycle
Op. 1 Op. 2 Op. 3
Clock Pulses
2.40
Combinational vs. Sequential
• Sequential logic (i.e. registers) is used to store
values
– Each register is analogous to a ___________ in
your software program (a variable stores a
number until you need it)
• Combinational logic is used to process bits (i.e.
perform operations on values
– Analogous to operators (+,-,*) in your software
program