Draw a Timing Diagram for the Circuit

Timing Diagram

Unified Modeling Linguistic communication

Janis Osis , Uldis Donins , in Topological UML Modeling, 2017

1.2.2.seven Timing Diagram

Timing diagram is used to show interactions when a chief purpose of the diagram is to reason about time; it focuses on conditions changing within and amongst lifelines along a linear time axis. Timing diagram is a special course of a sequence diagram. The well-nigh notable graphical difference between timing diagram and sequence diagram is that time dimension in timing diagram is horizontal and the time is increasing from left to the right and the lifelines are shown in separate compartments arranged vertically. The timing diagram is available since UML version 2.0 and includes elements such every bit message, lifeline, timeline, and object or role.

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Fundamentals

John Crowe , Barrie Hayes-Gill , in Introduction to Digital Electronics, 1998

Instance ane.21

Given the timing diagram in Fig. ane.12, write out the truth table for the circuit responsible for information technology, the Boolean equation describing its operation and draw the bodily excursion.

Fig. i.12. Timing diagram for Example ane.21

Solution

From the timing diagram we can determine the values of the output, Y, for given input values of A, B and C. These values tin exist used to produce the truth table in Fig. 1.13 together with the circuit.

Fig. ane.13. Truth table and circuit produced from the timing diagram in Fig. 1.12 (Instance 1.21)

Then, from the truth tabular array we can run into that the output is ane if either A = 1, irrespective of the values of B and C (i.e. the bottom four rows of the truth table), OR if ((B = 0) AND (C = 0)). So we can deduce that $Y=A+\left(\overline{B}\cdot \overline{C}\right)$ . (We will look at more than rigorous ways of obtaining such information in subsequently capacity.) Note that the truth table has been written in binary ordered fashion, as is usual, even though the values are not read off from the waveform in this order.

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Calculating Platforms

Marilyn Wolf , in Computers as Components (Third Edition), 2012

Draw a timing diagram with the following signals (where [ t ₁,t ₂] is the time interval starting at t ₁ and catastrophe at t ₂):

a.

signal A is stable [0,ten], changing [10,15], stable [15,30]

b.

betoken B is 1 [0,5], falling [5,7], 0 [7,20], changing [20,30]

c.

bespeak C is changing [0,ten], 0 [10,15], rising [15,18], 1 [18,25], changing [25,xxx]

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Enforcing Modularity with Clients and Services

Jerome H. Saltzer , Chiliad. Frans Kaashoek , in Principles of Computer System Design, 2009

4.1.two Client/Service Organization

One skilful style to enforce modularity is to limit the interactions amid modules to explicit messages. It is convenient to impose some structure on this system by identifying participants in a communication as clients or services.

Effigy iv.3 shows a common interaction between client and service. The client is the module that initiates a request: it builds a message containing all the information necessary for the service to carry out its task and sends it to a service. The service is the module that responds: it extracts the arguments from the request message, executes the requested operations, builds a response bulletin, sends the response message back to the client, and waits for the next request. The customer extracts the results from the response message. For convenience, the message from the customer to the service is chosen the request, and the message is called the response or respond.

Figure iv.three. Communication between client and service.

Figure iv.3 shows one common mode in which a customer and a service interact: a request is always followed past a response. Since a customer and a service can collaborate using many other sequences of messages, designers often correspond the interactions using message timing diagrams (come across Sidebar four.two). Figure four.3 is an case of a unproblematic timing diagram.

Sidebar 4.ii

Representation

Timing Diagrams

A timing diagram is a convenient representation of the interaction between modules. When the system is organized in a customer/service manner, this presentation is particularly convenient, because the interactions betwixt modules are limited to letters. In a timing diagram, the lifetime of a module is represented by a vertical line, with time increasing downwardly the vertical axis. The following example illustrates the employ of a timing diagram for a sewage pumping system. The label at the top of a timeline names the module (pump controller, sensor service, and pump service). The physical separation between modules is represented horizontally. Since it takes time for a message to go from 1 indicate to some other, a bulletin going from the pump controller to the pump service is represented past an arrow that slopes downward to the right.

The modules perform deportment, and send and receive messages. The labels next to the time indicate deportment taken by the module at a certain time. Modules tin have actions at the same time, for instance, if they are running on different processors.

The arrows signal messages. The start of the pointer indicates the time the bulletin is sent by the sending module, and the indicate of an arrow indicates the time the message is received at the destination module. The content of a bulletin is described by the label associated with the pointer. In some examples, messages tin be reordered (arrows cross) or lost (arrows terminate midflight before reaching a module).

The elementary timing diagram shown in this sidebar describes the interaction between a pump controller and two services: a sensor service and a pump service. There is a request containing the bulletin "measure tank level" from the customer to the sensor service, and a response reports the level read by the sensor. At that place is a third message, "get-go pump", which the client sends to the pump service when the level is too high. The second message has no response. The diagram shows three actions: reading the sensor, deciding whether the pump must be started, and starting the pump. Figure 7.7 [on-line] shows a timing diagram with a lost bulletin, and Effigy 7.9 [on-line] shows one with a delayed bulletin.

Conceptually, the client/service model runs customer and services on separate computers, continued by a wire. This implementation also allows customer and service to exist separated geographically (which tin can be good because it reduces the risk that both neglect owing to a common fault such as a power outage) and restricts all interactions to well-defined messages sent across a wire.

The disadvantage of this implementation is that it requires ane computer per module, which may be costly in equipment. It may also have a performance cost considering it may take a substantial corporeality of fourth dimension to send a message from one computer to some other, in detail if the computers are far abroad geographically. In some cases these disadvantages are unimportant; for cases in which it does matter, Chapter five will explain how to implement the client/service model inside a single reckoner using an operating system. For the residue of this affiliate we volition assume that the customer and the service each have their ain computer.

To attain high availability or handle large workloads, a designer may cull to implement a service using multiple computers. For instance, a file service might use several computers to achieve a loftier degree of fault tolerance; if ane reckoner fails, another one can take over its role. An case of a service running on a single reckoner is called a server.

To make the client/service model more concrete, let's rearrange our measure program into a simple client/service organization (see Figure four.4). To go a time from the service, the client procedure builds a request bulletin that names the service and specifies the requested performance and arguments (lines 2 and half-dozen). The requested operation and arguments must exist converted to a representation that is suitable for manual. For example, the customer computer may exist a big-endian calculator (see Sidebar 4.3), while the service reckoner may be a little-endian computer. Thus, the customer must convert arguments into a canonical representation so that the service can interpret the arguments.

Figure 4.4. Case client/service awarding: fourth dimension service.

Sidebar four.3

Representation

Big-Endian or Little-Endian?

2 common conventions be for numbering $.25 within a byte, bytes within a discussion, words within a page, and the similar. I convention is chosen big-endian, and the other lilliputian-endian *. In large-endian the most pregnant bit, byte, or word is numbered 0, and the significance of bits decreases every bit the address of the chip increases:

Words	0				ane
Bytes	0	1	…	seven	0	1	…	seven
$.25	202anetwo2…			…263	two021two2…			…ii63

In big-endian the hex number ABCD_hex would be stored in retention, so that if you read from retentivity in increasing memory address society, y'all would encounter A-B-C-D. The cord "john" would be stored in memory as john.

In little-endian, the other convention, the to the lowest degree significant bit, byte, or word is numbered 0, and the significance of bits increases equally the address of the scrap increases:

Words	n				n − i
Bytes	7	…	1	0	vii	…	1	0
Bits	263…			…222120	263…			…222120

In picayune-endian, the hex number ABCD_hex would be stored in retentiveness, so that if yous read from retentiveness in increasing retentiveness address order, you lot see D-C-B-A. The string "john" would still be stored in retentivity every bit john. Thus, code that extracts bytes from graphic symbol strings transports between architectures, but code that extracts bytes from integers does non send.

Some processors, such as the Intel x86 family, use the little-endian convention, simply others, such as the IBM PowerPC family unit, use the big-endian convention. As Danny Cohen pointed out in a frequently cited article "On holy wars and a plea for peace" [Suggestions for Further Reading 7.two.4], it doesn't matter which convention a designer uses as long as it is the aforementioned one when communicating between two processors. The processors must agree on the convention for numbering the bits sent over the wire (that is, send the about pregnant chip kickoff or send the to the lowest degree meaning fleck outset). Thus, if the communication standard is big-endian (as it is in the Internet protocols), then a customer running on a little-endian processor must marshal data in big-endian social club. This book uses the big-endian convention.

This volume as well follows the convention that flake numbers start with cypher. This choice is independent of the big-endian convention; we could accept chosen to apply one instead, as some processors do.

This conversion is called marshaling. We use the notation {a, b} to denote a marshaled bulletin that contains the fields a and b. Marshaling typically involves converting an object into an array of bytes with enough annotation so that the unmarshal procedure tin convert information technology back into a language object. In this example, nosotros show the marshal and unmarshal operations explicitly (e.m., the procedure calls starting with catechumen), but in many futurity examples these operations volition be implicit to avoid clutter.

After constructing the request, the client sends it (2 and 6), waits for a response (line 3 and 7), and unmarshals the time (4 and 8).

The service procedure waits for a asking (line 12) and unmarshals the request (lines 13 and 14). Then, information technology checks the asking (line 15), processes information technology (lines 16 through 19), and sends back a marshaled response (line xx).

The customer/service organization non merely separates functions (abstraction), information technology likewise enforces that separation (enforced modularity). Compared to modularity using procedure calls, the client/service organization has the following advantages:

■

The client and service don't rely on shared state other than the messages. Therefore, errors can propagate from the client to the service, and vice versa, in only ane way. If the services (as in line 15) and the clients bank check the validity of the asking and response messages, and then they tin control the ways in which errors propagate. Since the client and service don't rely on global, shared information structures such as a stack, a failure in the client cannot directly decadent data in the service, and vice versa.

■

The transaction betwixt a client and a service is an arm's-length transaction. Many errors cannot propagate from one to the other. For instance, the client does not have to trust the service to return to the appropriate return address, every bit it does using procedure calls. As another example, arguments and results are marshaled and unmarshaled, allowing the client and service to check them.

■

The client can protect itself fifty-fifty against a service that fails to return because the client can put an upper limit on the time it waits for a response. As a result, if the service gets into an infinite loop, or fails and forgets virtually the request, the client tin can detect that something has gone wrong and undertake some recovery procedure, such equally trying a different service. On the other hand, setting timers can create new problems considering it can be hard to predict how long a wait is reasonable. The problem of setting timers for service requests is discussed in detail in Section 7.v.2 [on-line]. In our example, the client isn't defensive against service errors; providing these defenses will make the program slightly more than complex only can assist eliminate fate sharing.

■

Client/Service organization encourages explicit, well-defined interfaces. Because the client and service can collaborate only through letters, the messages that a service is willing to receive provide a well-defined interface for the service. If those messages are well specified and their specification is public, a developer tin implement a new client or service without having to understand the internals of some other customer or the service. Clear specification allows clients and service to be implemented past dissimilar programmers, and tin encourage competition for the best implementation.

Separating country and passing well-defined messages reduce the number of potential interactions, which helps contain errors. If the programmer who developed the service introduces an error and the service has a disaster, the client has only a controlled problem. The client'south simply concern is that the service didn't deliver its part of the contract; apart from this wrong or missing value, the customer has no business organization for its ain integrity. The client is less vulnerable from faults in the service, or, in slightly unlike words, fate sharing tin can be reduced. Clients can exist mostly contained of service failures, and vice versa.

The customer/service system is an example of a sweeping simplification because the model eliminates all forms of interaction other than letters. Past separating the client and the service from each other using message passing, we have created a firewall betwixt them. As with firewalls in buildings, if there is a fire in the service, it will exist contained in the service, and, assuming the client tin can check for flames in the response, it will non propagate to the client. If the client and service are well implemented, so the only style to go from the client to the service and dorsum is through well-defined messages.

Of course, the client/service organization is not a panacea. If a service returns an wrong effect, then the client has a problem. This customer can bank check for certain issues (e.1000., syntactic ones) but not all semantic errors. The client/service organization reduces fate sharing but doesn't eliminate it. The degree to which the customer/service system reduces fate sharing is also dependent on the interface betwixt the client and service. As an extreme example, if the client/service interface has a message that allows a client to write any value to any address in the service's address space, then it is piece of cake for errors to propagate from the client to the service. It is the job of the organisation designer to define a skilful interface betwixt client and service so that errors cannot propagate easily. In this chapter and afterwards chapters, nosotros will see examples of adept message interfaces.

For ease of understanding, most of the examples in this chapter exhibit modules consisting of a single process. In the real world, designers ordinarily apply the customer/service organization betwixt software modules of a larger granularity. The trend toward larger granularity arises because the procedures within an awarding typically need to be tightly coupled for some practical reason, such equally they all operate on the same shared data construction. Placing every procedure in a dissever client or service would arrive difficult to manipulate the shared information. The designer thus faces a trade-off between ease of accessing the data that a module needs and ease of fault propagation within a module. A designer makes this trade-off by deciding which data and procedures to group into a coherent unit of measurement with the data that they dispense. That coherent unit so becomes a separate service, and errors are independent within the unit. The customer and service units are often complete awarding programs or similarly large subsystems.

Another factor in whether or not to utilize the client/service organization to ii modules is the plan for recovery when the service module fails. For case, in a simulator program that uses a role to compute the square root of its argument, it makes little sense to put that function into a split service because it doesn't reduce fate sharing. If the square-root office fails, the simulator program cannot proceed. Furthermore, a practiced recovery plan is for the programmer to reimplement the role correctly, as opposed to running two square-root servers, and declining over to the 2nd one when the first 1 fails. In this example, the square-root function might as well be part of the simulator program because the client/service organization doesn't reduce fate sharing for the simulator programme and thus in that location is no reason employ it.

A overnice example of a widely used organization that is organized in a client/service manner, with the client and service typically running on separate computers, is the Globe Wide Web. The Web browser is a client, and a Web site is a service. The browser and the site communicate through well-defined messages and are typically geographically separated. Equally long as the client and service check the validity of messages, a failure of a service results in a controlled trouble for the browser, and vice versa. The World Wide Web provides enforced modularity.

In Figures 4.3 and 4.4, the service e'er responds with a reply, just that is not a requirement. Figure 4.five shows the pseudocode for a pump controller for the sewage pumping system in Sidebar four.2. In this example, there is no need for the pump service to transport a reply acknowledging that the pump was turned off. What the client cares about is a confirmation from an contained sensor service that the level in the tank is going down. Waiting for a answer from the pump service, fifty-fifty for a brusque fourth dimension, would only delay sounding the alarm if the pump failed.

Figure 4.five. Case client/service awarding: controller for a sewage pump.

Other systems avert response messages for performance reasons. For example, the popular 10 Window System (encounter Sidebar 4.4) sends a series of requests that ask the service to draw something on a screen and that individually take no need for a response.

Sidebar iv.4

The Ten Window System

The X Window Organisation [Suggestions for Further Reading iv.ii.ii] is the window organisation of choice on practically every engineering workstation and many personal computers. It provides a adept example of using the customer/service arrangement to reach modularity. One of the main contributions of the X Window Organisation is that it remedied a defect that had crept into the unix system when displays replaced typewriters: the brandish and keyboard were the only hardware-dependent parts of the unix application programming interface. The Ten Window System immune brandish-oriented unix applications to exist completely contained of the underlying hardware.

The X Window System achieved this property by separating the service plan that manipulates the display device from the client programs that employ the display. The service module provides an interface to manage windows, fonts, mouse cursors, and images. Clients can request services for these resource through loftier-level operations; for example, clients perform graphics operations in terms of lines, rectangles, curves, and the like. The reward of this split is that the client programs are device independent. The addition of a new display type may require a new service implementation, but no application changes are required.

Another advantage of a client/service organisation is that an application running on i automobile can use the display on some other machine. This arrangement allows, for instance, a computing-intensive plan to run on a loftier-operation supercomputer, while displaying the results on a user's personal computer.

It is of import that the service exist robust to client failures because otherwise a buggy client could cause the entire display to freeze. The X Window system achieves this belongings by having client and service communicate through carefully designed remote procedure calls, a machinery described in Department four.2. The remote procedure calls have the property that the service never has to trust the clients to provide right data and that the service can process other customer requests if it has to wait for a client.

The service allows clients to send multiple requests back to dorsum without waiting for individual responses because the rate at which data tin can be displayed on a local display is ofttimes higher than the network data charge per unit between a client and service. If the client had to expect for a response on each request, then the user-perceived performance would be unacceptable. For case, at 80 characters per asking (1 line of text on a typical display) and a 5-millisecond round-trip fourth dimension betwixt client and service, but 16,000 characters per second can be drawn, while typical hardware devices are capable of displaying an order of magnitude faster.

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Sequential Logic Blueprint

Sarah L. Harris , David Harris , in Digital Design and Computer Architecture, 2022

Setup Time Constraint

Figure 3.39 is the timing diagram showing but the maximum filibuster through the path, indicated by the blue arrows. To satisfy the setup fourth dimension of R2, D2 must settle no later than the setup time before the next clock border. Hence, we notice an equation for the minimum clock period:

Figure 3.39. Maximum filibuster for setup time constraint

(three.13) $T_c\ge t_{\mathit{pcq}}+t_{\mathit{pd}}+t_{\text{setup}}$

In commercial designs, the clock period is often dictated by the Director of Engineering or past the marketing department (to ensure a competitive production). Moreover, the flip-flop clock-to-Q propagation delay and setup time, t _pcq and t _setup, are specified by the manufacturer. Hence, we rearrange Equation 3.xiii to solve for the maximum propagation delay through the combinational logic, which is ordinarily the only variable under the command of the individual designer.

(three.14) $t_{\mathit{pd}}\le T_c-(t_{\mathit{pcq}}+t_{\text{setup}})$

The term in parentheses, t _pcq + t _setup, is called the sequencing overhead. Ideally, the unabridged cycle fourth dimension T _c would exist available for useful ciphering in the combinational logic, t _pd . Yet, the sequencing overhead of the flip-flop cuts into this time. Equation 3.fourteen is called the setup time constraint or max-delay constraint because information technology depends on the setup time and limits the maximum delay through combinational logic.

If the propagation delay through the combinational logic is besides bully, D2 may non have settled to its final value by the time R2 needs information technology to be stable and samples information technology. Hence, R2 may sample an incorrect result or even an illegal logic level, a level in the forbidden region. In such a case, the circuit will malfunction. The trouble tin be solved past increasing the clock period or by redesigning the combinational logic to accept a shorter propagation delay.

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Shared-retentiveness programming

Gerassimos Barlas , in Multicore and GPU Programming, 2015

Exercises

ane.

Enumerate and create the other timing diagrams that show the alternatives of Effigy 3.4 when information technology comes to the final balance of the bank account.

2.

Research the term "fork flop" and write a programme that performs as such.

3.

Alter the producer-consumer instance shown in Listing 3.eleven and so that the threads end later the number 100 is generated.

4.

Suggest a modification to the program of Listing 3.12 so that the IntegrCalc threads can use any office that returns a double and takes a double as a parameter.

5.

In a remote region of Siberia there are single tracks joining railroad stations. Obviously merely ane train tin can use a piece of rail between 2 stations. The other trains can wait at the stations before they exercise their crossings. The following graph indicates the rail and station layout:

Write a Qt program that simulates the journey of three trains with the post-obit schedules:

•

A  → B  → Due east  → C

•

D  → B  → Eastward  → G

•

C  → Eastward  → B  → D  → F

As each trains arrives at a station, display a relative bulletin. You can assume that a station tin hold whatever number of trains waiting.

6.

Modify the program of the previous practice and then that each station can hold but 2 trains. Can this lead to deadlocks?

If you have not done so already, make sure that your program uses only one thread class.

7.

A desktop publishing application such every bit PageMaker has two threads running: i for running the GUI and one for doing background work. Simulate this application in Qt. Your implementation should have the thread corresponding to the GUI send requests to the other thread to run tasks on its behalf. The tasks should be (obviously merely press a message is enough for the simulation):

•

Printing

•

Post merging

•

PDF generation

Later on performing each requested task, the second thread should wait for a new request to exist sent to it. Make sure that the first thread does non have to wait for the second thread to stop earlier making new requests.

8.

A popular bakery has a baker that cooks a loaf of breadstuff at a time and deposits it on a counter. Incoming customers choice up a loaf from the counter and exit the baker. The counter can hold 20 loaves. If the counter is full, the bakery stops baking breadstuff. If it is empty, a customer waits. Employ semaphores to solve the coordination problem between the baker and the customers.

9.

Considering of customer need, the bakery owner is considering the following enhancements to his shop:

a.

Increment the capacity of the counter to grand

b.

Hire three more bakers

Alter the solution of the previous practice to accommodate these changes.

Which is the easiest option to implement?

ten.

A bank account class is defined as follows:

class BankAccount {

  protected:

  double balance;

  string holderName;

public:

  double getBalance( ) ;

  void eolith(double);

  void withdraw(double, int); // the highest the 2d ↩

  argument, the higher the priority of the request

};

Write the implementation of the three methods given above and then that withdraw operations are prioritized: If there are not plenty funds in the account for all, the withdrawals must be done in order of priority, regardless of whether there are some that can be performed with the available funds. You can assume that the priority level in the withdraw method is past default equal to 0, and that it is upper bounded by a fixed constant MAXPRIORITY.

xi.

The IT department of a big corporation is equipped with five loftier-speed printers that are used past a multitude of threads. The threads are part of the aforementioned accounting process. Each of the threads is supposed to perform the following (pseudocode) sequence in order to print any fabric:

…

printerID   =   get_available_printer ( ) ;

// print to printerID printer

releasePrinter(printerID);

…

Write an appropriate implementation for the 2 functions listed above using semaphores. Yous can assume that the bachelor printer IDs are stored in a shared buffer.

12.

Create three threads, each press out the letters A, B, and C. The printing must adhere to these rules:

•

The total number of Bs and Cs that have been output at any betoken in the output string cannot exceed the full number of Equally that have been output at that point.

•

After a C has been output, another C cannot exist output until one or more Bs have been output.

Use semaphores to solve the problem.

13.

Alter the previous do so that the printing is governed by this ready of rules:

•

One C must exist output afterwards two Every bit and three Bs are output.

•

Although there is no restriction on the order of printing A and B, the respective threads must wait for a C to exist printed when the previous status is met.

Use a monitor to solve the trouble.

14.

Accost the termination problem in the previous practice. How tin the three threads end after, for case, a stock-still number of Every bit take been output? Or when a fixed full number of characters accept been output?

15.

Create 4 threads, each printing out the letters A, B, C, and D. The printing must adhere to these rules:

•

The total number of Every bit and Bs that have been output at whatever point in the output string cannot exceed the total number of Cs and Ds that take been output at that point.

•

The full number of As that have been output at any point in the output string cannot exceed twice the number of Bs that have been output at that point.

•

After a C has been output, another C cannot exist output until i or more D have been output.

16.

Solve the problem using (a) semaphores and (b) a monitor.

xix.

Use semaphores to solve the typical cigarette smokers' problem, where the agent directly signals the smoker missing the two ingredients placed on the table.

17.

Solve the cigarette smokers' problem as described in Section 3.6.2 using semaphores.

18.

Model the moving-picture show-going process at a multiplex cinema using a monitor. Assume the following conditions:

•

In that location are iii different movies playing at the same time in three theaters.

The capacities of each theater are 4, 5, and seven, respectively.

•

1 hundred customers are waiting to see a randomly chosen picture show.

•

A cashier problems the tickets.

•

If a theater is full, a film begins to play.

•

A client cannot enter a theater while a motion-picture show is playing or while the previous viewers are exiting the theater.

•

A movie volition play for the last customers, even if the respective theater is not full.

19.

Write a multithreaded password cracker based on the producer-consumer paradigm. The producer should generate plaintext passwords according to a ready of rules, and the consumers should be hashing each password and checking whether information technology matches a target signature. All the threads should terminate upon the discovery of a matching password. You lot tin can use the MD5 cryptographic hash role for this do.

xx.

Write a multithreaded plan for finding the prime number numbers in a user-supplied range of numbers. Compare the following design approaches:

a.

Split the range in equal pieces and assign each one to a thread.

b.

Have a shared QAtomicInt variable that holds the adjacent number to be checked. Threads should read and increase this number before testing it.

c.

Have a shared "monitor" object that returns, upon request, a range of numbers to be tested. This tin be considered a generalization of the previous design.

Which of the designs is more efficient? Explain your findings.

21.

Use the QtConcurrent functionality to implement a prime number checker. Compare it in terms of speed, efficiency, and programming effort to your QThread -based attempt of the previous practise.

22.

Create a big array of randomly generated 2D coordinates (x, y). Each of the coordinates should be a number in the range [-1000, grand]. Use appropriate QtConcurrent functions to find the points that are in a ring of distances between 100 and 200 from the indicate of origin. Compare the performance of your solution against a sequential implementation.

23.

Utilise the QtConcurrent functionality to implement a parallel bucketsort. Does the number of buckets play a pregnant role in your implementation's operation?

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Digit-Serial Arithmetics

Miloš D. Ercegovac , Tomás Lang , in Digital Arithmetic, 2004

9.1.1 Modes of Functioning and Algorithm and Implementation Models

We consider the example in which the numerical values are represented in a radix-r number system. In some cases, we employ conventional representations, while in others redundant representations are preferable.

A series signal is a numerical input or output with one digit per clock cycle. Effigy 9.1 shows typical timing diagrams for a serial functioning, in which in each bicycle ane digit of each operand is applied and one digit of the output is delivered. Note that past convention nosotros denote as bicycle 1 the bicycle in which the first digit of the output is delivered. The total execution time is the sum of two components:

FIGURE 9.1. Timing characteristics of serial operation with northward = 12. (a) With δ = 0. (b) With δ = 3.

•

The initial delay δ, which corresponds to the additional number of operand digits required to determine the first result digit. That is, the kickoff output digit is delivered δ + 1 cycles after the application of the first input digits. So, every bit shown in Effigy 9.1(a), δ = 0 corresponds to the case in which the offset output digit is delivered 1 cycle after the awarding of the get-go input digits. Figure 9.1(b) shows a instance in which the get-go output is delivered in the cycle after four input digits have been applied (δ = iii).

•

The fourth dimension to deliver the n output digits. Since one digit is delivered per cycle, for an output of northward digits, this time is equal to n cycles.

Consequently, the execution fourth dimension is

9.1 $T_{\mathrm{due\; north}}+\delta +\mathrm{ane}+n$

Series Modes

Two serial modes are typical:

i.

Least-meaning digit first (LSDF) style. The digits of the operands (consequence) are applied serially starting from the to the lowest degree-pregnant digit. This mode is as well known as right-to-left fashion and, since it was the first serial mode, typically this mode is implied when the term 'serial arithmetics' is used.

Because of the guild of the digits, the indexing is simplified if right-to-left indexing is used, as in the representation of integers, namely,

9.2 $\mathrm{ten}+{\displaystyle \sum _{i=0}^{n-1}{\mathrm{10}}_i{r}^i}$

2.

Most-significant digit first (MSDF) mode. The digits are applied starting from the almost-significant digit (left-to-right mode). Arithmetics performed in this mode is known as online arithmetic, and the corresponding initial delay is chosen online delay.

The indexing is simplified hither past using left-to-right indexing, as in the representation of fractions, that is,

9.iii $x+{\displaystyle \sum _{i=1}^{\mathrm{northward}}{x}_i{r}^{-i}}$

Algorithm and Implementation Model

Nosotros at present draw a general model for a serial algorithm and its implementation. Consider an functioning with two n radix-r digit operands, x and y, and ane issue z. The input-output model is described as follows.

In cycle j the result digit z _j+1 is computed. Consequently the cycles are labeled from −δ, …, 0, 1, …, n so that in cycle j the operand digits x _j+1 and y _j+1+δ are received, output digit z _j+1 is computed, and output digit z_j is delivered (Figure 9.2(a)). To conform with both series modes, in LSDF (MSDF) manner digits are counted from the least-significant (about-meaning) side.

Effigy 9.2. Serial algorithm model: (a) Timing. (b) Implementation.

The algorithm consists of recurrences on numerical values. In each of the north + δ iterations, one digit of the operands is introduced (for the concluding δ iterations the input digits are set to zero), an internal state w (also chosen a residual) is updated, and i digit of the outcome is produced (zero for the first δ cycles). ^two An additional cycle is needed to deliver the last upshot digit.

Calling x[j],y[j], and z[j] the numerical values of the corresponding signals when the representation consists of the beginning j + δ digits for the operands and j digits for the consequence, iteration j is described by

9.4 $\begin{array}{ll}x\left[j+1\right]\hfill & =\left(\mathrm{ten}\left[j\right],x_{j+1+\delta }\right)\hfill \\ y\left[j+1\right]\hfill & =\left(y\left[j\right],y_{j+1+\delta }\right)\hfill \\ \hfill z_{j+1}& =F\left(\mathrm{west}\left[j\right],x\left[j\right],x_{j+\mathrm{i}+\delta },y\left[j\right],y_{j+1+\delta },z\left[j\right]\right)\hfill \\ z\left[j+\mathrm{ane}\right]\hfill & =\left(z\left[j\right],z_{j+1}\right)\hfill \\ w\left[j+1\right]\hfill & =G\left(w\left[j\right],x\left[j\right],{\mathrm{ten}}_{j+1+\delta },y\left[j\right],y_{j+1+\delta },z\left[j\right],z_{j+\mathrm{i}}\right)\hfill \end{array}$

Figure 9.2(b) depicts the serial algorithm and implementation model.

The initial delay δ depends on the serial mode and on the specific operation (Table nine.one). As can exist seen from the table, for the MSDF way all basic operations can exist performed with a pocket-size and fixed (independent of the precision) initial delay. On the other hand, for the LSDF mode, just addition and multiplication have a small initial filibuster, whereas division, square root, and max/min have an initial delay O (due north), which means that this way is not suitable for these operations. Moreover, the initial filibuster is also O (due north) for multiplication if simply the most-significant one-half of the product is required (see Figure nine.3(a)).

Table ix.i. Initial delay (δ).

Operation	LSDF	MSDF
Add-on	0	two (r = 2)
		i (r ≥ iv)
Multiplication	0	3 (r = 2)
		2 (r = 4)
Only MS half of product	n
Division	twodue north *	4
Square root	twon *	iv
Max/min	n	0

*

The result digits delivered LS starting time.

Effigy 9.iii. (a) LSDF and (b) MSDF modes.

As seen in Figure 9.3(b), online arithmetic is well-suited for variable precision computations: in one case a desired precision is obtained, the operation can end.

Composite Algorithm

Since the execution time of a series operation can be loftier, it is convenient to develop blended algorithms in which the execution of successive (dependent) operations overlap; that is, a successor operation tin begin every bit soon equally the event digits of its predecessors are available. This is illustrated in the following example where a sequence of operations is implemented past a network of digit-serial (online) arithmetic modules. The network in Figure 9.4(a) implements the expressions for the 2D vector normalization. ³

FIGURE ix.iv. Online computation in 2nd vector normalization: (a) Network. (b) Timing diagram.

9.v $\begin{array}{ll}c=\frac{x}{\sqrt{{\mathrm{10}}^2+y^{\mathrm{two}}}}\hfill & s=\frac{y}{\sqrt{{\mathrm{10}}^{\mathrm{ii}}+y^{\mathrm{ii}}}}\hfill \end{array}$

The corresponding timing diagram is given in Figure 9.4(b).

The online delay of the network is the sum of online delays of the operations on the longest path. For r = 2, we obtain from Table 9.1

ix.half dozen ${\Delta }_{norm}=\delta 1+\delta \mathrm{ii}+\delta 3+\delta 4=\mathrm{iii}+2+4+\mathrm{iv}=\mathrm{xiii}$

The total execution time for the composite operation is D_norm = δ_norm + four + n.

The more levels there are in a sequence of operations and the longer the precision, the more advantageous is the online approach.

To reduce further the execution fourth dimension, the iii modules in the dashed box in Figure nine.4(a) tin can be merged into a unmarried online module, called a composite module, with a shorter online delay than the sum of the online delays of the dependent components.

The latency in the case of LSDF arithmetic is obtained in a similar manner (Do 9.1).

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Questions for Affiliate xiv

Michael Jesse Chonoles , in OCUP Certification Guide, 2018

1.

Which diagram type is not a UML 2.five behavioral diagram?

A.

Use Case Diagram

B.

Sequence Diagram

C.

Interaction Diagram

D.

Collaboration Diagram

E.

Timing Diagram

ii.

Which i of the post-obit potential lifelines needs to be changed?

A.

A

B.

B

C.

C

D.

D

3.

Which of the post-obit messages is incorrectly fatigued?

A.

a

B.

b

C.

c

D.

d

E.

eastward

iv.

Which i of the following potential lifelines needs to be changed?

A.

A

B.

B

C.

C

D.

D

5.

Which of the messages in the below diagram is not compatible with the definitions shown in the course Player?

A.

m1

B.

m2

C.

m3

D.

m4

6.

In the Sequence Diagram fragment beneath, there are three messages and six occurrences. How many different traces are there in this diagram?

A.

i

B.

2

C.

3

D.

four

E.

5

F.

6

One thousand.

7

7.

A large X is used to attain what purpose in a Sequence Diagram?

A.

X is the graphical stop of the lifeline.

B.

X indicates the devastation of the lifeline.

C.

10 marks the spot.

D.

X marks where to dig.

E.

Ten marks the starting time of a balking message.

F.

X marks the first of a timed message.

8.

Which lifeline needs to be replaced?

A.

a

B.

b

C.

c

D.

d

9.

What is an Interaction?

A.

An Operation telephone call

B.

A use of an Interface

C.

A unit of Beliefs

D.

A Reception

E.

An instance of a Utilise Case

10.

What is wrong with the following Sequence Diagram?

A.

Nothing.

B.

It is not allowed to have two lifelines with the same proper name.

C.

At that place are no letters shown.

D.

Lifelines must be directly and may non cross.

xi.

What needs to exist inverse in the post-obit Sequence Diagram?

A.

The empty () needs to be removed or filled in.

B.

The first message should motility from right to left.

C.

The arrowhead on the dashed line should exist made into a solid arrowhead.

D.

The m1 is a signal and cannot have a return. Instead, modify m1 into a synchronous performance phone call by making it accept a solid arrowhead.

12.

How many occurrences are there in the post-obit Sequence Diagram?

UML two.five Specification Figure 17.2

A.

seven

B.

8

C.

10

D.

12

Due east.

xiv

F.

16

13.

Which arrow format below indicates an asynchronous bulletin?

A.

A

B.

B

C.

C

D.

D

Due east.

E

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Lasers, Solid-Country

Stephen A. Payne , Georg F. Albrecht , in Encyclopedia of Physical Science and Engineering science (Third Edition), 2003

Iii.C.four Cavity Dumping

A way of operation closely related to Q-switching is cavity dumping. The essential architecture is the aforementioned as that for Q-switching, and the timing diagram is given in Fig. 21. The commencement phase of cavity-dumped operation is similar to that of Q-switching in that energy is stored. Both of the resonator mirrors are selected to be 100% reflective, such that the amplified light remains trapped within the cavity. As the pinnacle intracavity intensity is reached, the Pockels cell rapidly switches the cavity transmission off once more. This ejects the calorie-free circulating in the cavity by reflection off the polarizer in a pulse whose duration is equal to two cavity passes. This technique is in essence the aforementioned as electrical engineers use in a cable discharge, and is used to produce pulses of a few nanoseconds duration, since the pulsewidth now depends on the length of the resonator cavity and not on the amount of inversion stored before switching. The peak power output is significantly limited in this method since the calorie-free circulating within the resonator can become intense plenty to destroy disquisitional components of the laser.

FIGURE 21. In the pump phase the timing diagram for the cavity-dumped example is identical to the Q-switched case. Later on switching the Pockels jail cell to enable lasing, the crenel loss now is very minor since, for a cavity-dumped architecture, the reflectivity of both resonator mirrors is 100%. Once the power in the cavity has reached the maximum value, the Pockels cell is again switched and ejects the intracavity intensity from the laser in a pulse equal to the round-trip time of the resonator cavity.

An architecture very closely related to the cavity-dumped oscillator is the regenerative amplifier. The principle divergence is that the light amplification by stimulated emission of radiation oscillation in a regenerative amplifier does non build up from spontaneous emission, just is initiated by a signal injected into the resonator from the exterior, equally the Pockels jail cell is switched to transmission. This injected point is then trapped in the cavity and amplified until it has reached maximum intensity, at which indicate it is ejected (dumped) from the cavity.

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Design Patterns for Embedding Concurrency and Resource Management

Bruce Powel Douglass PhD , in Design Patterns for Embedded Systems in C, 2011

Deadlock Avoidance Patterns

The last problem I want to address in this chapter is deadlock. Deadlock is a state of affairs in which multiple clients are simultaneously waiting for weather condition that cannot, in principle, occur.

Effigy four-22 shows an case of deadlock. In this example, the priority of Task i is higher than that of Task 2. The figure shows a timing diagram overlayed with a class diagram showing the structure. In add-on to the tasks, in that location are two resources, R1 and R2, shared by both tasks. The problem arises if the tasks lock the resources in contrary order and Chore 1 preempts Chore ii between Task i between locking R1 and R2. The following description refers to the named points in Effigy four-22.

Figure iv-22. Deadlock example

A

At this signal, Job two runs.

B

Chore 2 locks R1 and is but almost to lock R2.

C

Task 1 runs. Since it is higher priority than Task two, information technology preempts Job two.

D

Job one locks R2.

East

Chore 1 now attempts to lock R1, notwithstanding, R1 is currently locked by Task 2. If Task 1 blocks to permit Task 2 to run, Chore two must block as soon every bit it tries to lock R1. The organization is in deadlock.

It is enough to break any of the four required atmospheric condition for deadlock (below) conditions to ensure that deadlock cannot appear. The simultaneous locking, ordered locking, and critical region patterns all avoid the issues of deadlock. For case, had Task 2 enabled a critical region (i.due east., disallowed task switching) earlier it locked R1, then Chore 1 would not take been able to preempt information technology earlier information technology locked R2. If both tasks locked the resources in the same social club, deadlock would have been prevented. If Task 2 locks both resources at the same time, there would be no problem. Deadlock is piece of cake to prevent, just you must take careful steps to do so.

Leaving aside the common problems of software errors, deadlocks crave four weather to exist truthful:

1

common exclusion locking of resources

2

some resources are locked while others are requested

iii

preemption while resources are locked is immune

4

a circular waiting condition exists

Deadlock tin exist avoided by breaking whatsoever of these 4 atmospheric condition. Using the Critical Region Pattern, for example, breaks rules #1 and #3. The Queuing Pattern, because information technology uses asynchronous message passing avoids #1 (other than the lock on the queue access itself). This affiliate finishes upwardly with two other patterns that avoid deadlock.

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