COMPUTING INFORMATICS. Time: Three hours. Maximum Marks: Answer FIVE questions, taking ANY TWO from Group A,. ANY TWO from Group B and. Image Credits. Most of the images in the book, including the tiles on the cover, were generated by the author. Some of the tile images on the. Free Download Computing & Informatics study notes - Study Materials for Download Free Video Tutorials and Study soundofheaven.info for Material.
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Ċ, Compare and Contrast soundofheaven.info View Download, k, v. 1, Jul 7, , 6: 47 AM, jaimon j. Ċ, Computing and Informatics Class Notes for soundofheaven.info COMPUTING AND INFORMATICS. Time: Three hours. Maximum Marks: Answer FIVE questions~ taking ANY 1WO from Group A,. ANY 1WO [rom Group B. Computing and informatics. How to apply. Applicants should email their completed postgraduate application form to [email protected] by
Lastly, a very important reason for utilizing twos complement representation is that itwould be considerably more complex to create a subtraction circuit which would take - and give ie than it is to make one that returns The executable output by the linker may need another relocation pass when it is finallyloaded into memory just before execution. April 29, , Good Afternoon Everyone April 09, , Agroup of three-states driving a line with a suitable control circuit is basically equivalent toa multiplexer, which may be physically distributed over separate devices or plug-in cards. Commonly the output has a form suitable for processing by other programs e. This leads to a separate set of symbolswith inverted inputs and the opposite core symbol.
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Whether these glitches do occur depends on the physical nature of the implementation,and whether we need to worry about it depends on the application. The term is redundant in terms of the static logic of the system, but such redundant termsare often needed to assure race-free dynamic performance. When not to use K-mapsThe diagram becomes cluttered and hard to interpret if there are more than four variableson an axis.
This argues against the use of Karnaugh maps for expressions with more thansix variables. For such expressions, the Quine-McCluskey algorithm, also called themethod of prime implicants, should be used. This algorithm generally finds most of the optimal solutions quickly and easily, butselecting the final prime implicants after the essential ones are chosen may still requirea brute force approach to get the optimal combination though this is generally farsimpler than trying to brute force the entire problem.
Logic gateA logic gate performs a logical operation on one or more logic inputs and produces asingle logic output. The logic normally performed is Boolean logic and is mostcommonly found in digital circuits. Logic gates are primarily implemented electronicallyusing diodes or transistors, but can also be constructed using electromagnetic relays,fluidics, optical or even mechanical elements.
Logic levelsA Boolean logical input or output always takes one of two logic levels. These logic levelscan go by many names including: For consistency, the names 1 and 0 will be used below. Logic gatesA logic gate takes one or more logic-level inputs and produces a single logic-level output.
Because the output is also a logic level, an output of one logic gate can connect to theinput of one or more other logic gates. Two outputs cannot be connected together,however, as they may be attempting to produce different logic values. In electronic logicgates, this would cause a short circuit.
In electronic logic, a logic level is represented by a certain voltage which depends on thetype of electronic logic in use. Each logic gate requires power so that it can source andsink currents to achieve the correct output voltage.
In logic circuit diagrams the power isnot shown, but in a full electronic schematic, power connections are required. BackgroundThe simplest form of electronic logic is diode logic. To build a complete logicsystem, valves or transistors can be used.
The simplest family of logic gates using bipolartransistors is called resistor-transistor logic, or RTL. Unlike diode logic gates, RTL gatescan be cascaded indefinitely to produce more complex logic functions. These gates wereused in early integrated circuits. It was then discovered thatone transistor could do the job of two diodes in the space of one diode, so transistor-transistor logic, or TTL, was created.
In some types of chip, to reduce size and powerconsumption still further, the bipolar transistors were replaced with complementary field-effect transistors MOSFETs , resulting in complementary metal-oxide-semiconductor CMOS logic. For small-scale logic, designers now use prefabricated logic gates from families ofdevices such as the TTL series invented by Texas Instruments and the CMOS series invented by RCA, and their more recent descendants.
These devices usuallycontain transistors with multiple emitters, used to implement the AND function, whichare not available as separate components.
Increasingly, these fixed-function logic gatesare being replaced by programmable logic devices, which allow designers to pack a hugenumber of mixed logic gates into a single integrated circuit. The field-programmablenature of programmable logic devices such as FPGAs has removed the hard property ofhardware; it is now possible to change the logic design of a hardware system by Electronic logic gates differ significantly from their relay-and-switch equivalents.
Theyare much faster, consume much less power, and are much smaller all by a factor of amillion or more in most cases. Also, there is a fundamental structural difference. Theswitch circuit creates a continuous metallic path for current to flow in either direction between its input and its output.
The semiconductor logic gate, on the other hand, acts asa high-gain voltage amplifier, which sinks a tiny current at its input and produces a low-impedance voltage at its output. It is not possible for current to flow between the outputand the input of a semiconductor logic gate.
Another important advantage of standardised semiconductor logic gates, such as the and families, is that they are cascadable. This means that the output of one gate canbe wired to the inputs of one or several other gates, and so on ad infinitum, enabling theconstruction of circuits of arbitrary complexity without requiring the designer tounderstand the internal workings of the gates.
In practice, the output of one gate can only drive a finite number of inputs to other gates,a number called the fanout limit, but this limit is rarely reached in the newer CMOSlogic circuits, as compared to TTL circuits.
Also, there is always a delay, called thepropagation delay, from a change in input of a gate to the corresponding change in itsoutput. When gates are cascaded, the total propagation delay is approximately the sum ofthe individual delays, an effect which can become a problem in high-speed circuits.
Electronic logic levelsThe two logic levels in binary logic circuits are represented by two voltage ranges, "low"and "high". Each technology has its own requirements for the voltages used to representthe two logic levels, to ensure that the output of any device can reliably drive the input ofthe next device.
Usually, two non-overlapping voltage ranges, one for each level, aredefined. The difference between the high and low levels ranges from 0. They can be built from relays or transistors, or anyother technology that can create an inverter and a two-input AND or OR gate. For an input of 2 variables, there are 16 possible boolean algebra outputs.
These 16outputs are enumerated below with the appropriate function or logic gate for the 4possible combinations of A and B. Note that not all outputs have a corresponding For examples, see the series of CMOS logic chips or the series. The "distinctive shape" set, based ontraditional schematics, is used for simple drawings and is quicker to draw by hand. It issometimes unofficially described as "military", reflecting its origin if not its modernusage.
The "rectangular shape" set, based on IEC , has rectangular outlines forall types of gate, and allows representation of a much wider range of devices than ispossible with the traditional symbols.
The circle on the symbolis called a bubble, and is generally used in circuit diagrams to indicate an inverted inputor output. Additionally, Thisreflects the equivalency due to De Morgans law, but it also allows a diagram to be readmore easily, or a circuit to be mapped onto available physical gates in packages easily,since any circuit node that has bubbles at both ends can be replaced by a simple bubble-less connection and a suitable change of gate.
This is commonly seen inreal logic diagrams - thus the reader must not get into the habit of associating the shapesexclusively as OR or AND shapes, but also take into account the bubbles at both inputsand outputs in order to determine the "true" logic function indicated. The two input Exclusive-OR is true only when the two input values are different,false if they are equal, regardless of the value.
If there are more than two inputs, the gategenerates a true at its output if the number of trues at its input is odd .
In practice,these gates are built from combinations of simpler logic gates. The chip, containing four NANDs. This leads to a separate set of symbolswith inverted inputs and the opposite core symbol. These symbols can make circuitdiagrams for circuits using active low signals much clearer and help to show accidentalconnection of an active high output to an active low input or vice-versa. Storage of bitsRelated to the concept of logic gates and also built from them is the idea of storing a bitof information.
The gates discussed up to here cannot store a value: It is possible to make a storage element eitherthrough a capacitor which stores charge due to its physical properties or by feedback.
Connecting the output of a gate to the input causes it to be put through the logic again,and choosing the feedback correctly allows it to be preserved or modified through the useof other inputs. A set of gates arranged in this fashion is known as a "latch", and morecomplicated designs that utilise clocks signals that oscillate with a known period andchange only on the rising edge are called edge-triggered "flip-flops".
The combination ofmultiple flip-flops in parallel, to store a multiple-bit value, is known as a register.
These registers or capacitor-based circuits are known as computer memory. They vary inperformance, based on factors of speed, complexity, and reliability of storage, and manydifferent types of designs are used based on the application.
Three-state logic gates A tristate buffer can be thought of as a switch. If B is on, the switch is closed. If B is off,the switch is open. Main article: Tri-state bufferThree-state, or 3-state, logic gates have three states of the output: The high-impedance state plays no role in the logic, which remainsstrictly binary.
These devices are used on buses to allow multiple chips to send data.
Agroup of three-states driving a line with a suitable control circuit is basically equivalent toa multiplexer, which may be physically distributed over separate devices or plug-in cards.
Tri-state, a widely-used synonym of three-state, is a trademark of the NationalSemiconductor Corporation. MiscellaneousLogic circuits include such devices as multiplexers, registers, arithmetic logic units ALUs , and computer memory, all the way up through complete microprocessors whichcan contain more than a million gates. In reversible logic, Toffoli gates are used. History and developmentThe earliest logic gates were made mechanically.
Charles Babbage, around , devisedthe Analytical Engine. His logic gates relied on mechanical gearing to performoperations. Electromagnetic relays were later used for logic gates. In , AlmonStrowger patented a device containing a logic gate switch circuit U.
Patent Strowgers patent was not in widespread use until the s. Starting in , NikolaTesla filed for patents of devices containing logic gate circuits see List of Tesla patents. Eventually, vacuum tubes replaced relays for logic operations. Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switchingcircuits in Walther Bothe, inventor of the coincidence circuit, got part of the Nobel Prize in physics, for the first modern electronic AND gate in Active researchis taking place in molecular logic gates.
Adders electronics In electronics, an adder is a device which will perform the addition, S, of two numbers. Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers.
In caseswhere twos complement is being used to represent negative numbers it is trivial tomodify an adder into an adder-subtracter. For single bit adders, there are two general types. A half adder has two inputs, generallylabelled A and B, and two outputs, the sum S and carry output Co. Essentially the output of a half adder is thetwo-bit arithmetic sum of two one-bit numbers, with Co being the most significant ofthese two outputs.
The other type of single bit adder is the full adder which is like a half adder, but takes anadditional input carry Ci. A full adder can be constructed from two half adders byconnecting A and B to the input of one half adder, connecting the sum from that to aninput to the second adder, connecting Ci to the other input and or the two carry outputs.
The output of the full adder is the two-bitarithmetic sum of three one-bit numbers. The purpose of the carry input on the full-adder is to allow multiple full-adders to bechained together with the carry output of one adder connected to the carry input of thenext most significant adder. The carry is said to ripple down the carry lines of this sort ofadder, giving it the name ripple carry adder. Half adderHalf adder circuit diagramA half adder is a logical circuit that performs an addition operation on two binary digits.
The half adder produces a sum and a carry value which are both binary digits. Following is the logic table for a half adder: The full adder produces a sum and carry value, which are both binary digits. It can becombined with other full adders see below or work on its own. This is because the only discrepancy between OR andXOR gates occurs when both inputs are 1; for the adder shown here, one can check this isnever possible. Using only two types of gates is convenient if one desires to implementthe adder directly using common IC chips.
Ones complementAlternatively, a system known as ones complement can be used to represent negativenumbers. The ones complement form of a binary number is the bitwise NOT applied to it— the complement of its positive counterpart. Like sign-and-magnitude representation,ones complement has two representations of 0: To add two numbers represented in this system, one does a conventional binary addition,but it is then necessary to add any resulting carry back into the resulting sum.
The binary addition alone gives —not the correct answer! Only when the carryis added back in does the correct result appear. A remark on terminology: The system is referred to as "ones complement" because thenegation of x is formed by subtracting x from a long string of ones.
Twos complementarithmetic, on the other hand, forms the negation of x by subtracting x from a single largepower of two. It is also an operation of negation converting positive to negativenumbers or vice versa in computers which represent negative numbers using twoscomplement.
Its use is ubiquitous today because it doesnt require the addition andsubtraction circuitry to examine the signs of the operands to determine whether to add or Also, 0 has only a single representation, obviating the subtletiesassociated with negative zero which exists in ones complement.
The boundary between positive and negative numbers may theoretically be anywhere aslong as you check for it. For convenience, all numbers whose left-most bit is 1 areconsidered negative.
The largest number representable this way with 4 bits is 7 and the smallest number is To understand its usefulness for computers, consider the following. Adding 3 to -1 results in the seemingly-incorrect However, ignoring the 5th bit fromthe right , as we did when we counted backwards, gives us the actual answer, 2. Ignoring the 5th bit will work in all cases although you have to do the aforementionedoverflow checks when, eg, is added to Thus, a circuit designed for additioncan handle negative operands without also including a circuit capable of subtraction anda circuit which switches between the two based on the sign.
Moreover, by this methodan addition circuit can even perform subtractions if you convert the necessary operandinto the "counting-backwards" form.
The procedure for doing so is called taking the twos Lastly, a very important reason for utilizing twos complement representation is that itwould be considerably more complex to create a subtraction circuit which would take - and give ie than it is to make one that returns Doing theformer means you have to check the sign, then check if there will be a sign reversal, thenpossibly rearrange the numbers, and finally subtract.
Doing the latter means you simplysubtract, pretending theres an extra left-most bit hiding somewhere. If the sign bit is 0, the value is positive; if it is 1, the value is negative. To negate a twoscomplement number, invert all the bits then add 1 to the result. The absolute value of the mostnegative number cannot be represented with the same number of bits, because it is greaterthan the most positive number that twos complement number by exactly 1.
Using twos complement to represent negative numbers allows only one representation ofzero, and to have effective addition and subtraction while still having the most significantbit as the sign bit. Calculating twos complementIn finding the twos complement of a binary number, the bits are inverted, or "flipped", byusing the bitwise NOT operation; the value of 1 is then added to the resulting value. Bitoverflow is ignored, which is the normal case with zero. For example, beginning with the signed 8-bit binary representation of the decimal value5: To obtain thetwos complement, 1 is added to the result, giving: The most significant bit is 1, so the value is negative.
The twos complement of a negative number is the corresponding positive value. Also the twos complement ofthe most negative number representable e. This happens because the most negative numbers "positive counterpart" isoccupied by "0", which gets classed as a positive number in this argument.
Hence, thereappears to be an extra negative number. For example, to find the 4 bit representation of Which are very useful even for Section B Computer Science. You can access these free study materials and. Main Menu.
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