20702032 universal logic gates
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Universal logic gates
1. INTRODUCTION
2. LOGIC GATES
3. UNIVERSAL LOGIC GATES
4. WORKING
5. APPLICATIONS
INTRODUCTION
In this 20th century, world cannot be imagined without the use of
electronic devices and IC’s are the pillars for these devices and these
devices are mainly constructed using different combinations of logic gates
.The concept of logic gates brought a great revolution in the field of
electronic devices.A logic gate performs a logical operation on one or more logic inputs
and produces a single logic output. The 1st logic Gates was developed in
1837 by Charles Babbage and they are of mechanical form. From then a
large variety and different type of logic gates are constructed there are
different types of logic gates like And, Or, Nand, nor, ex-or etc, these logic
gates are also known as Boolean logic gates.
The fundamental logic gates are or & and Gates. But these are not the
basis for making of different gates. So there came the concept of
universal logic gates and the universal logic gated are nand and nor
gates, they are called so because using both these logic gates all the
other logic Gates can be constructed. They are like the pillars for making
all the Boolean logic gates. These are of digital in nature and their inputs
and outputs will be accounted in 1’s and 0’s i.e, operating at high and low
voltages.
It looks very amazing that why AND & OR gates are not extensively used
gates their complements are the most extensively used gates. This is
because such circuits involve transistors where inversion occurs
automatically.
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We can see of these gates by implementing other basic logic gates with
the help of these gates only. Otherwise, mathematically also it has been
tried to prove the universality of these functions in Boolean algebra.
LOGIC GATES
Logic gates are used in the constructing digital circuits. Logic gates are
primarily implemented electronically using diodes or transistors, but can
also be constructed using
electromagnetic relays, fluidics, optics, molecules, or even mechanical
elements. The complexity of their construction depends upon the
materials from which they are made and the simplest one is diode logic
and these cannot be used to construct complex functional logics. Now
diode logic has evolved to transistor-transistor logics (TTL) following
resistor –transistor logics and then diode-transistor logics levels. The
transistors used are BJT (bipolar junction transistor) so as to reduce the
space occupied and to increase the level of complexity in logics.TT implies
that one transistor amplify the functions and the other helps in the logic
gating function.
Electronic logic gates are generally preferred than the mechanical ones
because of its qualities like speed, size and they consume less power.
Semiconductor logic gates are also built which act as high gain voltage
amplifier. The inputs and outputs levels, which are represented by voltage or
current, can be tabulated and that is known as a truth table. So for each
logic gate a unique truth table and a symbol can be associated. The
fundamental logic gates are or & and gates and the other logics include
inverter, Nand, or, Ex-or gates
Example:
Symbol of and gate:
Truth table of and gate
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UNIVERSAL LOGIC GATES
As said before Nand & nor gates are said to be the universal logic
gates
Symbol Rectangular symbol Function Truth table
NAND
NOR
INPUT OUTPUT
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1
INPUT OUTPUT
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0
INPUT OUTPUT
A B A NOR B
0 0 1
0 1 0
1 0 0
1 1 0
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2 input TTL nand gate
Explanation: we know that the voltage of the collector should be greater
than the base voltage which in turn should be greater than emitter
voltage for proper functioning of the transistor. The input is always given
through the emitter of the transistor because of the low impedance.
When both the inputs are high i.e., 1 then the transistor will be in reversed
bias, thus allowing the charge in the base flows through the transistor
On applying an input as 0 or low then T1 will be forward biased (base-
emitter junction) and current flows out through the collector. The stored
base charge in T2 will be discharged through T1 and taking it into a cut-off
region so current doesn’t flow through the transistor, since there is no
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base current inT4 it will be in cut-off region. The current from Vcc goes
into the transistor T3 through the resistor and making it into the
saturation level and because of that the output will be high.
Similarly when both the inputs are high or 1 the T1 will be in reversed bias
(base-emitter junction). So the current flows through resistor R1 into the
base of T2 making T2 into saturation level and the stored charge from the
base of the T3 will flow from it to the emitter ofT2 and make the T4 into
cut-off region making the output to be 0 or low .And T3 will also be in the
cut-off region so no current flows through it. So the output will be low.
So from the figure we can say that unless both the inputs are high the
output cannot be high.
VOLTAGE LEVELS
The definitions for high level and low level will be different for different
ones used for the building of nand gate. Like for TTL nand gate the idealvoltage at which it is operated is 5+%5 volts. The definition for high input
is any voltage between 2v and 5v and the low is between 0v to 0.8v.
The output high value will be possible when the output value voltage is
between 2.7v and 5v. And low means the voltage levels between 0v and
0.5v
Similarly for CMOS the input high means 3.5v to 5v and low corresponds
to 0v to 1.5v and the output high corresponds to 4.95 to 5v and the low
corresponds to 0v to 0.05v. But unlike TTL the CMOS can be operated atdifferent voltage levels like 12v and 15v etc.
Factors affecting voltage levels:
The values are not exactly 5 for high and 0 for low because some
resistance in the transistor present is responsible in that and the noise
margin also affects the output voltage levels. If the noise is greater than
the noise margin the output will be affected. So care should be taken such
that noise should be less than noise margin i.e., to minimize the noise or
to maximise the signal.
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The advantage of using CMOS in building the NAND gate is that the noise
margin will be high for CMOS compared to BJT’s.
Since ideal nand gates are not possible so one can try to make it more
closer towards the ideal nature.
REALISATION OF LOGICAL FUNCTION USING NAND
GATES:
Any logic function can be implemented using nand gates only. First the
logic functions are converted to POS (product of sum) form, then it is very
easy to implement it using nand gates .
Consider the following SOP expression
F = W.X.Y + X.Y.Z + Y.Z.W
The above expression can be implemented with three AND gates in firststage and one OR gate in second stage as shown in figure.
If bubbles are introduced at AND gates output and OR gates inputs (thesame for NOR gates), the above circuit becomes as shown in figure.
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Now replace OR gate with input bubble with the NAND gate. Now we havecircuit which is fully implemented with just NAND gates.
NOR GATE
It is the second universal logic gate. Same as nand gate any entire logicsystem can be implemented using only NOR gate. It is basicallycomplement of OR logic gate and denoted by different ways. Logic norgate function is sometimes called the ‘pierce function’ and denoted by A B
.the other way to represent it is A+B.A NOR gate gives high output only when all the inputs given to it are lowotherwise the output remains high.
CONSTRUCTION AND WORKING NOR GATE:
NOR gate is constructed following different types of circuitry
(TTL,CMOS,NMOS etc).depending upon circuitry the limitations and other
characteristics may be somewhat different.
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Structure of NMOS NOR gate Idealised
corresponding circuit
This consists of two identical NMOS enhancement drivers and one
depletion load. For ideal inverters, the behaviour of this circuit is
analogous to the second circuit. In 2
nd
circuit the switches are open forinputs of V(0) and closed for input V(1).consequently if either one of the
inputs is at V(1),a switch is closed and output will be 0.the output will be
SUPPLIED VOLTAGE only if when both
Inputs A and B are at V(0).
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CMOS NOR GATE AND ITS IDEALISED ANALOGOUS
CIRCUIT
If we represent this CMOS NOR GATE with analogous idealised circuit then
it will be like 2nd circuit. If either A or B is at logic 1, the output is ground.
No path is permissible between the output node and the power supply
Vdd .if either or both inputs are at 1, then output gives 0.if both switches
are open output will be Vdd.
REALISATION OF LOGICAL FUNCTION USING NOR GATES
As we know any logical function can be implemented using NOR gates. Inorder to do this at first, the logic function is converted to POS (product of
sum) form.
After converting logical expression to corresponding pos form it is very
convenient to implement it using NOR gate.
Like the POS expression
F = (X+Y) . (Y+Z)
Like other POS expression this can also be implemented very easily stepby step.
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The above expression can be implemented with three OR gates in firststage and one AND gate in second stage as shown in figure.
If bubble are introduced at the output of the OR gates and the inputs of AND gate, the above circuit becomes as shown in figure.
Now replace AND gate with input bubble with the NOR gate. Now we havecircuit which is fully implemented with just NOR gates.
Comparison between NAND & NOR gates
Although both gates are universal, they differ in their performance The NOR gate has a higher logical effort than the NAND (5/3 versus 4/3 fora 2-input gate), and thus is slower. I don't know what exactly you mean by"reliability" at high speed, but the NAND gate is faster.
The logical effort of a gate is basically the product of its input capacitanceand drive resistance, divided by the input capacitance and driveresistance of an inverter, which is used for reference.
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The typical inverter has an input capacitance of 3 units, since the PMOS istypically twice the size of the NMOS. The inverter's drive resistance istaken to be 1, and thus the bottom of the fraction is always 3.
To achieve the same drive strength as the inverter, the 2-input NAND
must have an input capacitance of four units (as seen by each input), andthus its logical effort is taken to be 4/3. The 2-input NOR has an inputcapacitance of five units (as seen by each input) and thus its logical effortis taken to be 5/3.
More complex gates necessarily have more input capacitance than theinverter, and thus are slower, given identical output drive strengths.Logical effort captures this in a single number; gates with higher logicaleffort are slower.
Applications of universal gates
NOR & NAND gates are two pillars of logic and logic circuits are widelymade by them only. Logic circuits include devices such as multiplexers,registers, arithmetic logic units (ALUs) and computer memory all the wayup through complete micro processors which contain 100 million logic
gates.In computer memory the most debated application of these gates is flashmemory.
Flash memory, it is a type of non-volatile memory allocation. Flashmemory stores information in an array of memory cells made fromfloating-gate transistors. Flash is used as secondary storage devices suchas hard disks, memory cards, memory stick, micro SD, xD-Picture Card, Intelligent Stick.etc. The most commonly used flash memories are NOR flash & NAND flash.
Both have their own qualities and drawbacks.NOR flash
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NOR flash memory wiring and structure on siliconIntel saw the massive potential of the invention and introduced the firstcommercial NOR type flash chip in 1988.In NOR gate flash, each cell has one end connected directly to ground,and the other end connected directly to a bit line. This arrangement iscalled "NOR flash" because it acts like a NOR gate when one of the wordlines is brought high, the corresponding storage transistor acts to pull theoutput bit line low.
Programming
Programming a NOR memory cell (setting it to logical 0), via hot-electron
injection.
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A single-level NOR flash cell in its default state is logically equivalent to abinary "1" value, because current will flow through the channel underapplication of an appropriate voltage to the control gate. A NOR flash cellcan be programmed, or set to a binary "0" value, by the followingprocedure:
• an elevated on-voltage (typically >5 V) is applied to the CG
• the channel is now turned on, so electrons can flow from the sourceto the drain (assuming an NMOS transistor)
• the source-drain current is sufficiently high to cause some highenergy electrons to jump through the insulating layer onto the FG,via a process called hot-electron injection
Erasing
Erasing a NOR memory cell (setting it to logical 1), via quantum tunneling.
To erase a NOR flash cell (resetting it to the "1" state), a large voltageof the opposite polarity is applied between the CG and source, pulling theelectrons off the FG through quantum tunneling. Modern NOR flashmemory chips are divided into erase segments (often called blocks orsectors). The erase operation can only be performed on a block-wisebasis; all the cells in an erase segment must be erased together.
Programming of NOR cells, however, can generally be performed one byteor word at a time.
NAND flash:
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NAND flash memory wiring and structure on silicon
NAND flash architecture was introduced by Toshiba in 1989
NAND flash also uses floating-gate transistors, but they are connected in away that resembles a NAND gate several transistors are connected inseries, and only if all word lines are pulled high (above the transistors' V T)is the bit line pulled low. These groups are then connected via someadditional transistors to a NOR-style bit line array.
To read, most of the word lines are pulled up above the V T of aprogrammed bit, while one of them is pulled up to just over the V T of anerased bit. The series group will conduct (and pull the bit line low) if theselected bit has not been programmed.
Despite the additional transistors, the reduction in ground wires and bit
lines allows a denser layout and greater storage capacity per chip. Inaddition, NAND flash is typically permitted to contain a certain number of faults (NOR flash, as is used for a BIOS ROM, is expected to be fault-free).Manufacturers try to maximize the amount of non-faulty storage byshrinking the size of the transistor below the size where they can be madereliably, to the size where further reductions would increase the numberof faults faster than it would increase the total storage available.
NAND flash uses tunnel injection for writing and tunnel release for erasing.NAND flash memory forms the core of the removable USB storage devicesknown as USB flash drivers and most memory card formats available
today.
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