Logic Gates and Intergrated Circuits2020 " Project done by Mohan Krishna
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LOGIC GATES AND INTEGRATED CIRCUITS
Logic Gates
INTRODUCTION
A logic gate is an elementary building block of a digital circuit. It makes "logical decisions" based on the different combinations of digital signals present on its inputs. Digital logic gates may have more than one input but generally only have one digital output. Most logic gates have two inputs and one output.
Knowledge Cloud
A gate is a digital circuit that is designed for performance a particular logical operation. As it works according to some logical relationship between input and output voltages, so it is generally known as "LOGIC GATES"
At any given moment, every terminal is in one of the two binary conditions low (0) or high (1), represented by different voltage levels. The logic state of a terminal can, and generally does, change often, as the circuit processes data. In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V).
Individual logic gates can be connected together to form combinational or sequential circuits or larger logic gate functions. Different types of logic gate implements different Boolean function, that is, it performs a logical operation on one or more logic inputs and produces a single logic output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device.
Logic gates are primarily implemented electronically using diodes or transistors, but can also be constructed using electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.
A large number of electronic circuits (in computers, control units, and so on) are made up of logic gates. These process signals represent either true or false. The most common symbols used to represent logic gates are shown below.
TYPES OF LOGIC GATES:
AND gate:
The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table. A HIGH output (1) results only if both the inputs to the AND gate are HIGH (1). If neither or only one input to the AND gate is HIGH, a LOW output results. In another sense, the function of AND effectively finds the minimum between two binary digits, just as the OR function finds the maximum. Therefore, the output is always 0 except when all the inputs are 1.
We will start with a 2 input AND gate. The symbol for a 2 input AND gate is as follows.
ABQABQ
A
B
Q
A
B
Q
The truth table for the 2 input AND gate is shown below.
Inputs
Output
B
A
Q
0
0
0
0
1
0
1
0
0
1
1
1
The Boolean expression for a 2 input AND gate is
OR gate:
The OR gate is a digital logic gate that implements logical disjunction - it behaves according to the truth table. A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is high, a LOW output (0) results. In another sense, the function of OR effectively finds the maximum between two binary digits, just as the complementary AND function finds the minimum. We will start with a 2 input OR gate. The symbol for a 2 input OR gate is as follows.
ABQABQ
A
B
Q
A
B
Q
The truth table for the 2 input OR gate is shown below.
Inputs
Output
B
A
Q
0
0
0
0
1
1
1
0
1
1
1
1
The Boolean expression for a 2 input OR gate is
NOT gate (or inverter):
This is the simplest form of logic gate and has only 1 input and 1 output. Simply the purpose of this gate is to invert the input signal so if a Logic 0 is at the input, the output will be at Logic 1 and vice versa. The symbol for a NOT gate is as follows. (Next page)
The truth table for a NOT gate is the simplest of all Truth Tables and is shown below.
Input
Output
A
Q
0
1
1
0
The Boolean expression for a NOT gate is
NAND gate:
In digital electronics, a NAND gate (negative-AND) is a logic gate which produces an output that is false only if all its inputs are true; thus its output is complement to that of the AND gate. A LOW (0) output results only if both the inputs to the gate are HIGH (1); if one or both inputs are LOW (0), a HIGH (1) output results. It is made using transistors. By De Morgan's theorem, AB=A+B, a NAND gate is equivalent to inverters followed by an OR gate. The NAND gate is significant because any Boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness.
We will start with a 2 input NAND gate. The symbol for a 2 input NAND gate is as follows. (Next page)
ABQABQ
A
B
Q
A
B
Q
The truth table for the 2 input NAND gate is shown below.
Inputs
Output
B
A
Q
0
0
1
0
1
1
1
0
1
1
1
0
The Boolean expression for a 2 input NAND gate is
NOR gate:
The NOR gate is a digital logic gate which behaves according to the truth table. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator. It can also be seen as an AND gate with all the inputs inverted. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. By contrast, the OR operator is monotonic as it can only change LOW to HIGH but not vice versa.
We will start with a 2 input NOR gate. The symbol for a 2 input NOR gate is as follows. (Next page)
ABQABQ
A
B
Q
A
B
Q
The truth table for the 2 input NOR gate is shown below.
Inputs
Output
B
A
Q
0
0
1
0
1
0
1
0
0
1
1
0
The Boolean expression for a 2 input NOR gate is
XNOR gate:
ABQABQ The XNOR gate has 2 inputs and is the inverted form of the EXOR gate. The XNOR gate (sometimes spelled "exnor" or "enor" and rarely written NXOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. A HIGH output (1) results if both of the inputs to the gate are the same. If one but not both inputs are HIGH (1), a LOW output (0) results. The symbol for a 2 input XNOR gate is as follows.
A
B
Q
A
B
Q
The truth table for the 2 input XNOR gate is shown below.
Inputs
Output
B
A
Q
0
0
1
0
1
0
1
0
0
1
1
1
The Boolean expression for a 2 input XNOR gate is
EXOR gate.
ABQABQThe EXOR gate has 2 inputs and is a specialised version of the OR gate. The XOR gate (sometimes EOR gate, or EXOR gate and pronounced as Exclusive OR gate) is a digital logic gate that implements an exclusive or; that is, a true output (1/HIGH) results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "one or the other but not both". The symbol for a 2 input EXOR gate is as follows.
A
B
Q
A
B
Q
The truth table for the 2 input EXOR gate is shown below.
Inputs
Output
B
A
Q
0
0
0
0
1
1
1
0
1
1
1
0
The Boolean expression for a 2 input EXOR gate is
Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arrayed together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space. Arrays of logic gates are found in digital integrated circuits (ICs).
As IC technology advances, the required physical volume for each individual logic gate decreases and digital devices of the same or smaller size become capable of performing ever-more-complicated operations at ever-increasing speeds.
Summary of 2-input Logic Gates
The following Truth Table compares the logical functions of the 2-input logic gates above.
Inputs
Truth Table Outputs For Each Gate
A
B
AND
NAND
OR
NOR
EX-OR
EX-NOR
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
The following table gives a list of the common logic functions and their equivalent Boolean notation.
Logic Function
Boolean Notation
AND
A.B
OR
A+B
NOT
A
NAND
A .B
NOR
A+B
EX-OR
(A.B) + (A.B) or A B
EX-NOR
(A.B) + or A B
Universal logic gates
NAND and NOR gates as digital building blocks.
The repeated use of the OR, the AND or the NOT gates alone cannot give a different gate. But the repeated use of the NAND or the NOR gates alone can give all basic gates like OR, AND and NOT gate. Hence the NAND and the NOR gates are also called Universal Logic Gates. In digital circuits, these gates serve as digital building blocks.
Knowledge Cloud
Charles Sanders Peirce (winter of 1880–81) showed that NOR gates alone (or alternatively NAND gates alone) can be used to reproduce the functions of all the other logic gates, but his work on it was unpublished until 1933.The first published proof was by Henry M.Sheffer in 1913, so the NAND logical operation is sometimes called Sheffer stroke; the logical NOR is sometimes called Peirce's arrow.
Integrated Circuits
INTRODUCTION
An integrated circuit (IC), sometimes called a chip or microchip, is a semiconductor wafer on which thousands or millions of tiny resistors, capacitors, and transistors are fabricated. An IC can function as an amplifier, oscillator, timer, counter, computer memory, or microprocessor.
Integrated Circuits or IC's as they are more commonly called, can be grouped together into families according to the number of transistors or "gates" that they contain. For example, a simple AND gate my contain only a few individual transistors, were as a more complex microprocessor may contain many thousands of individual transistor gates. A particular IC is categorized as either linear (analog) or digital, depending on its intended application.
Classification of Integrated Circuits
Small Scale Integration or (SSI) – Contain up to 10 transistors or a few gates within a single package such as AND, OR, NOT gates.
Medium Scale Integration or (MSI) – between 10 and 100 transistors or tens of gates within a single package and perform digital operations such as adders, decoders, counters, flip-flops and multiplexers.
Large Scale Integration or (LSI) – between 100 and 1,000 transistors or hundreds of gates and perform specific digital operations such as I/O chips, memory, arithmetic and logic units.
Very-Large Scale Integration or (VLSI) – between 1,000 and 10,000 transistors or thousands of gates and perform computational operations such as processors, large memory arrays and programmable logic devices.
Super-Large Scale Integration or (SLSI) – between 10,000 and 100,000 transistors within a single package and perform computational operations such as microprocessor chips, micro-controllers, basic PICs and calculators.
Ultra-Large Scale Integration or (ULSI) – more than 1 million transistors –used in computers CPUs, GPUs, video processors, micro-controllers, FPGAs and complex PICs.
While the "ultra large scale" ULSI classification is less well used, another level of integration which represents the complexity of the Integrated Circuit is known as the System-on-Chip or (SOC) for short. Here the individual components such as the microprocessor, memory, peripherals, I/O logic etc., are all produced on a single piece of silicon and which represents a whole electronic system within one single chip, literally putting the word "integrated" into integrated circuit.
These complete integrated chips which can contain up to 100 million individual silicon-CMOS transistor gates within one single package are generally used in mobile phones, digital cameras, micro-controllers, PIC's and robotic type applications.
Merits and Demerits
Merits of Integrated Circuits
Miniature in size. As fabrication process is used for the integration of active and passive components on to a silicon chip, the IC becomes a lot smaller. When compared to a discrete circuit, it may be at least a thousand times smaller.
Due to small size, the weight of the IC also reduces, when compared to the discrete circuit.
To produce hundreds of discrete circuits on a PCB (Printed circuit board) for the same logic takes more time and increase the cost factor. But for the production of hundreds of ICs the cost of production will be very low and less time consuming.
The PCB (Printed circuit board) consisting soldered joints will be less reliable. This problem is omitted in IC's because of no soldered joints, with fewer interconnections, and thus highly reliable.
The small size of ICs causes lesser power consumption and lesser power loss.
In a discrete circuitry, if a single transistor becomes faulty, the whole circuit may fail to work. This transistor has to be desoldered and replaced. It is difficult to find out which component has failed. This problem can be omitted in an IC by replacing an entire IC as it is low in cost.
Increased operating speed because of absence of parasitic capacitance (is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other) effect.
As the IC's are produced in bulk the temperature coefficients and other parameters will be closely matching.
Improved functional performance as more complex circuits can be fabricated for achieving better characteristics.
All IC's are tested for operating ranges in very low and very high temperatures.
As all the components are fabricated very close to each other in an IC, they are highly suitable for small signal operation, as there won't be any stray electrical pickup.
As all the components are fabricated inside the chip, there will not be any external projections.
Demerits of Integrated Circuits
The power rating for most of the IC's does not exceed more than 10 watts. Thus it is not possible to manufacture high power IC's.
Some components like transformers and inductors cannot be integrated into an IC. They have to be connected externally to the semiconductor pins.
There is a large value of saturation resistance of transistors.
The IC will not work properly if wrongly handled or exposed to excessive heat.
It is difficult to achieve low temperature coefficient and fabricate an IC with low noise.
It is not possible to fabricate capacitors that exceed a value of 30pF. Thus, high value capacitors are to be connected externally to the IC.
There is a large value of saturation resistance of transistors
Some complex IC's maybe costly. If such integrated circuits are used roughly and become faulty, they have to be replaced by a new one. They cannot be repaired as the individual components inside the IC are too small.
Application of Integrated Circuits
Because of the above mentioned advantages IC's found numerous applications from cars (automotive controls), televisions, computers, microwaves, portable devices like laptops, MP3, play stations, cameras, cellular phones to ship equipment's, aero planes, space craft's. These are also used in switching telephone circuits and data processing. They also found applications in military equipment's. The most common application of IC is digital watch which tells hour, second, minute, day and month. Another common but important application is scientific calculator which can perform basic functions like addition, subtraction, multiplication and division as well as complex functions like square root, cube, permutations, combinations , trigonometric functions, etc.
IC's are of Linear, digital and mixed types. Linear IC's also known as analog Integrated circuits are used in:
Power amplifiers
Small-signal amplifiers
Operational amplifiers
Microwave amplifiers
RF and IF amplifiers
Voltage comparators
Multipliers
Radio receivers
Voltage regulators
Moore's Law
In 1965, Gordon Moore co-founder of the Intel corporation predicted that "The number of transistors and resistors on a single chip will double every 18 months" regarding the development of semiconductor gate technology. This is popularly known as Moore's law. When Gordon Moore made his famous comment way back in 1965 there were approximately only 60 individual transistor gates on a single silicon chip or die.
The world's first microprocessor in 1971 was the Intel 4004 that had a 4-bit data bus and contained about 2,300 transistors on a single chip, operating at about 600 kHz. Today, the Intel Corporation have placed a staggering 1.2 Billion individual transistor gates onto its new Quad-core i7-2700K Sandy Bridge 64-bit microprocessor chip operating at nearly 4GHz, and the on-chip transistor count is still rising, as newer faster microprocessors and micro-controllers are developed. The number of transistors per chip has risen exponentially and each year computers are becoming more powerful, yet cheaper than the year before.
It is intimated from current trends that the computers available in 2020 will operate at 40 GHz (40,000 MHz) and would be much smaller, more efficient and less expensive than present day computers.
Knowledge Cloud
The explosive growth in the semiconductor industry and computer technology is best expressed by a famous quote from Gordon Moore: "If the auto industry advanced as rapidly as the semiconductor industry, a Rolls Royce would get half a million miles per gallon, and it would be cheaper to throw it away than to park it".
Result
We had mainly discussed about the design, property and operation of various logic gates
Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arranged together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space.
Arrays of logic gates are found in digital integrated circuits (ICs). As IC technology advances, the required physical volume for each individual logic gate decreases and digital devices of the same or smaller size become capable of performing ever-more-complicated operations at ever-increasing speeds.
Bibliography
I would like to declare the array of references hereby and submit that I took help from following sources
Comprehensive Physics Practical
A textbook for Physics practical's ISBN 978-81-318-0384-4
Wikipedia.com
The Online Encyclopedia indexing world's best articles with genuine references
TCYonline.com
An online video tutorial and educational Centre
Meritnation.com
The leading educational site in India
http://projects.icbse.com/forums
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