Open Always
Email: support@globalcompose.com Call Now! +1-315 515-4588
Open Always
Email: support@globalcompose.com Call Now! +1-315 515-4588

Sample Essay on Phrasing the Attachment

This sample paper on (Sample Essay on Phrasing the Attachment) was uploaded by one our contributors and does not necessarily reflect how our professionals write our papers. If you would like this paper removed from our website, please contact us our Contact Us Page.

A Database of over Million Scholarly Resources. Start your Search Now

Sample Essay on Phrasing the Attachment

Introduction

 

Booth’s algorithm provides a faster and simpler method that can be used to multiply two n-bits binary numbers that can be either positive or negative. The main instructions it uses are shifting an adding. However, Booth technique is preferred to other methods of multiplying numbers because it uses a smaller number of logic elements compared to the others. This report, therefore, focuses on how to use the Booth algorithm to design a multiplier that has the ability to multiply two 8-bits signed numbers to give an output result in 16-bits.

Design

     Its design has three main registers named A, P, and S that are 2N+1 in input size, multiplicand, multiplier, and the 2’s complement of the multiplicand respectively. The registers implement the Booth’s algorithm multiplier operation. When the input size is 8 bit wide, then the output ought to be as double as that, 16 bits wide. The logic used to implement the multiplier is shown in the diagram below.

 

Figure1. State Diagram of the Booth’s Algorithm Multiplier Design.

 

    

     Figure1 above depicts the different states that are used when designing a multiplier. The initial state is ‘init’ and it can’t move to the next stage called ‘Load’ unless the ‘start count’ is increased. The Load state loads inputs into their respective registers whereby the two smallest significant bits, 2LSB of the register P determines the operations to be performed as appropriate. For instance, if the 2LSB of the register P is “01”, the state goes to “(P+A)&shift” which adds A to P and shifts by 1 bit to the right. If the 2LSB of the register P is increased to “10”, the state will go to “(P+S)&shift” which will add the values of P to the 2’complements of A and shift it 1 bit to the right. Other values of the 2LSB of the register P make the state to go to “Do_nothing&shift” state and shift it one bit to the right. The shift operation is, therefore, performed to result to either the 2LSB of register P equal or differ.

      The states then transform from “(P+S)&shift”, “Do_nothing&shift”, or “(P+A)&shift” to “shift state”. On reaching “shift state,” there are two conditions involved; state to move to one of the following states determined by the 2LSB of register P, “(P+S)&shift” or “Do_nothing&shift”, or “(P+A)&shift,” or move to “Done” state which is determined by the Count signal. The Count signal is, however, required to be equal to the input size in order for the state to move to “Done.” At this point, note that if the two least significant bits of P are equal, then the shift constitutes to one count. But, when they are equal to logic “01”, it will result to both an addition and a shift to the right, thus making another count. When one complete process is over, the state reaches “Done” and in this case there should be an increased “start_count” should to start next process.

     Figure1 which shows the state diagram of the Booth’s algorithm multiplier is used to design the code in VHDL. The code includes the following components; a state machine instantiation that performs the proper operation to be executed, an instantiation of the counter to keep track of the shifts and additions, an instantiation of the multiplier that performs the shifts or additions or 2’s complement in the registers, and a product output that shows how the process occurs and seven segment code to display the result in the seven segments display.

     Furthermore, a test bench code is created to test the correct operation of the booth’s multiplier. The code reads from an input file that contains comma separated values, .csv. It evaluates these values to generate an output following the process discussed above.

Results

 

ModelSim software is used to check and simulate the VHDL code in order to make sure that the results and process are correct. Quartus software would then compile the VHDL code in order to know the number of created logics and implement the design onto DE2 board, as well. The following figure shows the results obtained from the Modelsim.

Figure 2. Simulation results of Booth’s algorithm multiplier design(A).

From the figure above, initially it can be seen that the input 1 and input 2 are at unknown state. When start is increased, the next rising edge of the clock loads the multiplier into the product register. Since the 2LSB are logic 10, the expected operation takes the 2’s complement of the multiplicand, input1 and add to the product register and then perform a shift operation. The process continues until the data ready becomes 1 as shown in the figure below.

 

Figure 2. Simulation Results of Booth’s Algorithm Multiplier Design(B).

When data ready becomes high, the output is compared with the expected output from the test bench. If the results are identical, no error is generated unless the otherwise. The figure below shows the flow summery of the design after the code compiled in Quratus.

Figure 3. The Flow Summery of the Booth’s Algorithm Multiplier.

From the figure above it can be seen that the design consumes about 116 logic elements which constitute less than one percent of the total logic elements. The total number of register used is 50 registers, estimated to be about 9% of the overall number of registers.

Conclusion

 

With its two main functions of addition and shifting, Booth’s multiplier is an excellent technique to perform multiplication of both positive and negative numbers. When compared to other multipliers, Booth has fewer logic elements thus giving it the advantage of faster shifting and addition regardless of short timing.

 

Sharing is: CARING

Are you looking for homework writing help? Click on Order Now button below to Submit your assignment details.

Homework Writing Help
We Can Help you with this Assignment right now!
Sample Essay on Phrasing the Attachment

Are you looking for homework writing help on (Sample Essay on Phrasing the Attachment)?Well, you can either use the sample paper provided to write your paper or you could contact us today for an original paper. If you are looking for an assignment to submit, then click on ORDER NOW button or contact us today. Our Professional Writers will be glad to write your paper from scratch.

We ensure that assignment instructions are followed, the paper is written from scratch. If you are not satisfied by our service, you can either request for refund or unlimited revisions for your order at absolutely no extra pay. Once the writer has completed your paper, the editors check your paper for any grammar/formatting/plagiarism mistakes, then the final paper is sent to your email.

Privacy| Confidentiality

Sample Essay on Phrasing the Attachment

We do not share your personal information with any company or person. We have also ensured that the ordering process is secure; you can check the security feature in the browser. For confidentiality purposes, all papers are sent to your personal email. If you have any questions, contact us any time via email, live chat or our phone number.

Our Clients Testimonials

  • I appreciate help on the assignment. It was hard for me but am good to go now

    Impact of pollution on Environment
  • Am happy now having completed the very difficult assignment

    Creative Message Strategies
  • Your writer did a fine job on the revisions. The paper is now ok

    Ethics: Theory and Practice
  • The paper was so involving but am happy it is done. Will reach you with more assignments

    Title: Privatization in or of America
  • I expected perfection in terms of grammar and I am happy. Lecturer is always on our head but was pleased with my paper. Once again, thanks a lot

    Title: Bundaberg Inquiry
  • The paper looks perfect now, thank to the writer

    Health Care Systems
  • You helped me complete several other tasks as you handled paper. wonna thank you

    Critique Paper on Political Change

Related Articles

Sample Essay on Phrasing the Attachment

Get more from us…

Would you like this sample paper to be sent to your email or would you like to receive weekly articles on how to write your assignments? You can simply send us your request on how to write your paper and we will email you a free guide within 24-36 hours. Kindly subscribe below!

Email Address: support@globalcompose.com