In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing, automated reasoning, other tasks; as an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input, the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states producing "output" and terminating at a final ending state; the transition from one state to the next is not deterministic. The concept of algorithm has existed for centuries. Greek mathematicians used algorithms in the sieve of Eratosthenes for finding prime numbers, the Euclidean algorithm for finding the greatest common divisor of two numbers; the word algorithm itself is derived from the 9th century mathematician Muḥammad ibn Mūsā al-Khwārizmī, Latinized Algoritmi.
A partial formalization of what would become the modern concept of algorithm began with attempts to solve the Entscheidungsproblem posed by David Hilbert in 1928. Formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's Formulation 1 of 1936, Alan Turing's Turing machines of 1936–37 and 1939. The word'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to algorismus. Al-Khwārizmī was a Persian mathematician, astronomer and scholar in the House of Wisdom in Baghdad, whose name means'the native of Khwarazm', a region, part of Greater Iran and is now in Uzbekistan. About 825, al-Khwarizmi wrote an Arabic language treatise on the Hindu–Arabic numeral system, translated into Latin during the 12th century under the title Algoritmi de numero Indorum; this title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.
Al-Khwarizmi was the most read mathematician in Europe in the late Middle Ages through another of his books, the Algebra. In late medieval Latin, English'algorism', the corruption of his name meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός'number', the Latin word was altered to algorithmus, the corresponding English term'algorithm' is first attested in the 17th century. In English, it was first used in about 1230 and by Chaucer in 1391. English adopted the French term, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu, it begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. Which translates as: Algorism is the art by which at present we use those Indian figures, which number two times five; the poem is a few hundred lines long and summarizes the art of calculating with the new style of Indian dice, or Talibus Indorum, or Hindu numerals.
An informal definition could be "a set of rules that defines a sequence of operations". Which would include all computer programs, including programs that do not perform numeric calculations. A program is only an algorithm if it stops eventually. A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers. Boolos, Jeffrey & 1974, 1999 offer an informal meaning of the word in the following quotation: No human being can write fast enough, or long enough, or small enough† to list all members of an enumerably infinite set by writing out their names, one after another, in some notation, but humans can do something useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human, capable of carrying out only elementary operations on symbols.
An "enumerably infinite set" is one whose elements can be put into one-to-one correspondence with the integers. Thus and Jeffrey are saying that an algorithm implies instructions for a process that "creates" output integers from an arbitrary "input" integer or integers that, in theory, can be arbitrarily large, thus an algorithm can be an algebraic equation such as y = m + n – two arbitrary "input variables" m and n that produce an output y. But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of: Precise instructions for a fast, efficient, "good" process that specifies the "moves" of "the computer" to find and process arbitrary input integers/symbols m and n, symbols + and =... and "effectively" produce, in a "reasonable" time, output-integer y at a specified place and in a specified format
United States Census Bureau
The United States Census Bureau is a principal agency of the U. S. Federal Statistical System, responsible for producing data about the American people and economy; the Census Bureau is part of the U. S. Department of Commerce and its director is appointed by the President of the United States; the Census Bureau's primary mission is conducting the U. S. Census every ten years, which allocates the seats of the U. S. House of Representatives to the states based on their population; the Bureau's various censuses and surveys help allocate over $400 billion in federal funds every year and it helps states, local communities, businesses make informed decisions. The information provided by the census informs decisions on where to build and maintain schools, transportation infrastructure, police and fire departments. In addition to the decennial census, the Census Bureau continually conducts dozens of other censuses and surveys, including the American Community Survey, the U. S. Economic Census, the Current Population Survey.
Furthermore and foreign trade indicators released by the federal government contain data produced by the Census Bureau. Article One of the United States Constitution directs the population be enumerated at least once every ten years and the resulting counts used to set the number of members from each state in the House of Representatives and, by extension, in the Electoral College; the Census Bureau now conducts a full population count every 10 years in years ending with a zero and uses the term "decennial" to describe the operation. Between censuses, the Census Bureau makes population projections. In addition, Census data directly affects how more than $400 billion per year in federal and state funding is allocated to communities for neighborhood improvements, public health, education and more; the Census Bureau is mandated with fulfilling these obligations: the collecting of statistics about the nation, its people, economy. The Census Bureau's legal authority is codified in Title 13 of the United States Code.
The Census Bureau conducts surveys on behalf of various federal government and local government agencies on topics such as employment, health, consumer expenditures, housing. Within the bureau, these are known as "demographic surveys" and are conducted perpetually between and during decennial population counts; the Census Bureau conducts economic surveys of manufacturing, retail and other establishments and of domestic governments. Between 1790 and 1840, the census was taken by marshals of the judicial districts; the Census Act of 1840 established a central office. Several acts followed that revised and authorized new censuses at the 10-year intervals. In 1902, the temporary Census Office was moved under the Department of Interior, in 1903 it was renamed the Census Bureau under the new Department of Commerce and Labor; the department was intended to consolidate overlapping statistical agencies, but Census Bureau officials were hindered by their subordinate role in the department. An act in 1920 changed the date and authorized manufacturing censuses every two years and agriculture censuses every 10 years.
In 1929, a bill was passed mandating the House of Representatives be reapportioned based on the results of the 1930 Census. In 1954, various acts were codified into Title 13 of the US Code. By law, the Census Bureau must count everyone and submit state population totals to the U. S. President by December 31 of any year ending in a zero. States within the Union receive the results in the spring of the following year; the United States Census Bureau defines four statistical regions, with nine divisions. The Census Bureau regions are "widely used...for data collection and analysis". The Census Bureau definition is pervasive. Regional divisions used by the United States Census Bureau: Region 1: Northeast Division 1: New England Division 2: Mid-Atlantic Region 2: Midwest Division 3: East North Central Division 4: West North Central Region 3: South Division 5: South Atlantic Division 6: East South Central Division 7: West South Central Region 4: West Division 8: Mountain Division 9: Pacific Many federal, state and tribal governments use census data to: Decide the location of new housing and public facilities, Examine the demographic characteristics of communities and the US, Plan transportation systems and roadways, Determine quotas and creation of police and fire precincts, Create localized areas for elections, utilities, etc.
Gathers population information every 10 years The United States Census Bureau is committed to confidentiality, guarantees non-disclosure of any addresses or personal information related to individuals or establishments. Title 13 of the U. S. Code establishes penalties for the disclosure of this information. All Census employees must sign an affidavit of non-disclosure prior to employment; the Bureau cannot share responses, addresses or personal information with anyone including United States or foreign government
A household consists of one people who live in the same dwelling and share meals. It may consist of a single family or another group of people. A dwelling is considered to contain multiple households; the household is the basic unit of analysis in many social and government models, is important to economics and inheritance. Household models include families, blended families, shared housing, group homes, boarding houses, houses of multiple occupancy, single room occupancy. In feudal societies, the Royal Household and medieval households of the wealthy included servants and other retainers. For statistical purposes in the United Kingdom, a household is defined as "one person or a group of people who have the accommodation as their only or main residence and for a group, either share at least one meal a day or share the living accommodation, that is, a living room or sitting room"; the introduction of legislation to control houses of multiple occupation in the UK Housing Act required a tighter definition of a single household.
People can be considered a household if they are related: full- or half-blood, step-parent/child, in-laws, a married couple or unmarried but "living as...". The United States Census definition hinges on "separate living quarters": "those in which the occupants live and eat separately from any other persons in the building." According to the U. S. census, a householder is the "person in whose name the housing unit is owned or rented". The U. S. government used "head of the household" and "head of the family", but those terms were replaced with "householder" in 1980. In the census definition of a household, it... includes all the persons who occupy a housing unit. A housing unit is a house, an apartment, a mobile home, a group of rooms, or a single room, occupied as separate living quarters. Separate living quarters are those in which the occupants live and eat separately from any other persons in the building and which have direct access from the outside of the building or through a common hall.
The occupants may be a single family, one person living alone, two or more families living together, or any other group of related or unrelated persons who share living arrangements. On July 15, 1998, Statistics Canada said: "A household is defined as being composed of a person or group of persons who co-reside in, or occupy, a dwelling." Although a one-income-stream economic theory simplifies modeling, it does not reflect reality. Many, if not most, households have several income-earning members. Most economic models do not equate households and traditional families, there is not always a one-to-one relationship between households and families. In social work, a household is defined similarly: a residential group in which housework is divided and performed by householders. Care may be delivered by one householder to another, depending upon their respective needs and disabilities. Household composition may affect health expectations and outcomes for its members. Eligibility for community services and welfare benefits may depend upon household composition.
In sociology, household work strategy is the division of labour among members of a household. Household work strategies vary over the life cycle as household members age, or with the economic environment. Feminism examines. In The Second Shift and The Time Bind, sociologist Arlie Russell Hochschild presents evidence that in two-career couples men and women spend about equal amounts of time working. Cathy Young says that in some cases, women may prevent the equal participation of men in housework and parenting. Household models in the English-speaking world include traditional and blended families, shared housing, group homes for people with support needs. Other models which may meet definitions of a household include boarding houses, houses in multiple occupation, single room occupancy. In feudal or aristocratic societies, a household may include servants or retainers who derive their income from the household's principal income. A 1961–62 National Housing Institute survey estimated that 13.8 percent of Belgian dwellings were unfit and incapable of improvement.
A further 19.5 percent were unfit but had the potential to be improved, 54 percent were considered suitable for modern living standards. Seventy-four percent of dwellings lacked a shower or bath, 19 percent had inadequate sewage disposal, 3.6 percent lacked a drinking-water supply. According to a 1964 study, 13 percent of Belgium's housing consisted of slums. Between 1954 and 1973, the percentage of French homes with a shower or bath increased from 10 to 65 percent. During that period, the percentage of homes without flush toilets fell from 73 to 30 percent. A 1948 law permitted gradual, long-term rent increases for existing flats on the condition that part of the money was spent on repairs. According to John Ardagh, the law, "vigorously applied, was successful in its twofold aim: to encourage both repairs and new building." After World War II, a large percentage
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of called programs; these programs enable computers to perform an wide range of tasks. A "complete" computer including the hardware, the operating system, peripheral equipment required and used for "full" operation can be referred to as a computer system; this term may as well be used for a group of computers that are connected and work together, in particular a computer network or computer cluster. Computers are used as control systems for a wide variety of industrial and consumer devices; this includes simple special purpose devices like microwave ovens and remote controls, factory devices such as industrial robots and computer-aided design, general purpose devices like personal computers and mobile devices such as smartphones. The Internet is run on computers and it connects hundreds of millions of other computers and their users.
Early computers were only conceived as calculating devices. Since ancient times, simple manual devices like the abacus aided people in doing calculations. Early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analog calculations in the early 20th century; the first digital electronic calculating machines were developed during World War II. The speed and versatility of computers have been increasing ever since then. Conventionally, a modern computer consists of at least one processing element a central processing unit, some form of memory; the processing element carries out arithmetic and logical operations, a sequencing and control unit can change the order of operations in response to stored information. Peripheral devices include input devices, output devices, input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and they enable the result of operations to be saved and retrieved.
According to the Oxford English Dictionary, the first known use of the word "computer" was in 1613 in a book called The Yong Mans Gleanings by English writer Richard Braithwait: "I haue read the truest computer of Times, the best Arithmetician that euer breathed, he reduceth thy dayes into a short number." This usage of the term referred to a human computer, a person who carried out calculations or computations. The word continued with the same meaning until the middle of the 20th century. During the latter part of this period women were hired as computers because they could be paid less than their male counterparts. By 1943, most human computers were women. From the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations; the Online Etymology Dictionary gives the first attested use of "computer" in the 1640s, meaning "one who calculates". The Online Etymology Dictionary states that the use of the term to mean "'calculating machine' is from 1897."
The Online Etymology Dictionary indicates that the "modern use" of the term, to mean "programmable digital electronic computer" dates from "1945 under this name. Devices have been used to aid computation for thousands of years using one-to-one correspondence with fingers; the earliest counting device was a form of tally stick. Record keeping aids throughout the Fertile Crescent included calculi which represented counts of items livestock or grains, sealed in hollow unbaked clay containers; the use of counting rods is one example. The abacus was used for arithmetic tasks; the Roman abacus was developed from devices used in Babylonia as early as 2400 BC. Since many other forms of reckoning boards or tables have been invented. In a medieval European counting house, a checkered cloth would be placed on a table, markers moved around on it according to certain rules, as an aid to calculating sums of money; the Antikythera mechanism is believed to be the earliest mechanical analog "computer", according to Derek J. de Solla Price.
It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, has been dated to c. 100 BC. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later. Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use; the planisphere was a star chart invented by Abū Rayhān al-Bīrūnī in the early 11th century. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235. Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, c. 1000 AD.
The sector, a calculating instrument used for solving problems in proportion, trigonometry and division, for various functions, such as squares and cube roots, was developed in
Information systems are formal, organizational systems designed to collect, process and distribute information. In a sociotechnical perspective, information systems are composed by four components: task, people and technology. A computer information system is a system composed of people and computers that processes or interprets information; the term is sometimes used in more restricted senses to refer to only the software used to run a computerized database or to refer to only a computer system. Information Systems is an academic study of systems with a specific reference to information and the complementary networks of hardware and software that people and organizations use to collect, process and distribute data. An emphasis is placed on an information system having a definitive boundary, processors, inputs and the aforementioned communication networks. Any specific information system aims to support operations and decision-making. An information system is the information and communication technology that an organization uses, the way in which people interact with this technology in support of business processes.
Some authors make a clear distinction between information systems, computer systems, business processes. Information systems include an ICT component but are not purely concerned with ICT, focusing instead on the end use of information technology. Information systems are different from business processes. Information systems help to control the performance of business processes. Alter argues for advantages of viewing an information system as a special type of work system. A work system is a system in which humans or machines perform processes and activities using resources to produce specific products or services for customers. An information system is a work system whose activities are devoted to capturing, storing, retrieving and displaying information; as such, information systems inter-relate with data systems on the one hand and activity systems on the other. An information system is a form of communication system in which data represent and are processed as a form of social memory. An information system can be considered a semi-formal language which supports human decision making and action.
Information systems are the primary focus of study for organizational informatics. Silver et al. provided two views on IS that includes software, data and procedures. Zheng provided another system view of information system which adds processes and essential system elements like environment, boundary and interactions; the Association for Computing Machinery defines "Information systems specialists focus on integrating information technology solutions and business processes to meet the information needs of businesses and other enterprises."There are various types of information systems, for example: transaction processing systems, decision support systems, knowledge management systems, learning management systems, database management systems, office information systems. Critical to most information systems are information technologies, which are designed to enable humans to perform tasks for which the human brain is not well suited, such as: handling large amounts of information, performing complex calculations, controlling many simultaneous processes.
Information technologies are a important and malleable resource available to executives. Many companies have created a position of chief information officer that sits on the executive board with the chief executive officer, chief financial officer, chief operating officer, chief technical officer; the CTO may serve as CIO, vice versa. The chief information security officer focuses on information security management; the six components that must come together in order to produce an information system are: Hardware: The term hardware refers to machinery. This category includes the computer itself, referred to as the central processing unit, all of its support equipment. Among the support, equipment are input and output devices, storage devices and communications devices. Software: The term software refers to computer programs and the manuals that support them. Computer programs are machine-readable instructions that direct the circuitry within the hardware parts of the system to function in ways that produce useful information from data.
Programs are stored on some input/output medium a disk or tape. Data: Data are facts that are used by programs to produce useful information. Like programs, data are stored in machine-readable form on disk or tape until the computer needs them. Procedures: Procedures are the policies that govern the operation of a computer system. "Procedures are to people what software is to hardware" is a common analogy, used to illustrate the role of procedures in a system. People: Every system needs people if it is to be useful; the most overlooked element of the system are the people the component that most influence the success or failure of information systems. This includes "not only the users, but those who operate and service the computers, those who maintain the data, those who support the network of computers." <Kroenke, D. M.. MIS Essentials. Pearson Education>'. D
Herman Hollerith was an American inventor who developed an electromechanical punched card tabulator to assist in summarizing information and accounting. He was the founder of the Tabulating Machine Company, amalgamated in 1911 with three other companies to form a fifth company, the Computing-Tabulating-Recording Company, renamed IBM in 1924. Hollerith is regarded as one of the seminal figures in the development of data processing, his invention of the punched card tabulating machine marks the beginning of the era of semiautomatic data processing systems, his concept dominated that landscape for nearly a century. Herman Hollerith was born the son of German immigrant Prof. Georg Hollerith from Großfischlingen in Buffalo, New York, where he spent his early childhood, he entered the City College of New York in 1875, graduated from the Columbia University School of Mines with an "Engineer of Mines" degree in 1879 at age 19, in 1890 asked for a Ph. D based on his development of the tabulating system.
In 1882 Hollerith joined the Massachusetts Institute of Technology where he taught mechanical engineering and conducted his first experiments with punched cards. He moved to Washington, D. C. living in Georgetown, with a home on 29th Street and a business building at 31st Street and the C&O Canal, where today there is a commemorative plaque installed by IBM. He died in Washington D. C. of a heart attack. At the urging of John Shaw Billings, Hollerith developed a mechanism using electrical connections to increment a counter, recording information. A key idea was that a datum could be recorded by the presence or absence of a hole at a specific location on a card. For example, if a specific hole location indicates marital status a hole there can indicate married while not having a hole indicates single. Hollerith determined that data in specified locations on a card, the now-familiar rows and columns, could be counted or sorted electromechanically. A description of this system, An Electric Tabulating System, was submitted by Hollerith to Columbia University as his doctoral thesis, is reprinted in Randell's book.
On January 8, 1889, Hollerith was issued U. S. Patent 395,782, claim 2 of which reads: The herein-described method of compiling statistics, which consists in recording separate statistical items pertaining to the individual by holes or combinations of holes punched in sheets of electrically non-conducting material, bearing a specific relation to each other and to a standard, counting or tallying such statistical items separately or in combination by means of mechanical counters operated by electro-magnets the circuits through which are controlled by the perforated sheets as and for the purpose set forth. Hollerith had left teaching and begun working for the United States Census Bureau in the year he filed his first patent application. Titled "Art of Compiling Statistics", it was filed on September 23, 1884. S. Patent 395,782 was granted on January 8, 1889. Hollerith did business under his own name, as The Hollerith Electric Tabulating System, specializing in punched card data processing equipment.
He provided tabulators and other machines under contract for the Census Office, which used them for the 1890 census. The net effect of the many changes from the 1880 census: the larger population, the data items to be collected, the Census Bureau headcount, the scheduled publications, the use of Hollerith's electromechanical tabulators, was to reduce the time required to process the census from eight years for the 1880 census to six years for the 1890 census. In 1896 Hollerith founded the Tabulating Machine Company. Many major census bureaus around the world leased his equipment and purchased his cards, as did major insurance companies. Hollerith's machines were used for censuses in England, Germany, Austria, France, Puerto Rico and the Philippines, again in the 1900 census, he invented the first keypunch. The 1890 Tabulator was hardwired to operate on 1890 Census cards. A control panel in his 1906 Type I Tabulator simplified rewiring for different jobs; the 1920s removable control panel supported near instant job changing.
These inventions were among the foundations of the data processing industry and Hollerith's punched cards continued in use for a century. In 1911 four corporations, including Hollerith's firm, were amalgamated to form a fifth company, the Computing-Tabulating-Recording Company. Under the presidency of Thomas J. Watson, CTR was renamed International Business Machines Corporation in 1924. By 1933 The Tabulating Machine Company name had disappeared as subsidiary companies were subsumed by IBM. Hollerith is buried at Oak Hill Cemetery in the Georgetown neighborhood of Washington, D. C. Hollerith cards were named after Herman Hollerith, his great-grandson, the Rt. Rev. Herman Hollerith IV, was the Episcopal bishop of the Diocese of Southern Virginia, another great-grandson, Randolph Marshall Hollerith, is an Episcopal priest and the dean of Washington National Cathedral in Washington, D. C. For more on Punched card history, see: Unit record equipment#Further reading For IBM see: IBM#Further reading and History of IBM#Further reading Ashurst, Gareth.
Pioneers of Computing. Frederick Muller. Pp. 77–90. Beniger, James R; the Control Revolution: Technological and Economic Origins of the Information Socie
Bookkeeping is the recording of financial transactions, is part of the process of accounting in business. Transactions include purchases, sales and payments by an individual person or an organization/corporation. There are several standard methods of bookkeeping, including the single-entry and double-entry bookkeeping systems. While these may be viewed as "real" bookkeeping, any process for recording financial transactions is a bookkeeping process. Bookkeeping is the work of a bookkeeper, who records the day-to-day financial transactions of a business, they write the daybooks, document each financial transaction, whether cash or credit, into the correct daybook—that is, petty cash book, suppliers ledger, customer ledger, etc.—and the general ledger. Thereafter, an accountant can create financial reports from the information recorded by the bookkeeper. Bookkeeping refers to the record-keeping aspects of financial accounting, involves preparing source documents for all transactions and other events of a business.
The bookkeeper brings the books to the trial balance stage: an accountant may prepare the income statement and balance sheet using the trial balance and ledgers prepared by the bookkeeper. The origin of book-keeping is lost in obscurity, but recent researches indicate that methods of keeping accounts have existed from the remotest times of human life in cities. Babylonian records written with styli on small slabs of clay have been found dating to 2600 BCE; the term "waste book" was used in colonial America, referring to the documenting of daily transactions of receipts and expenditures. Records were made in chronological order, for temporary use only. Daily records were transferred to a daybook or account ledger to balance the accounts and to create a permanent journal; the bookkeeping process records the financial effects of transactions. An important difference between a manual and an electronic accounting system is the former's latency between the recording of a financial transaction and its posting in the relevant account.
This delay, absent in electronic accounting systems due to nearly instantaneous posting to relevant accounts, is characteristic of manual systems, gave rise to the primary books of accounts—cash book, purchase book, sales book, etc.—for documenting a financial transaction. In the normal course of business, a document is produced each time. Sales and purchases have invoices or receipts. Deposit slips are produced. Checks are written to pay money out of the account. Bookkeeping first involves recording the details of all of these source documents into multi-column journals. For example, all credit sales are recorded in the sales journal; each column in a journal corresponds to an account. In the single entry system, each transaction is recorded only once. Most individuals who balance their check-book each month are using such a system, most personal-finance software follows this approach. After a certain period a month, each column in each journal is totalled to give a summary for that period. Using the rules of double-entry, these journal summaries are transferred to their respective accounts in the ledger, or account book.
For example, the entries in the Sales Journal are taken and a debit entry is made in each customer's account, a credit entry might be made in the account for "Sale of class 2 widgets". This process of transferring summaries or individual transactions to the ledger is called posting. Once the posting process is complete, accounts kept using the "T" format undergo balancing, a process to arrive at the balance of the account; as a partial check that the posting process was done a working document called an unadjusted trial balance is created. In its simplest form, this is a three-column list. Column One contains the names of those accounts in the ledger. If an account has a debit balance, the balance amount is copied into Column Two; the debit column is totalled, the credit column is totalled. The two totals must agree—which is not by chance—because under the double-entry rules, whenever there is a posting, the debits of the posting equal the credits of the posting. If the two totals do not agree, an error has been made, either in the journals or during the posting process.
The error must be located and rectified, the totals of the debit column and the credit column recalculated to check for agreement before any further processing can take place. Once the accounts balance, the accountant makes a number of adjustments and changes the balance amounts of some of the accounts; these adjustments must still obey the double-entry rule: for example, the inventory account and asset account might be changed to bring them into line with the actual numbers counted during a stocktake. At the same time, the expense account associated with usage of inventory is adjusted by an equal and opposite amount. Other adjustments such as posting depreciation and prepayments are done at this time; this results in a listing called the adjusted trial balance. It is the accounts in this list, their corresponding debit or credit balances, that are used to prepar