Download Memory and Capacitors

MEMORY
Digital Principles, Roger Tokheim
Chapter 9
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Combinatorial Logic vs.
Sequential Logic
A circuit is said to be “combinatorial” if its
output is determined solely by its inputs.
Such a circuit can be realized in terms of logical gates
(ANDs, ORs and NOTs).
A circuit is said to be “sequential” if its output is
in part determined by its history.
History dependence here means bits (high or low
states) that were previously stored by the circuit.
If the sole purpose of the circuit is to store
values, it is called memory.
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Flip-flops and Registers
A circuit that can store a single bit is known
as a flip-flop.
A group of flip-flops working in parallel as
a unit to hold a “word” is known as a
register.
A group of addressable registers (done with
a decoder) is known as memory.
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Memory Address Register
The Memory Address Register is for
holding the address of the memory that is
currently being processed.
It is the input to the decoder. The decoder in
turn connects to a series of registers.
At this lowest level, addresses are absolute
but at a higher level addresses may be
relative or absolute.
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Like an Array
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Address
Value
0000
AB
0001
34
0002
73
0003
84
0004
CC
…
…
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Reading and Writing
The action of placing a value in a memory circuit
(a.k.a. a cell) is called writing.
Putting a high value into a cell is referred to as
“setting.”
Putting a low value into a cell is referred to as
“resetting.”
Accessing the value in a memory cell without
affecting it is called reading.
Grammatically, the CPU is the subject; the
memory is the object
The CPU writes to memory.
The CPU reads from memory.
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The Clock
The timing of these actions, especially the “write”
are controlled by the clock.
One can think of a computer’s clock as something
that steadily oscillates betweens the values 0 and 1
Units of memory (flip flops) will can have three
types of input:
Control: whether or not to write
Timing: when to write
Data: what to write
Sometimes control and timing are combined.
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ROM
Read Only Memory
As the name suggests the user only reads this type
of memory; the writing is typically done by the
manufacturer.
ROM is nonvolatile, that is, a supply of energy is
not required to keep the data intact.
That is, ROM is not lost when the computer is turned
off.
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Using ROM
Most personal computers contain a small
amount of ROM that stores critical
programs such as the program that boots the
computer. In addition, ROMs are used
extensively in calculators and peripheral
devices such as laser printers, whose fonts
are often stored in ROMs.
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Types of ROM
ROM: data is written by manufacturer
PROM: programmable read-only memory,
data is written by user
PROMs are manufactured as blank chips on
which data can be written with a special device
called a PROM programmer (a.k.a. burner)
Like burning a CD-R
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Types of PROM
PROM usually implies “write once”
EPROM erasable programmable read only
memory data can be erased and rewritten
Some use ultraviolet (UV) light, requires removing it
from the computer
EEPROM, electrically erasable programmable
read-only memory, is erased by electronic means
Does not have to be removed from computer
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Uses Of ROM
Microcode portion of CPU
The lowest-level instructions that directly control a
microprocessor.
A “plus” instruction will be stored in a program in
RAM; the code that tells the hardware what to do when
it encounters a plus is in ROM
Basic Input/Output System (BIOS)
Code burned into motherboard’s ROM; it handles
interfacing between the operating system and
peripherals (IO).
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RAM
RAM Random Access Memory
Data can be accessed (read)
Sequentially: you start at the beginning and go through
the sequence of locations
• Like a cassette or video tape
Randomly: you can jump to any location without
proceeding through all previous locations
• Like a CD or DVD (no need for fast-forwarding, rewinding,
etc.)
ROM is also random access, but the term RAM
refers to volatile memory, memory requiring an
energy source.
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Types of RAM
SRAM: Static RAM
The objective of memory is to hold a value, so
being static is good. The value is held without
the need for “refreshing.”
Fast but expensive.
DRAM: Dynamic RAM
The value must be “refreshed” or it will
become lost or corrupted.
Slow but cheap.
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Types of DRAM
Synchronous DRAM (SDRAM) actually
synchronizes itself with the CPU's bus
Deals with data in “bursts” so it doesn’t have to go
through the addressing process of successive data
locations
DDR SDRAM – Double Data Rate SDRAM
Double data refers to the number of times that data
can be sent along the bus connecting processor
and memory
Also DDR2 and DDR3
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Blurring the distinction between
RAM and ROM
NVRAM: Non-Volatile Random Access
Memory, is RAM that does not lose its data
when the power goes off.
A separate power source such as a battery
allows the RAM to hold onto its information
until it can be written to more permanent form:
to EEPROM or to storage (disk)
Some modems use it to keep phone numbers
and/or modem profiles.
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Blurring the Distinction II
Flash memory: A version of EEPROM
that can be erased and reprogrammed in
blocks rather than one byte at a time. This
makes writing (burning) easier/faster.
Many PCs use flash memory for their BIOS –
a flash BIOS.
Flash memory is often used in modems, as it
allows the manufacturer to support new
protocols as they become standardized.
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Cache
A generic term used to describe guessing what
data will be used next and placing it where it can
be accessed more quickly
A cache hit is a correct guess
A cache miss is an incorrect guess
Memory Cache uses SRAM which is faster than
DRAM
L1: SRAM that is right on the microprocessor
chip
L2: (originally) not on the chip
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Cache
When writing to cache, there are different
scenarios
Write back: updates cache first and memory
later (faster)
Write through: updates cache and memory
together (slower but maintains consistency)
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SRAM Pros
Speed
SRAM is faster than DRAM, because DRAM
requires refreshing which takes time
Simplicity
SRAM is simpler to use than DRAM, again
because DRAM requires refreshing
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SRAM Cons
Size
SRAM is a more complicated circuit, it involves more
transistors than DRAM, and hence it is larger
Cost
Again SRAM is more transistors and so it costs more
Power
Since SRAM involves a constant current, it uses more
power than DRAM
Heat
Again since SRAM involves a constant current, it
produces more heat
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Error Detection
Parity
Odd parity: add an extra bit to a word and insist
that the total number of 1’s be odd
Even parity, ditto but number of 1’s even
Example of odd parity
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
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Vertical parity
0
0
0
0
0
0
0
0
1
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0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
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Error Detection and Error Correction
Code
If a parity check reveals a parity error, one
can request data be resent
Parity
CRC (cyclic redundancy check)
checksum
Error Correction Code: in addition to
detecting a mistake can help fix it
Hamming code
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Capacitance
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What is a capacitor?
A capacitor is an electronic component that
stores electric charge (and electric energy)
A simple version of a capacitor is the
parallel-plate capacitor; it consists of two
conducting plates separated by an insulating
material
The insulating material is called a dielectric in
this context.
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Parallel-plate capacitor
1. Battery (not
shown) pushes
charges out
conducting plates
+
+
I
+
+
2. Positive charges
+
accumulates on
+
first plate;
dielectric does not +
let them through
-
dielectric
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3. Neutral atoms on
other plate are made
up positive and
negative charges
I
4. Negative charges are
attracted and stay behind,
while positive charges are
repelled and move out giving
rise to the current on other
side
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We can’t go on like this
conducting plates 3. When the push from the
1. There are
positive charges
battery is equal to the push
coming from the
back from the plate, the
+
battery
capacitor stops charging
+
I
I
+
+
2. There are
4. The bigger the push from
+
positive charges on
the battery (i.e. voltage), the
+
the first plate. Like
more charge goes onto the
+
charges repel.
plate. The voltage and
charge are proportional.
dielectric
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Q = VC
When we talk about the charge on a
capacitor, we mean the charge on one of the
plates.
The charge is proportional to the voltage: Q
 V.
The proportionality constant C is called the
capacitance.
Solving for V, the equation becomes
V =
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Q
C
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Farad
The standard unit of capacitance is the farad
(F).
A farad is quite large, usually you see
millifarad
microfarad
nanofarad
picofarad
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mF
F
nF
pF
(1 mF = 10-3 F)
(1  F = 10-6 F)
(1 nF = 10-9 F)
(1 pF = 10-12 F)
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Capacitance Q=VC
The capacitance is a measure of how easy it is to
put charge on the plates, it is
directly proportional to the surface area of the plates,
bigger plates can hold more charge
inversely proportional to the distance between the
plates, the interaction between the positive and negative
charges is greater when they are closer
dependent on the material (dielectric) separating the
plates, having a good insulator between them is like
their being further apart
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Capacitive keyboards
Capacitive keyboards detect which key was pressed by
looking at changes in capacitance.
Under each key are two oppositely charged plates ( a
capacitor).
Pressing a key moves its upper plate closer to its lower
plate, changing its capacitance, and hence changes the
amount of charge the plates can hold for a given voltage.
The keyboard circuitry detects this change and sends the
appropriate information (interrupt request and ASCII code)
to the CPU.
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DRAM
Capacitors can be put on integrated circuit (IC)
chips.
Together with transistors, they are used in
dynamic random access memory (D-RAM).
The charge or lack thereof of the capacitor
corresponds to a stored bit. Since these capacitors
are small, their capacitance is pretty low.
DRAM has to be recharged (refreshed) thousands
of times per second or it loses its data.
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Power Supply
Large capacitors are used in the power supplies of
computers and peripherals.
The capacitors (along with diodes) are used in
rectifying: turning the alternating current (AC)
into smoothed out direct current (DC).
Capacitors do the smoothing part.
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Monitors
Monitors (CRT’s) are another place that
large capacitors are found.
Since capacitors store charge, monitors and
power supplies can be dangerous even when
the power is off.
If you don’t know what you’re doing, don’t
even open them up.
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Equivalent Capacitance
When a combination of capacitors can be
replaced by a single capacitor, which has
the same effect as the combination, the
capacitance of the single capacitor is called
the equivalent capacitance.
Having the same effect means that same
voltage results in the same amount of
charge being stored.
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Capacitors in parallel
Recall that things in parallel have the same voltage
V
C1
C2
And the charge is split between the capacitors.
The charge has a choice, some will go onto one
capacitor, the rest on the other.
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Capacitors in parallel
Individual capacitors obey basic equation
Q1 = C1 V and
Q2 = C2 V
Equivalent capacitor obeys basic equation
Qtotal = Ceq V
The total charge is the sum of the individual charges
Qtotal = Q1 + Q2
Solve basic equations for Q’s and substitute
Ceq V = C1 V + C2 V
Divide by common factor V
Ceq = C1 + C2
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Capacitors in series
V
C1
C2
Capacitors in series have the same charge
When the capacitors are uncharged, the region including the
lower plate of C1 and the upper plate of C2 is electrically
neutral. This region is isolated and so this remains true; the
negative charge on the lower plate of C1 when added to the
positive charge on the upper plate of C2 would give zero
The voltage is split between them
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Capacitors in series
Individual capacitors obey basic equation
V1 = Q1 / C1 and V2 = Q2 / C2
Equivalent capacitor obeys basic equation
Vtotal = Qtotal / Ceq
The total voltage is the sum of the individual voltages
Vtotal = V1 + V2
Substitute basic equations into voltage equation
Qtotal / Ceq = Q1 / C1 + Q2 / C2
All of the charges are the same (Qtotal = Q1 = Q2 = Q),
divide out the common factor
1 / Ceq = 1 / C1 + 1 / C2
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Example
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Example (Cont.)
Something must take the brunt of the
voltage when the battery is first connected,
that’s why the 0.2-k resistor is there.
The 2.5-F and 1.5-F are in parallel, so
they can be replaced with one 4.0-F
capacitor.
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Example (Cont.)
The 3.5-F and 4.0-F capacitors are in
series, so they can be replaced with one
1.87-F capacitor.
The charge on it Q=CV would be 9.33 C
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Example (Cont.)
Going back to the 3.5-F and 4.0-F
capacitors are in series, capacitors in series
have the same charge, so Q3.5 = 9.33 C
Then V3.5 = Q3.5 / C3.5 or V3.5 = 2.67 V
And V4.0 = Q4.0 / C4.0 or V4.0 = 2.33 V
(Note that V3.5 + V4.0 = 5)
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Example (Cont.)
The 4.0-F capacitor was really a 1.5-F
and a 2.5-F in parallel
Things in parallel have the same voltage, so
V1.5 = V2.5 = 2.33 V
Since Q1.5 = V1.5 C1.5, Q1.5 = 3.50 C
Similarly, Q2.5 = 5.83 C
(Note Q1.5 + Q2.5 = 9.33 C)
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Testing in Electronics
Workbench
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Two Cautions
When the switches are closed, there is an easy
path from one side of the capacitor to another, this
makes sure that the capacitors are discharged.
Even when the switches are open there is a path
from one side to another for the upper capacitors,
it is through the voltmeter. The voltmeter must be
made extremely ideal (very high resistance) to get
agreement with theory.
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RC circuits: Charging
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What happens
When you connect an uncharged capacitor and a
resistor in series to a battery, the voltage drop is
initially all across the resistor.
Because the voltage drop across a capacitor is
proportional to the charge on it and there is not charge
on it at the beginning.
But charge starts to build up on the capacitor, so
some voltage is dropped across the capacitor now.
Capacitors have a gap and while current gets all the
way around the circuit, individual charges are
trapped on one side of the capacitor.
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What happens (Cont.)
Since some voltage is dropped across the capacitor, less
voltage (than before) is dropped across resistor. With less
voltage being dropped across the resistor, the current drops
off.
V = IR (smaller V  smaller I)
With less current, the rate at which charge goes onto the
capacitor decreases.
The charge continues to build up, but the rate of the build
up continues to decrease.
In mathematical language, the charge as a function of time
Q(t) increases but its slope decreases.
Theory says the charge obeys Q(t) = C V (1 - e- t /  )
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Time Constant
Q(t) = C V (1 - e- t /  )
 in that equation is known as the “time constant” and
is given by  = RC
Note that since R = V / I , resistance has units volt/ampere
Since C = Q / V, capacitance has units coulomb/volt
RC = (V / I)  (Q / V) = Q / I
Then RC has units coulomb/ampere but an ampere is
coulomb/second
RC = Q / (Q / T) = T
So RC has units of second
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Charging Capacitor
Charge on capacitor
RC Circuit (Charging)
95%
63%
Time
1
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3
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Voltage is similar
If the charge on the capacitor varies
according to the expression
Q(t) = C V (1 - e- t /  )
then since the voltage across a capacitor is
V=Q/C the voltage is
V(t) = V (1 - e- t /  )
the voltage approaches its “saturation” value,
which in a simple RC circuit in the battery’s
voltage.
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Time Constant
The time constant ( = RC) is the time required
for a certain percentage (63%) of the saturation
charge (the charge after a very long time) to be put
on the capacitor.
If the resistance is large, the currents are small,
even from the start and it requires more time to
charge up the capacitor (  R)
If the capacitance is large, the capacitor can take a
lot of charge and again it requires more time to
charge up the capacitor (  C)
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RC circuits: Discharging
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What happens
This time we imagine that there are already
charges on the capacitor, but there is no battery.
With no battery to "push" the charges around, the
opposite charges on the two capacitor plates
would prefer to be together.
They must pass through the resistor before they
can reunite.
With all those like charges on one plate, there is a
strong incentive for charges to leave the plate.
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What happens (Cont.)
However, as charges leave the plate, the voltage
across the capacitor decreases (V = Q C) and the
incentive for charges to leave the capacitor
decreases, thus the rate at which charges leave
decreases as well.
In mathematical language, this time the charge as
a function of time Q(t) decreases and its slope
decreases.
Theory says the charge obeys Q(t) = Q0 e- t /  .
Same time constant as before.
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Discharging Capacitor
Charge on the capacitor
RC Circuit (Discharging)
37%
5%
Time
1
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3
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