Stored-program architecture

Several developers of ENIAC, recognizing its flaws, came up with a far more flexible and elegant design, which came to be known as the "stored program architecture" or von Neumann architecture. This design was first formally described by John von Neumann in the paper First Draft of a Report on the EDVAC, distributed in 1945. A number of projects to develop computers based on the stored-program architecture commenced around this time, the first of these being completed in Great Britain. The first working prototype to be demonstrated was the Manchester Small-Scale Experimental Machine (SSEM or "Baby") in 1948. The Electronic Delay Storage Automatic Calculator (EDSAC), completed a year after the SSEM at Cambridge University, was the first practical, non-experimental implementation of the stored program design and was put to use immediately for research work at the university. Shortly thereafter, the machine originally described by von Neumann's paper—EDVAC—was completed but did not see full-time use for an additional two years.

Nearly all modern computers implement some form of the stored-program architecture, making it the single trait by which the word "computer" is now defined. While the technologies used in computers have changed dramatically since the first electronic, general-purpose computers of the 1940s, most still use the von Neumann architecture.

Beginning in the 1950s, Soviet scientists Sergei Sobolev and Nikolay Brusentsov conducted research on ternary computers, devices that operated on a base three numbering system of −1, 0, and 1 rather than the conventional binary numbering system upon which most computers are based. They designed the Setun, a functional ternary computer, at Moscow State University. The device was put into limited production in the Soviet Union, but supplanted by the more common binary architecture.

Theoretical computer science

The broader field of theoretical computer science encompasses both the classical theory of computation and a wide range of other topics that focus on the more abstract, logical, and mathematical aspects of computing.

Mathematical logic Number theory Graph theory Category theory Quantum computing theory
Theory of computation
Main article: Theory of computation
According to Peter J. Denning, the fundamental question underlying computer science is, "What can be (efficiently) automated?" The study of the theory of computation is focused on answering fundamental questions about what can be computed and what amount of resources are required to perform those computations. In an effort to answer the first question, computability theory examines which computational problems are solvable on various theoretical models of computation. The second question is addressed by computational complexity theory, which studies the time and space costs associated with different approaches to solving a multitude of computational problem.
The famous "P=NP?" problem, one of the Millennium Prize Problems, is an open problem in the theory of computation.

Anaytical Engine

generally considered the first computer, designed and partly built by the English inventor Charles Babbage in the 19th century (he worked on it until his death in 1871). While working on the Difference Engine, a simpler calculating machine commissioned by the British government, Babbage began to imagine ways to improve it. Chiefly he thought about generalizing its operation so that it could perform other kinds of calculations. By the time funding ran out for his Difference Engine in 1833, he had conceived of something far more revolutionary: a general-purpose computing machine called the Analytical Engine.
The Analytical Engine was to be a general-purpose, fully program-controlled, automatic mechanical digital computer. It would be able to perform any calculation set before it. There is no evidence that anyone before Babbage had ever conceived of such a device, let alone attempted to build one. The machine was designed to consist of four components: the mill, the store, the reader, and the printer. These components are the essential components of every computer today. The mill was the calculating unit, analogous to the central processing unit (CPU) in a modern computer; the store was where data were held prior to processing, exactly analogous to memory and storage in today's computers; and the reader and printer were the input and output devices.
As with the Difference Engine, the project was far more complex than anything theretofore built. The store was to be large enough to hold 1,000 50-digit numbers; this was larger than the storage capacity of any computer built before 1960. The machine was to be steam-driven and run by one attendant. The printing capability was also ambitious, as it had been for the Difference Engine: Babbage wanted to automate the process as much as possible, right up to producing printed tables of numbers.
The reader was another new feature of the Analytical Engine. Data (numbers) were to be entered on punched cards, using the card-reading technology of the Jacquard loom. Instructions were also to be entered on cards, another idea taken directly from Joseph-Marie Jacquard. The use of instruction cards would make it a programmable device and far more flexible than any machine then in existence. Another element of programmability was to be its ability to execute instructions in other than sequential order. It was to have a kind of decision-making ability in its conditional control transfer, also known as conditional branching, whereby it would be able to jump to a different instruction depending on the value of some data. This extremely powerful feature was missing in many of the early computers of the 20th century.
By most definitions, the Analytical Engine was a real computer as understood today—or would have been, had Babbage not run into implementation problems again. Actually building his ambitious design was judged infeasible given the current technology, and Babbage's failure to generate the promised mathematical tables with his Difference Engine had dampened enthusiasm for further government funding. Indeed, it was apparent to the British government that Babbage was more interested in innovation than in constructing tables.
All the same, Babbage's Analytical Engine was something new under the sun. Its most revolutionary feature was the ability to change its operation by changing the instructions on punched cards. Until this breakthrough, all the mechanical aids to calculation were merely calculators or, like the Difference Engine, glorified calculators. The Analytical Engine, although not actually completed, was the first machine that deserved to be called a computer.

punched card

The slide rule, also known colloquially as a slipstick, is a mechanical analog computer. The slide rule is used primarily for multiplication and division, and also for functions such as roots, logarithms and trigonometry, but is not normally used foraddition or subtraction.

Slide rules come in a diverse range of styles and generally appear in a linear or circular form with a standardized set of markings (scales) essential to performing mathematical computations. Slide rules manufactured for specialized fields such as aviation orfinance typically feature additional scales that aid in calculations common to that field.

William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were being gradually introduced; but around 1974 the electronic scientific calculator made it largely obsolete and most suppliers left the business.

Basic concepts

In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers. These common operations can be time-consuming and error-prone when done on paper. More elaborate slide rules allow other calculations, such as square roots,exponentials, logarithms, and trigonometric functions.

Scales may be grouped in decades, which are numbers ranging from 1 to 10 (i.e. 10ⁿ to 10ⁿ⁺¹). Thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.

In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product,quotient, or other calculated result.

The user determines the location of the decimal point in the result, based on mental estimation. Scientific notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.

Most slide rules consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change.

Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip (which can usually be pulled out, flipped over and reinserted for convenience), still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales.

Napier's bones

Napier's bones is an abacus created by John Napier for calculation of products and quotients of numbers that was based on Arab mathematics and lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab^[1]and Fibonacci writing in the Liber Abaci. Also called Rabdology (from Greek ῥάβδoς [r(h)abdos], "rod" and -λογία [logia], "study"). Napier published his version of rods in a work printed in Edinburgh, Scotland, at the end of 1617 entitled Rabdologiæ. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. More advanced use of the rods can even extractsquare roots. Note that Napier's bones are not the same as logarithms, with which Napier's name is also associated.

The abacus consists of a board with a rim; the user places Napier's rods in the rim to conduct multiplication or division. The board's left edge is divided into 9 squares, holding the numbers 1 to 9. TheNapier's rods consist of strips of wood, metal or heavy cardboard.Napier's bones are three dimensional, square in cross section, with four different rods engraved on each one. A set of such bonesmight be enclosed in a convenient carrying case.

A rod's surface comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line. The first square of each rod holds a single digit, and the other squares hold this number's double, triple, quadruple, quintuple, and so on until the last square contains nine times the number in the top square. The digits of each product are written one to each side of the diagonal; numbers less than 10 occupy the lower triangle, with a zero in the top half.

A set consists of 10 rods corresponding to digits 0 to 9. The rod 0, although it may look unnecessary, is obviously still needed for multipliers or multiplicands having 0 in them.

Abacus

The abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of wood, stone, or metal. The abacus was in use centuries before the adoption of the written modern numeral system and is still widely used by merchants, traders and clerks in Asia, Africa, and elsewhere. The user of an abacus is called an abacist.

Mesopotamian abacus

The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.^[6]

Some scholars point to a character from the Babylonian cuneiform which may have been derived from a representation of the abacus.^[7] It is the belief of Carruccio (and other Old Babylonian scholars) that Old Babylonians "may have used the abacus for the operations of addition andsubtraction; however, this primitive device proved difficult to use for more complex calculations".

Egyptian abacus

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered,^] casting some doubt over the extent to which this instrument was used.

Persian abacus

During the Achaemenid Persian Empire, around 600 BC the Persians first began to use the abacus.^[10] Under Parthian and Sassanian Iranianempires, scholars concentrated on exchanging knowledge and inventions by the countries around them – India, China, and the Roman Empire, when it is thought to be expanded over the other countries.

Greek abacus

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC. The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

A tablet found on the Greek island Salamis in 1846 AD dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) long, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.

Roman abacus

The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles, calculi, were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the tenth century. Due to Pope Sylvester II's reintroduction of the abacus with very useful modifications, it became widely used in Europe once again during the 11th century 

Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.^[

One example of archaeological evidence of the Roman abacus, shown here in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives –five units, five tens etc., essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman ounces.

Chinese abacus

The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.

The Chinese abacus, known as the suànpán (算盤, lit. "Counting tray"), is typically 20 cm (8 in) tall and comes in various widths depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom for both decimal andhexadecimal computation. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. If you move them toward the beam, you count their value. If you move away, you don't count their value. The suanpan can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center.

Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root andcube root operations at high speed. There are currently schools teaching students how to use it.

In the famous long scroll Along the River During the Qingming Festival painted by Zhang Zeduan (1085–1145 AD) during the Song Dynasty(960–1297 AD), a suanpan is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).

The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2, allowing use with a hexadecimal numeral system. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model run in grooves, presumably making arithmetic calculations much slower.

Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907 AD) when travel in the Indian Ocean and theMiddle East would have provided direct contact with India, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.

types of computer based on size

Microcomputers (Personal computers)

Microcomputers are the most common type of computers in existence today, whether at work in school or on the desk at home. The term “microcomputer” was introduced with the advent of single chipmicroprocessors. The term “microcomputer” itself is now practically an anachronism.

These computers include:

§  Desktop computers – A case and a display, put under and on a desk.

§  In-car computers (“carputers”) – Built into a car, for entertainment, navigation, etc.

A separate class is that of mobile devices:

§  Laptops, notebook computers and Palmtop computers – Portable and all in one case. Varying sizes, but other than smartbooks expected to be “full” computers without limitations.

§  Tablet PC – Like laptops, but with only a touch-screen instead of a physical keyboard.

§  Smartphones, smartbooks and PDAs (personal digital assistants) – Small handheld computers with limited hardware.

§  Programmable calculator– Like small handhelds, but specialised on mathematical work.

§  Game consoles – Fixed computers specialized for entertainment purposes (computer games).

§  Handheld game consoles – Ditto, but small and portable.

Minicomputers (Midrange computers)

A minicomputer (colloquially, mini) is a class of multi-user computers that lies in the middle range of the computing spectrum, in between the smallest multi-user systems (mainframe computers) and the largest single-user systems (microcomputers or personal computers). The contemporary term for this class of system is midrange computer, such as the higher-end SPARC, POWER and Itanium -based systems from Sun Microsystems, IBM and Hewlett-Packard.

Mainframe Computers

The term mainframe computer was created to distinguish the traditional, large, institutional computer intended to service multiple users from the smaller, single user machines. These computers are capable of handling and processing very large amounts of data quickly. Mainframe computers are used in large institutions such as government, banks and large corporations. These institutions were early adopters of computer use, long before personal computers were available to individuals. "Mainframe" often refers to computers compatible with the computer architectures established in the 1960s. Thus, the origin of the architecture also affects the classification, not just processing power.

Mainframes are measured in millions of instructions per second or MIPS. An example of integer operation is moving data around in memory or I/O devices. A more useful industrial benchmark is transaction processing as defined by the Transaction Processing Performance Council. Mainframes are built to be reliable for transaction processing as it is commonly understood in the business world: a commercial exchange of goods, services, or money. A typical transaction, as defined by the Transaction Processing Performance Council, would include the updating to a database system for such things as inventory control (goods), airline reservations (services), or banking (money). A transaction could refer to a set of operations including disk read/writes, operating system calls, or some form of data transfer from one subsystem to another.

Supercomputer

A supercomputer is focused on performing tasks involving intense numerical calculations such as weather forecasting, fluid dynamics, nuclear simulations, theoretical astrophysics, and complex scientific computations. A supercomputer is a computer that is at the frontline of current processing capacity, particularly speed of calculation. The term supercomputer itself is rather fluid, and today's supercomputer tends to become tomorrow's ordinary computer. Supercomputer processing speeds are measured in floating point operations per second or FLOPS. Example of floating point operation is the calculation of mathematical equations in real numbers. In terms of computational capability, memory size and speed, I/O technology, and topological issues such as bandwidth and latency, Supercomputers are the most powerful. Supercomputers are very expensive and not cost-effective just to perform batch or transaction processing. Transaction processing is handled by less powerful computer such as server computer or mainframe.