1. For 0, there are two representations: -0 and +0 which should not be the case as 0 is neither –ve nor +ve. 2. Out of 2^n bits for representation, we are able to utilize only 2^{n-1} bits. 3. Numbers are not in cyclic order i.e. After the largest number (in this, for example, +7) the next number is not the least number (in this, for example, +0). 4. For negative numbers signed extension does not work.
Example: Signed extension for +5
Signed extension for -5
5. As we can see above, for +ve representation, if 4 bits are extended to 5 bits there is a need to just append 0 in MSB. 6. But if the same is done in –ve representation we won’t get the same number. i.e. 10101 ≠ 11101.
1’s Complement representation of a signed integer
In 1’s complement representation the following rules are used:
1. For +ve numbers the representation rules are the same as signed integer representation. 2. For –ve numbers, we can follow any one of the two approaches:
1’s complement of 0 = 1 and 1’s complement of 1 = 0 Example: (-5) in 1’s complement: +5 = 0101 -5 = 1010
Example: –X = -5 for n=4 2^4-1-5=10 ->1010(Unsigned)
3. The range of 1’s complement integer representation of n-bit number is given as –(2^{n-1}-1) to 2^{n-1}-1.
1’s Complement Representation:
Positive Numbers | ||
---|---|---|
Sign | Magnitude | Number |
0 | 0 0 0 | +0 |
0 | 0 0 1 | +1 |
0 | 0 1 0 | +2 |
0 | 0 1 1 | +3 |
0 | 1 0 0 | +4 |
0 | 1 0 1 | +5 |
0 | 1 1 0 | +6 |
0 | 1 1 1 | +7 |
1 | 0 0 0 | -7 |
1 | 0 0 1 | -6 |
1 | 0 1 0 | -5 |
1 | 0 1 1 | -4 |
1 | 1 0 0 | -3 |
1 | 1 0 1 | -2 |
1 | 1 1 0 | -1 |
1 | 1 1 1 | -0 |
Drawbacks :
Merits over Signed bit representation:
1. Numbers are in cyclic order i.e. after the largest number (in this, for example, +7) the next number is the least number (in this, for example, -7). 2. For negative number signed extension works.
Signed extension for -5
3. As it can be seen above, for +ve as well as -ve representation, if 4 bits are extended to 5 bits there is a need to just append 0/1 respectively in MSB.
2’s Complement representation
In 2’s Complement representation the following rules are used:
1. For +ve numbers, the representation rules are the same as signed integer representation. 2. For –ve numbers, there are two different ways we can represent the number.
Example: (-5) in 4-bit representation 2^4-5=11 -→1011(unsigned)
To take 2’s complement simply take 1’s complement and add 1 to it. Example: (-5) in 2’s complement (+5) = 0101 1’s complement of (+5) = 1010 Add 1 in 1010: 1010+1 = 1011 Therefore (-5) = 1011
3. Range of representation of n-bit is –(2^{n-1} ) to (2)^{(n-1)-1}.
2’s Complement representation (4 bits)
Due to all of the above merits of 2’s complement representation of a signed integer, binary numbers are represented using 2’s complement method instead of signed bit and 1’s complement.
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Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.
Investopedia / Madelyn Goodnight
Researchers can create a simple random sample using a couple of methods. With a lottery method, each member of the population is assigned a number, and numbers are then selected at random.
An example of a simple random sample would be to choose the names of 25 employees out of a hat from a company of 250 employees. In this case the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen. Random sampling is used in science to conduct randomized control tests or for blinded experiments.
The example in which the names of 25 employees out of 250 are chosen out of a hat is an example of the lottery method at work. Each of the 250 employees would be assigned a number between one and 250, after which 25 of those numbers would be chosen at random.
Because individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected. In most cases this creates a balanced subset that carries the greatest potential for representing the larger group as a whole.
A manual lottery method can be quite onerous for larger populations. Selecting a random sample from a large population usually requires a computer-generated process. The same methodology as the lottery method is used, only the number assignments and subsequent selections are performed by computers, not humans.
With a simple random sample, there has to be room for error represented by a plus and minus variance ( sampling error ). For example, if a survey is taken to determine how many students are left-handed in a high school of 1,000 students, random sampling can determine that eight out of the 100 sampled are left-handed. The conclusion would then be that 8% of the student population of the high school are left-handed, when in fact the global average would be closer to 10%.
The same is true regardless of the subject matter. A survey on the percentage of the student population that has green eyes or a physical disability would result in a mathematical probability based on a simple random survey, but always with a plus or minus variance. The only way to have 100% accuracy rate would be to survey all 1,000 students which, while possible, would be impractical.
Although simple random sampling is intended to be an unbiased approach to surveying, sample selection bias can occur. When a sample set of the larger population is not inclusive enough, representation of the full population is skewed and requires additional sampling techniques.
The simple random sampling process entails six steps, each performed in sequential order.
The starting point of statistical analysis is to determine the population base. This is the group about which you wish to learn more, confirm a hypothesis , or determine a statistical outcome. This step is simply to identify what that population base is and ensure that the group will adequately cover the outcome you are trying to ascertain.
Example: You want to learn how the stocks of the largest companies in the United States have performed over the past 20 years. Your population would be the largest companies in the United States as determined by the S&P 500.
Before picking the units within a population, we need to determine how many to select. This sample size may be constrained by the amount of time, capital rationing , or other resources available to analyze the sample. However, be mindful to pick a sample size large enough to be genuinely representative of the population. In the example above, there are constraints in analyzing the performance for every stock in the S&P 500, so we only want to analyze a subset of this population.
Example: Your sample size will be 20 companies from the S&P 500.
In our example the items within the population are easy to determine, as they've already been identified for us (i.e., the companies listed within the S&P 500). However, imagine analyzing the students currently enrolled at a university or food products being sold at a grocery store. This step entails crafting the entire list of all items within your population.
Example: Using exchange information, you copy the companies comprising the S&P 500 into an Excel spreadsheet.
The simple random sample process calls for every unit within the population to receive an unrelated numerical value. This is often assigned based on how the data may be filtered. For example, you could assign the numbers one to 500 to the companies based on market cap , alphabetical order, or company formation date. How the values are assigned isn’t relevant; all that matters is that each value is sequential and has an equal chance of being selected.
Example: You assign the numbers one through 500 to the companies in the S&P 500 based on alphabetical order of the current CEO's surname, with the first company receiving the value one and the last company receiving the value 500.
In step 2 we chose 20 as the number of items we wanted to analyze within our population. We now randomly select 20 number values out of the 500. There are multiple ways to do this, as discussed later in this article.
Example: Using a random number table (see below), you select the numbers 2, 7, 17, 67, 68, 75, 77, 87, 92, 101, 145, 201, 222, 232, 311, 333, 376, 401, 478, and 489.
Each of the random variables selected in the prior step corresponds to an item within our population. The group sample is selected by identifying which random values were chosen and which population items those values match.
Example: Your sample consists of the companies that correspond to the values chosen in step 5.
There is no single method for determining the random values to be selected in step 5. The analyst can’t choose completely random numbers on their own, as there may be factors influencing their decision. For example, the analyst’s wedding anniversary may be the 24th, so they may consciously (or subconsciously) pick the random value 24. Instead, the analyst may choose one of the following methods:
When pulling together a sample, consider getting assistance from a colleague or an independent person. They may be able to identify biases or discrepancies of which you may not be aware.
Simple random vs. stratified random sample.
A simple random sample is used to represent the entire data population. A stratified random sample divides the population into smaller groups, known as “strata,” based on shared characteristics.
Unlike simple random samples, stratified random samples are used with populations that can be easily broken into different subgroups or subsets. These groups are based on certain criteria, then elements from each are randomly chosen in proportion to the group’s size versus the population. In our example above, S&P 500 companies could have subsets defined by type of industry or geographical region of the company’s headquarters.
This method of sampling means there will be selections from each different group—the size of which is based on its proportion to the entire population. Researchers must ensure that the strata do not overlap. Every point in the population must only belong to one stratum, because they should be mutually exclusive . Overlapping strata would increase the likelihood that some data are included, thus skewing the sample.
Systematic sampling entails selecting a single random variable that determines the interval of how the population items are selected. For example, if the number 37 was chosen, the 37th company on the list sorted by last name of the CEO would be selected by the sample. Then, the 74th (i.e., the next 37th) and the 111st (i.e. the next 37th after that) would be added as well.
Simple random sampling does not have a starting point; therefore, there is the risk that the population items selected at random may cluster. In our example there may be an abundance of CEOs with a last name that starts with the letter 'F.' Systematic sampling strives to even further reduce bias by ensuring that these clusters do not happen.
Cluster sampling (also known as “multistage random sampling”) can occur as a one-stage or two-stage cluster. In the former, items within a population are put into comparable groupings (using our example, companies are grouped by year formed), then sampling occurs within these clusters.
Two-stage cluster sampling occurs when clusters are formed through random selection. The population is not clustered with other similar items. Sample items are then randomly selected within each cluster.
Simple random sampling does not cluster any population sets. Clustering (especially two-stage clustering) can enhance the randomness of sample items. In addition, cluster sampling may provide a deeper analysis on a specific snapshot of a population, which may or may not enhance the analysis.
While simple random samples are easy to use, they do come with key disadvantages that can render the data useless.
Ease of use represents the biggest advantage of simple random sampling. Unlike more complicated sampling methods, such as stratified random sampling and probability sampling, there is no need to divide the population into subpopulations or take any other additional steps before selecting members of the population at random.
A simple random sample is meant to be an unbiased representation of a group. It is considered a fair way to select a sample from a larger population, as every member of the population has an equal chance of getting selected. Therefore, it has less chance of sampling bias.
A sampling error can occur with a simple random sample if the sample does not end up accurately reflecting the population it is supposed to represent. For example, in a simple random sample of 25 employees, it would be possible to draw 25 men even if the population consisted of 125 women, 125 men, and 125 nonbinary people.
For this reason simple random sampling is more commonly used when the researcher knows little about the population. If the researcher knows more, it is better to use a different sampling technique, such as stratified random sampling, which helps to account for the differences within the population, such as age, race, or gender.
Other disadvantages include the fact that for sampling from large populations, the process can be time-consuming and costly compared with other methods. Researchers may find that a project not worth the endeavor of its cost-benefit analysis does not generate positive results.
As every unit has to be assigned an identifying or sequential number prior to the selection process, this task may be difficult based on the method of data collection or size of the data set.
Each item within a population has an equal chance of being selected.
There is less of a chance of sampling bias, as every item is randomly selected.
It is easy and convenient for data sets already listed or digitally stored.
Incomplete population demographics may exclude certain groups from being sampled.
Random selection means the sample may not be truly representative of the population.
Depending on the data set size and format, random sampling may be a time-intensive process.
No easier method exists to extract a research sample from a larger population than simple random sampling. Selecting enough subjects completely at random from the larger population also yields a sample that can be representative of the group being studied.
Among the disadvantages of this technique are difficulty gaining access to respondents that can be drawn from the larger population, greater time, greater costs, and the fact that bias can still occur under certain circumstances.
A stratified random sample first divides the population into smaller groups, or strata, based on shared characteristics. Therefore, a stratified sampling strategy will ensure that members from each subgroup are included in the data analysis. Stratified sampling is used to highlight differences among groups in a population, as opposed to simple random sampling, which treats all members of a population as equal, with an equal likelihood of being sampled.
Using simple random sampling allows researchers to make generalizations about a specific population and leave out any bias. Using statistical techniques, inferences and predictions can be made about the population without having to survey or collect data from every individual in that population.
Simple random sampling is the most basic form of analyzing a population, allowing every item within it to have the same probability of being selected. There are also more complicated sampling methods that attempt to correct for possible shortcomings in the simple method. However, they don’t match the ease of simple random sampling for smaller populations.
Yale University. " Sampling. "
Business Research Methodology. " Simple Random Sampling ."
U.S. Department of Commerce: National Institute of Standards and Technology. " Appendix B. Random Number Tables. "
Calculator.net. " Random Number Generator. "
Microsoft. " RANDBETWEEN Function ."
Penn State University Eberly College of Science. " 8.1 - Systematic Sampling ."
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With the development of neural networks, research on adversarial attacks has become a hot topic. However, most existing adversarial attacks target natural images, and very few approaches focus on attacking the style features of artistic images. In ...
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IMAGES
COMMENTS
representation: [noun] one that represents: such as. an artistic likeness or image. a statement or account made to influence opinion or action. an incidental or collateral statement of fact on the faith of which a contract is entered into. a dramatic production or performance. a usually formal statement made against something or to effect a ...
REPRESENTATION definition: 1. a person or organization that speaks, acts, or is present officially for someone else: 2. the…. Learn more.
Representation definition: . See examples of REPRESENTATION used in a sentence.
REPRESENTATION meaning: 1. a person or organization that speaks, acts, or is present officially for someone else: 2. the…. Learn more.
A representation acts or serves on behalf or in place of something. A lawyer provides legal representation for his client. A caricature is an exaggerated representation or likeness of a person. ... DISCLAIMER: These example sentences appear in various news sources and books to reflect the usage of the word 'representation'.
a : a statement made to influence the opinions or actions of others. Her representation of the situation was very confusing. He was accused of making false representations. b chiefly British : a formal and official complaint about something. Our ambassador has made representations to their government.
Representation definition: The act of representing or the state of being represented.
10 meanings: 1. the act or an instance of representing or the state of being represented 2. anything that represents, such as a.... Click for more definitions.
Examples of REPRESENTATION in a sentence, how to use it. 97 examples: They contrast with syntactic representations, which are structured in terms of…
representation in American English. (ˌrɛprɪzɛnˈteɪʃən ) noun. 1. a representing or being represented (in various senses); specif., the fact of representing or being represented in a legislative assembly. 2. legislative representatives, collectively. 3. a likeness, image, picture, etc.
representation by a lawyer; direct representation in Parliament; Whether guilty or innocent, we are still entitled to legal representation. They had a strong representation in government. The task force had broad representation with members drawn from different departments. The party has increased its representation in Parliament.
Definitions of 'representation'. 1. If a group or person has representation in a legislature or on a committee, someone in the legislature or on the committee supports them and makes decisions on their behalf. [...] 2. See also proportional representation. 3.
1 [uncountable, countable] the act of presenting someone or something in a particular way; something that shows or describes something synonym portrayal the negative representation of single mothers in the media The snake swallowing its tail is a representation of infinity.
The best recent example of representation being done right is a film: 2016's The Accountant, in which the main character, played by Ben Affleck, is high-functioning autistic.While the character is written in a very predictable fashion—aural oversensitivity, emotional vacancy—Affleck's performance provides nuance that elevates the entire story.
When representation is not enough. However, representation simply is not enough—especially when it is one-dimensional, superficial, or not actually representative. Some scholars describe how ...
Getting to grips with representation and the media is a challenge. If you want to develop your understanding of the key concepts, you need to analyse the representation of people, places and products in a broad range of media texts. The following examples are a good place to start.
Political representation is the activity of making citizens "present" in public policy-making processes when political actors act in the best interest of citizens according to Hanna Pitkin's Concept of Representation (1967). [1] [2]This definition of political representation is consistent with a wide variety of views on what representing implies and what the duties of representatives are. [3]
Representation. Learners differ in the ways they perceive and make meaning of information. For example, those with sensory disabilities (e.g., blindness or deafness), learning disabilities (e.g., dyslexia), and those representing diverse or non-dominant cultures and/or languages all approach content differently.
Representational art is an artistic style in which the artist attempts to depict a representation of real-life subject matter, that is recognisable to the viewer. This is opposed to non-representational art, which does not depict subjects, objects or scenes from the real world. Art described as representational can be realistic, or less ...
The latter type of art is known as representational art. Representational arts are artworks that depict real situations. The sources of inspiration for a representational work are generally real objects, people, or scenes. For instance, the painting of a cat is considered to be representational art because it describes a real-world subject.
1. Introduction. Words can be represented with distributed word representations, currently often in the form of word embeddings. Similarly to how words can be embedded, so can languages, by associating each language with a real-valued vector known as a language representation, which can be used to measure similarities between languages.
Proportional voting, or proportional representation, is an electoral system in which a party's seat share in the legislature is proportional to its vote share. So, for example, a party with 40% of ...
In the signed integer representation method the following rules are followed: 1. The MSB (Most Significant Bit) represents the sign of the Integer. 2. Magnitude is represented by other bits other than MSB i.e. (n-1) bits where n is the no. of bits. 3. If the number is positive, MSB is 0 else 1.
Simple Random Sample: A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. An example of a simple random ...
This consultation is seeking views on our proposed approach to revising the NPPF. It also seeks views on a series of wider national planning policy reforms.
Two effective attack methods are proposed by relying on the optimization-based and gradient-based adversarial example strategies. Extensive experimental evaluations verify that the proposed attacks can sharply reduce the tampering localization accuracy while preserving high visual quality for the attacked images.
Casino as a prime example. When The Cordish Cos. developed the property in South Philadelphia , it became a model for development citywide, Johnson said. A development agreement was put in place ...