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Serial Addition Of Binary Numbers Computer Science

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The chief purpose of this undertaking is to plan a 1-bit consecutive adder, simulate it ‘s functionality and obtain a layout on Si, utilizing the 0.35Aµ procedure from AMS. The circuit designed shows a working consecutive adder clocking at ( 100MHz of nsecs ) with a hold of 0.56910nsec. The country of the layout is 99.30×16.35 Aµm2 in this engineering. The circuit performs an 8-bit add-on in 0.56910×8 nsesc. The circuit uses a standard 1-bit full adder and it has a feedback cringle utilizing a D-flip-flop in order to convey the carry spot to the following input value.

The concluding layout merchandise has 3-input tablets and 2-output tablets, with power and land tablets.

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Introduction

The procedure known as consecutive add-on of binary Numberss is good known in the computer science and units capable of executing such consecutive binary add-on normally consist a basic part of more complex calculation devices. In the past, such consecutive adders for binary Numberss have employed vacuity tubing circuitry for the most portion and have consequently been capable to the disadvantages that they are comparatively in big size, fragile in constellation and are capable to runing failures.

These factors raise serious inquiries of temperament of constituents and jobs of care. The present innovation serves to rid of the foregoing troubles and in kernel provides a consecutive adder construction capable of executing full add-on of binary Numberss. It is consequently an object of the present innovation to supply an improved consecutive adder for usage in calculating applications.

An object of the present innovation resides in the proviso of an improved consecutive adder for binary digital applications using magnetic amplifiers as constituents thereof. Another object of the present innovation is the proviso of the consecutive adder for binary Numberss which adders can be made in comparatively smaller sizes. A still farther object of the present innovation resides in the proviso of a calculation device comprising, in combination, a plurality of magnetic amplifiers and a plurality of gating devices so interrelated with one another that the mathematical procedure known as a consecutive spot add-on. The binary adder of the present innovation includes proviso for selective matching the input train pulsations to be added every bit good as carry pulsations produced by the device itself to the plurality of Gatess, and the Gatess are adapted by themselves to selectively go through signal pulsations required for the operation or suppression of the plurality of magnetic amplifiers mentioned supra. In digital systems, digital signal processing and control systems we can command it when we are able to number. Addition is the cardinal operation for all these systems.

The speed and truth are extremely influenced by the adders we are use for the circuit design. Adders are really of import constituents in the digital constituents because of their extended usage in digital operations such as generation, minus and division. The executing of binary operations inside a circuit would be greatly advanced by bettering the public presentation of the digital adders. The chief purpose of planing the spot consecutive adder is to

Perform one spot at a clip, utilizing the first spot operation consequences to act upon the processing of subsequent spots. It reduces the sum of hardware required as it passes all the spots in the same logic. However this attack needs 1/nth portion of hardware when compared to the n-bit analogue adders. As we are utilizing 1-bit alternatively of n-bits its construction reduces the signal routing and performs at high velocity as we are utilizing 1bit registry for the impermanent storage and one full adder instead than an n-bit adder. The decrease in the monetary value of the logic consequences in taking n clock rhythms to put to death this consecutive hardware, whereas parallel hardware executes in one clock rhythm. This spot construction trades with the spot stream hence this have been successfully used in many applications like digital systems, digital signal processing, control systems etc. It was highly popular in 2-5u engineering scope. The public presentation of a digital circuit block is gauged by analyzing its power dissipation, layout country and its operating velocity.

The chief purpose of this undertaking is to plan a 1-bit consecutive adder. Through this undertaking research we get the cognition of working behavior and public presentation of the 1-bit consecutive adder. Adders are the basic constituents for the designing of any digital circuit. Adders are really of import constituents in the digital constituents because of their extended usage in digital operations such as generation, minus and division. The executing of binary operations inside a circuit would be greatly advanced by bettering the public presentation of the digital adders. The chief purpose of planing the spot consecutive adder is to execute one spot at a clip, utilizing the first spot operation consequences to act upon the processing of subsequent spots. Here in this instance the one spot consecutive adder is designed by utilizing a flip-flop and full adder. .

This circuit has two phases full adder phase for the add-on of two spots that are entered serially and 2nd phase is flip-flop phase which temporarily shops the carry until the following phase is processed. The impermanent storage of the carry in the flip-flop depends on the clock pulsation. Its design rule shows how the two inputs entered serially. These two inputs will be added by the full adder along with the carry which was temporarily stored by the flip-flop and gives us the amount end product and carry end product. The normal 1-bit consecutive adder uses the XOR Gatess from the available nucleus library. But in this XOR gate there is an OR gate which normally reduces the public presentation of the XOR gate. Hence the circuit has been modified by planing the XOR gate by utilizing the NAND Gatess.

What we would wish to make now is happen the easy manner to utilize the bomber tractor along with the consecutive adder circuit. By utilizing this sub tractor we can deduct the lower spot value from higher value.

This binary bomber tractor has been added to one of the input which we are believing to deduct the value. In our consecutive adder circuit the bomber tractor is attached to the 1 of the inputs Y which is normally a XOR gate. This consequences in the minus of Y value from higher spot values.

Background

2.1 Addition:

Addition is a procedure of adding spots. Binary add-on means adding binary spots 0 ‘s and 1 ‘s and sum and carry generated in binary farm in any signal processing. Now lets see the 4-bit add-on illustration,

As shown above A and B spots added giving Sum out by ruffling the carry at each phase and C4 as concluding carry obtained.

2.2 Subtraction:

Subtraction is a procedure of adding a positive spot to the negative spot. Negative of a spot means 2 ‘s compliment of it. This is nil but adding 1 spot to LSB of its 1 ‘s compliment. 1 ‘s compliment is nil but change by reversaling the logic of the spots. Now lets see the 4-bit minus illustration,

The above minus technique dedicated to the deducting a smaller double star from a larger binary. If it changes it merely followed by few more stairss as alteration mark spot ( MSB ) to zero, so alter it to its 2 ‘s compliment as before procedure.

Metal-Oxide-Silicon Field-Effect transistors ( Mosfet ‘s )

NMOS Transistor

Here is a diagram of nmos transistor

The beginning and drain are connected to the two blobs of n-type semiconducting material stuff. The

gate is on top, separated ( and electrically insulated ) from the remainder of the transistor by a thin bed of Si dioxide ( same stuff as sand — does n’t carry on at all ) . The beginning and drain are separated by p-type stuff. This forms two rectifying tubes pointed in opposite waies ( when you have n-type following to p-type stuff, you get a rectifying tube ) , so no current can flux between the beginning and drain. When a high electromotive force ( higher than the voltage degree of the beginning, which is defined as the lower electromotive force of the two terminal terminuss ) is applied to the gate, it puts a positive charge on the gate. This attracts a negative charge in the part underneath the gate ( opposite charges attract ) , organizing a “ channel of negative charge bearers ” or an n-channel between the beginning and drain, which allows current to flux. So the nMOS transistor behaviors when the gate is raised to the high electromotive force degree, which we consider to be the logic degree for 1 ( true ) .

PMOS TRANSISTOR

The pMOS transistor is the dual of the nMOS transistor. You can look at the same diagram, but swap every N and P, and every + and – . Now, when the electromotive force at the gate is lower than the beginning ( the higher electromotive force of the two terminal terminuss for a pMOS transistor ) , we end up with a negative charge on the gate, which induces a positive channel underneath the gate, which allows current to flux. So the pMOS transistor conducts when the gate electromotive force is low, which we consider to be the logic degree for 0 ( false ) .

The full names of what is being described are “ enhancement manner n-channel or p-channel metal-oxide semiconducting material field consequence transistors ( MOSFET ) ” . “ Enhancement manner ” refers to the fact that we have to make the channel by using electromotive force to the gate. ( There are besides “ depletion manner ” transistors that have a channel built in to get down with. ) “ Field consequence ” refers to the fact that we ‘re utilizing the electric field from the charge at the gate to command things. “ Metal-oxide semiconducting material ” refers to the fact that we ‘re utilizing an oxide to insulate the gate from the remainder of the transistor. The two types of transistors are named for the channel: nMOS has an n-channel ; pMOS has a p-channel.

Cmos

There are many ways to do logic Gatess ( non to be confused with the gate of the transistor ) out of transistors. What I ‘m demoing here is the dominant manner that Gatess are done in digital electronics today, but there are many fluctuations out at that place. This is called “ inactive CMOS logic ” . “ Inactive ” refers to the fact that there are non redstem storksbills involved. “ CMOS ” stands for “ complementary metal-oxide semiconducting material ” . The “ complementary ” means we have both nMOS and pMOS transistors.

The intuition behind this design manner is simple. First, you do n’t desire to hold nMOS and pMOS transistors mixed up near to each other, because they need to be created on different types of substrate. So the natural manner is to hold a clump of nMOS transistors together that draw the end product one manner for certain input values, and a clump of pMOS transistors together that draw the end product the other way for the other input values. It turns out to work better to hold the nMOS transistors pull down toward logic 0 and the pMOS transistors pull up toward logic 1. This is both for electrical grounds ( nMOS conducts 0 better ; pMOS conducts 1 better ) and besides to do it easy to acquire inverting Gatess.

The undermentioned diagram demoing how to do an inverter ( a NOT gate ) :

Such that we developed CMOS Technology by combination of Pull-up web of PMOS Transistors and Pull-down web of NMOS Transistors. All the CMOS Gatess are constructed utilizing as shown below.

CMOS Constructed by, PMOS transistors in Pull-up web phase and NMOS transistors in Pull-down web phase.

End product traveling 1- & gt ; 0

A The Pull-down NMOS transistors discharges the end product electrical capacity.

End product traveling 0- & gt ; 1

The end product electrical capacity is charged through Pull-up PMOS transistors.

MOSFETs passage provinces in CMOS Transistor:

CMOS logic is better logic than PMOS and NMOS executions separately. Because PMOS transistors are great at conveying a logic 0 to1 electromotive force without signal loss, NMOS transistors are great at conveying a logic 1 to 0 electromotive force.

4.2 NAND Gate:

Constructed by, As shown below PMOS transistors in analogue and NMOS transistors in series.

End product traveling 1- & gt ; 0

A The series NMOS transistors discharges the end product electrical capacity.

End product traveling 0- & gt ; 1

The end product electrical capacity is charged through parallel PMOS transistors.

Circuit diagram of NAND Gate:

Logic symbol of NAND Gate:

Truth tabular array of NAND Gate:

A

Bacillus

End product

0

0

1

0

1

1

1

0

1

1

1

0

4.3 NOR Gate:

Constructed by, As shown NMOS transistors in analogue and PMOS transistors in series.

End product traveling 1- & gt ; 0

The parallel NMOS transistors discharges the end product electrical capacity.

End product traveling 0- & gt ; 1

The end product electrical capacity is charged through series PMOS transistors.

Circuit diagram of NOR Gate:

Logic symbol of NOR Gate:

Truth tabular array of NOR Gate:

XOR Gate:

XOR is besides called Exclusive OR gate or EOR gate. This is a digital logic gate, which is used to show the map of Exclusive Disjunction. Its behaviour is similar to or gate with sole status. Usually it is a 2-1 input end product IC severally.

An end product HIGH ( 1 ) will be resulted if one, and merely one of its 2 inputs is HIGH ( 1 ) . Consequence of end product LOW ( 0 ) both the inputs should be same either low or high. We can state EX-OR gate as “ One or another, but non both ” .

XOR gate is used to develop a binary add-on. It gives the amount for given input spots. As shown above xor of 2 spots A and B gives its amount.

A xor B = A.B ‘ + A’.B

Circuit diagram of xor gate:

BASIC ADDER UNIT

Addition of two binary Numberss is the most basic arithmetic operation i.e. two spots. A combinable circuit which can add merely two spots is known as half adder. A full adder is one that adds more than two spots i.e. three spots. Full adder uses two adders in its execution. In this survey full adder is the basic add-on employed in all adders.

HALF ADDER

One-half is a basic adder circuit that can execute add-on of two spots and gives the end product of amount and carry. Half adder circuit uses an Exclusive-OR and AND Gatess for amount and carry end products. XOR gate gives the amount end product and carry end product is given by the AND gate. Ten and Y are inputs S is sum and C0 is carry.

S = X.Y ‘ + X’.Y = X i?… Y

C = X.YIts conventional representation is as shown in the figure.

The truth tabular array of half adder is as shown below.

Ten

Yttrium

Sum

C0

0

0

0

0

0

1

1

0

1

0

1

0

1

1

0

1

K-MAPPING of half adder circuit is given as shown below.

Sum, S = X i?… Y

Carry, C0 = X.Y

FULL-ADDER

Full adder can be formed by uniting two half-adder circuits followed by the OR gate. It can execute the add-on of three spots along with the carry input given as end product from the old 1. The difference between half adder and full adder is that half adder can non number more than two spots and can non add the carry input which will be possible in full adder circuit. In this circuit, amount end product is given by the XOR gate and the carry end product is given by the AND gate followed by the OR gate. The block diagram of full adder circuit is as shown below.

FULLADDER

Sum S = X i?… Y i?… CI = ( X i?… Y ) i?… CI

Carry C0 = ( X.Y ) + ( X i?… Y ) .CI

As shown in the above figure X, Y and CI are the adder inputs.

The truth tabular array of the above circuit is as shown below.

Ten

Yttrium

Curie

Sum

C0

0

0

0

0

0

0

0

1

1

0

0

1

0

1

0

0

1

1

0

1

1

0

0

1

0

1

0

1

0

1

1

1

0

0

1

1

1

1

1

1

By utilizing K-mapping we will acquire SUM and CARRY as follows

Sum S,

Carry c0,

D – FLIP FLOP

D- Flip floating-point operation is used in many applications. RS somersault floating-point operation is the cardinal edifice block for the D- somersault floating-point operation. It has merely one information input. That is connected to the input S of RS somersault floating-point operation where as D is reciprocally connected to the R input.. D- Flip floating-point operation is besides holding 2nd input for keeping the information which is known as Enable, merely represented as EN. The enable input is AND-ed with the D- Flip floating-point operation. D- Flip floating-point operation holds the informations harmonizing to the clock pulsation.

It is constructed by utilizing AND Gatess and NOR Gatess as shown in the below figure. D and EN are the inputs and Q and Q ‘ are end products. The block diagram of the D-flip floating-point operation is as shown below.

D- Flip floating-point operation Acts of the Apostless as impermanent informations storage in the 1- spot consecutive adder. Its storage capacity depends on the figure of phases. The storage capacity of the D- somersault floating-point operation in this consecutive adder is the entire figure spots ( 0 and 1 ) of digital informations it can retain.

Its truth tabular array is a shown below.

Calciferol

En

Q

QN

0

Falling border

0

Ten

0

Rising border

0

1

1

Falling border

Qprev

Ten

1

Rising border

1

0

.

The moving ridge signifiers are attached in the consequences.

Chapter 2

SERIAL ADDER

The procedure known as consecutive add-on of binary Numberss is good known in the digital and units capable of executing such consecutive binary add-on normally consist a basic part of more complex calculation devices. In the past, such consecutive adders for binary Numberss have employed vacuity tubing circuitry for the most portion and have consequently been capable to the disadvantages that they are comparatively in big size, fragile in constellation and are capable to runing failures. These factors raise serious inquiries of temperament of constituents and jobs of care. The present innovation serves to rid of the foregoing troubles and in kernel provides a consecutive adder construction capable of executing full add-on of binary Numberss. It is consequently an object of the present innovation to supply an improved consecutive adder for usage in digital systems.

The chief purpose of planing the spot consecutive adder is to execute one spot at a clip, utilizing the first spot operation consequences to act upon the processing of subsequent spots. Here in this instance the one spot consecutive adder is designed by utilizing a D-flip floating-point operation and full adder. .

This circuit has two phases full adder phase for the add-on of two spots that are entered serially and 2nd phase is D-flip floating-point operation phase which temporarily shops the carry until the following phase is processed. The impermanent storage of the carry in the D-flip floating-point operation depends on the clock pulsation. Its design rule shows how the two inputs entered serially. These two inputs will be added by the full adder along with the carry which was temporarily stored by the flip-flop and gives us the amount end product and carry end product. This is a practical consecutive adder that is used to add a

watercourse of two spots add-on. First it takes the Least Significant Bits ( LSB ) in add-on. Its block diagram is as shown in the figure.

As shown in the above figure the inputs Xi and Yi are serially entered into the full adder along with the impermanent carry from the D-flip floating-point operation i.e. Ci and gives the carry end product Ci+1 and amount end product Si.

Hence consecutive adder is simple and because of feedback looping spot holds are expected. It can be constructed with really low cost and it is the perfect adder at low velocity operations.

Si = Ci i?… Yi i?… Xi

Ci + 1 = Yi. Ci + Xi. Ci + Xi. Yi = Ci. ( Eleven i?… Yi ) + Xi. Lolo

The above equations represent the Sum and Carry outputs utilizing Boolean equations.

The building of 1-bit consecutive adder is as shown in the figure. As shown in the figure the inputs X and Y are serially entered through the full adder along with the carry input which was the feedback end product of full adder. In this circuit, amount end product is given by the XOR gate and the carry end product is given by the AND gate followed by the OR gate. D- Flip floating-point operation used in this circuit acts as a impermanent storage of carry.

Truth Table

Ten

Yttrium

C00

Second

Carbon monoxide

0

0

1

1

0

0

1

1

0

1

1

0

1

0

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

1

1

1

1

0

1

1

1

0

0

1

This full design procedure and simulation can be done by utilizing the wise man artworks version 2005 package.

Chapter 3

Nand gate design of consecutive adder:

4.4 NAND gate is BETTER THAN NOR.

As PMOS in analogue and NMOS in series the attendant passage hold at NAND gate is lesser than hold of NOR gate architecture.

To do PMOS as fast as NMOS we need enlarge channel and P-regions, but that leads to big Si layout, and more cost and power wastage. So At same velocity NOR is ever larger than NAND. So it makes NAND more efficient than NOR. W/L ratio of NAND gate is smaller than NOR gate.

If inputs for Gatess are more so, NAND will be really faster than NOR.

So we use sop execution instead than Po.

XOR GATE USING NAND GATES

In PMOS holes flow really easy when compared to the negatrons in the NMOS engineering. Hence NMOS is faster than PMOS transistor. In NOR gate PMOS transistors are connected in series and in NAND gate PMOS transistors are connected in parallel hence NAND gate is faster than the NOR gate. Now sing another instance to do this one spot consecutive adder small spot faster compared to the normal one spot consecutive adder the XOR gate is constructed by utilizing the NAND Gatess which works faster than the normal XOR gate. The ground for building this XOR gate is that in the nucleus library we are utilizing to plan the full circuit XOR gate internally contains an OR gate which normally reduces the public presentation of XOR gate. Its circuit diagram is as follows.

Ten

Yttrium

OUT

0

0

0

0

1

1

1

0

1

1

1

0Its truth tabular array is as shown below.

D- Flip Flop utilizing nand Gatess:

D Flip-Flop is the most popular Flip-Flop. As its end product takes the value of informations ( D ) input when the positive border of clock pulsation. D Flip-flop can be interpreted as a crude memory cell.

D Reversals are fundamentally used as Shift registries. As a D Flip-flop can bring forth a end product signal with a clip period hold of given clock pulsation for an input signal i.e. , one spot shifted right to the input given signal. The rule of D reversal is it captures the signal at the minute the clock goes high, and subsequent alterations of the information lines do non act upon Q until the rise of following clock border. therefore it works as a border triping manner at clock signal rise.

D Flip-flop is constructed utilizing NAND Gatess as shown above, where D and CLOCK are the inputs and Q and QN are the out puts.

Ten

Yttrium

C00

Second

Carbon monoxide

0

0

1

1

0

0

1

1

0

1

1

0

1

0

1

1

1

0

0

1

0

0

1

1

0

0

1

1

0

1

1

1

1

0

1

1

1

0

0

1

Chapter 3

SUBSTRACTOR

Up to now we have seen how simple logic Gatess perform binary add-on. It is merely logical to presume that the same circuit can besides execute the binary minus. If we look at the possibilities involved in deducting one spot figure from another, we can rapidly see that three of the four possible combinations are easy and consecutive forward. The 4th one involves a spot more.

0 – 0 = 0

1 – 0 = 1

1 – 1 = 0

0 – 1 = 1, with a borrow spot.

That borrow spot is merely like a borrow in denary minus: it subtracts from the following higher order of magnitude in the overall figure. The truth tabular array of this sub tractor circuit looks like as shown below.

This is an interesting consequence. The difference, X-Y, is still an exclusive-OR map, merely as the amount for add-on. The borrow is still an AND map, but is X’Y alternatively of XY.

Adder/Subtractor logic developed utilizing NAND gate ( lower from higher ) :

Addition is adding positive two spots. Subtraction is nil but an add-on where we add one positive spot to another negative spot. That means the 2nd spot will be the positive figure with negative mutual opposition. We can change over positive binary to negative binary by its 2 ‘s compliment.

2 ‘s compliment is nil but adding 1 spot to the LSB side of 1 ‘s compliment.

1 ‘s compliment is in any binary codification if we swap spots by 1 spot with 0 spot and 0 spot with 1 spot. That is flip the binary codification image.

1 ‘s compliment can be generated utilizing XOR logic. when we give one pin of XOR gate dedicated to positive as logic 1, and other pin connected to the input binary spot, so end product of EXOR will be swapped by 1 ‘s with 0 ‘s and 0 ‘s with 1 ‘s. At the same clip other advantage is if the dedicated input pin is given logic, so out put will be same as input binary codification.

Such that in that whole circuit by altering selective pin as 0 logic it works as adder and by altering selective pin as 1 logic it works as subtractor ‘s 1 ‘s compliment input.

Let we see A + B it is a simple add-on,

For

A – Bacillus = A + ( – Bacillus ) = A + ( B 1 ‘s compliment + 1 )

= A + B 1 ‘s compliment + 1

As shown above to happen A – Bacillus we give the full adder inputs as a to A, B to B 1 ‘s compliment and eventually c in every bit positive logic 1. Therefore adding 2 spots of A And B in this manner we get A- B.

Above developed subtractor circuit subtracts lower value spot from higher value spot so in 0-1 status its non valid.

ADDER TRUTH TABLE WHEN EN =0

En

Ten

Yttrium

C00

Second

Carbon monoxide

0

0

0

1

1

0

0

0

1

1

0

1

0

1

0

1

0

1

0

1

1

0

0

1

SUBSTRACTOR TRUTH TABLE WHEN EN =1

En

Ten

Yttrium

C00

Second

Carbon monoxide

1

0

0

1

0

0

1

0

1

1

Ten

Ten

1

1

0

1

1

0

1

1

1

1

0

1

Execution

The full procedure of planing and layout of the 1-bit consecutive adder circuit is done by utilizing the wise man artworks version 2005. The needed logic Gatess and somersault floating-point operation has been taken from the nucleus library. Once taking all the needed constituents from the nucleus library wiring has been done once more utilizing the nucleus library. One wiring has been done the sheet has been saved and done the conventional cheque. Once the conventional cheque has been done successfully so the position point has been created. Once position point has been done successfully the circuit has been run for simulation. After holding done the simulation successfully the end product wave forms has been checked. This end product waveforms consequences the working of the full circuit design. Once we got the end products precisely what we are looking for we so go for layout design. This layout design is besides done by utilizing the nucleus library which is known as Si layout. After completing the layout we will look into the flood of the IC which we will acquire at the terminal of the procedure.

Decision:

In the undertaking of One Bit Consecutive Adder we obtained the cognition about the functionality of adders and developed a fast adder utilizing NAND gate Logic. We even obtain the cognition about CMOS engineering and functionality of IC Gates. As we developed utilizing NAND gate logic execution the architecture of IC will be much faster and efficient.

From the obtained consequences of Consecutive adder wave forms and IC design by comparing the theoretical and practical values are verified each other. Such that I can reason the developed IC ‘s are good working in any application epoch with a hold of 0.5921ns.

Finally I concluded that a 1-bit Consecutive adder is developed in Conventional, NAND gate architecture and Adder/Subtractor architectures IC design and layout of IC design obtained and verified without mistakes. Functional and Electric Characteristics studied similar to CMOS engineering as they developed.

Cite this Serial Addition Of Binary Numbers Computer Science

Serial Addition Of Binary Numbers Computer Science. (2016, Nov 27). Retrieved from https://graduateway.com/serial-addition-of-binary-numbers-computer-science-essay/

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