The influence of the difference engine and the analytical engine on the computer development

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National Technical University

«Kharkhiv Polytechnic Institute»

Project Work

«The influence of the difference engine and the analytical engine on the computer development»

Student of

Group CIT-65 V.Promskyi

2015

DIFFERENCE ENGINE

The invention of the computer all began with a man who had a vision to change the country. His name was Charles Babbage, and he was the first person to create a digital mechanical computer engine. In 1821, Babbage began to build a small demonstration model of a mechanical calculator named "The Difference Engine".

Babbage began in 1822 with what he called the difference engine, made to compute values of polynomial functions. It was created to calculate a series of values automatically. By using the method of finite differences, it was possible to avoid the need for multiplication and division.

For a prototype difference engine, Babbage brought in Joseph Clement to implement the design, in 1823. Clement worked to high standards, but his machine tools were particularly elaborate. Under the standard terms of business of the time, he could charge for their construction, and would also own them. He and Babbage fell out over costs around 1831.

Some parts of the prototype survive in the Museum of the History of Science, Oxford. This prototype evolved into the "first difference engine." It remained unfinished and the finished portion is located at the Science Museum in London. This first difference engine would have been composed of around 25,000 parts, weigh fifteen tons (13,600 kg), and would have been 8 ft (2.4 m) tall. Although Babbage received ample funding for the project, it was never completed. He later (1847-1849) produced detailed drawings for an improved version,"Difference Engine No. 2", but did not receive funding from the British government. His design was finally constructed in 1989-1991, using his plans and 19th century manufacturing tolerances. It performed its first calculation at the London Science Museum, returning results to 31 digits.

babbag demonstration model computer

Nine years later, the Science Museum completed the printer Babbage had designed for the difference engine.

Prone to the above, This invention was designed:

· with a number of gears for performing two operations: addition and subtraction.

· without the capability to perform multiplication and division, which were a lot more difficult to carry out.

Babbage's demonstration model thoroughly worked quite well, so he chose to make the final full frame version, known as the "Difference Engine". This machine included:

· the power to go up to 20 decimal places.

· the ability to produce hard copy inked printout on paper as a checking copy but also automatically compresses the result on soft material.

Unfortunately, Babbage did not have the courage and strength to overcome the difficulties associated with creating the full-frame "Difference Engine". However, this did not impede with Babbage's plans to invent the "perfect" engine, which would develop into the "Analytical Engine". Unlike the former "Difference Engine", the "Analytical Engine" was programmable and followed instructions from a series of punch cards. Furthermore, this Engine had a store and a mill, where intermediate results were held and the arithmetic processing was executed, respectively.

Complete models

The London Science Museum has constructed two Difference Engines according to Babbage's plans for the Difference Engine No 2. One is owned by the museum. The other, owned by the technology multimillionaire Nathan Myhrvold, went on exhibition at the Computer History Museum in Mountain View, California on 10 May 2008. The two models that have been constructed are not replicas; Myhrvold's engine is the first design by Babbage, and the London Science Museum's is a later model.

Babbage continued working on his "Analytical Engine" until the end of his life. He isolated himself, filling in notebook after notebook with hundreds of notes and ideas. Unfortunately, in 1871, he died without attaining his goal of making a complete engine. Even so Babbage is widely-recognized throughout the US and the rest of the world for designing the main elements of the modern computer, which included the central processor, memory and data organization. His work had a great impact on our society by opening the way to future inventions in computing.

Operations

The difference engine consists of a number of columns, numbered from 1 to N. The machine is able to store one decimal number in each column. The machine can only add the value of a column n+1 to column n to produce the new value of n. Column N can only store a constant, column 1 displays (and possibly prints) the value of the calculation on the current iteration.

The engine is programmed by setting initial values to the columns. Column 1 is set to the value of the polynomial at the start of computation. Column 2 is set to a value derived from the first and higher derivatives of the polynomial at the same value of X. Each of the columns from 3 to N is set to a value derived from the first and higher derivatives of the polynomial.

Timing

In the Babbage design, one iteration (i.e., one full set of addition and carry operations) happens for each rotation of the main shaft. Odd and even columns alternately perform an addition in one cycle. The sequence of operations for column is thus:

1. Count up, receiving the value from column (Addition step)

2. Perform carry propagation on the counted up value

3. Count down to zero, adding to column

4. Reset the counted-down value to its original value

Steps 1,2,3,4 occur for every odd column, while steps 3,4,1,2 occur for every even column.

While Babbage's original design placed the crank directly on the main shaft, it was later realized that the force required to crank the machine would have been too great for a human to handle comfortably. Therefore, the two models that were built incorporate a 4:1 reduction gear at the crank, and four revolutions of the crank are required to perform one full cycle.

Steps

Each iteration creates a new result, and is accomplished in four steps corresponding to four complete turns of the handle shown at the far right in the picture below. The four steps are:

· Step 1. All even numbered columns (2,4,6,8) are added to all odd numbered columns (1,3,5,7) simultaneously. An interior sweep arm turns each even column to cause whatever number is on each wheel to count down to zero. As a wheel turns to zero, it transfers its value to a sector gear located between the odd/even columns. These values are transferred to the odd column causing them to count up. Any odd column value that passes from "9" to "0" activates a carry lever.

· Step 2 carry propagation is accomplished by a set of spiral arms in the back that poll the carry levers in a helical manner so that a carry at any level can increment the wheel above by one. That can create a carry, which is why the arms move in a spiral. At the same time, the sector gears are returned to their original position, which causes them to increment the even column wheels back to their original values. The sector gears are double-high on one side so they can be lifted to disengage from the odd column wheels while they still remain in contact with the even column wheels.

· Step 3. This is like Step 1, except it is odd columns (3,5,7) added to even columns (2,4,6), and column one has its values transferred by a sector gear to the print mechanism on the left end of the engine. Any even column value that passes from "9" to "0" activates a carry lever. The column 1 value, the result for the polynomial, is sent to the attached printer mechanism.

· Step 4. This is like Step 2, but for doing carries on even columns, and returning odd columns to their original values.

Subtraction

The engine represents negative numbers as ten's complements. Subtraction amounts to addition of a negative number. This works in the same manner that modern computers perform subtraction, known as two's complements.

The Analytical Engine

It was first described in 1837 as the successor to Babbage's difference engine, a design for a mechanical computer. The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete. In other words, the logical structure of the Analytical Engine was essentially the same as that which has dominated computer design in the electronic era.

Babbage was never able to complete construction of any of his machines due to conflicts with his chief engineer and inadequate funding. It was not until the 1940s that the first general-purpose computers were actually built, more than a century after Babbage had proposed the pioneering Analytical Engine in 1837.

Design

Babbage's first attempt at a mechanical computing device, the Difference Engine, was a special-purpose machine designed to tabulate logarithms and trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, Joseph Clement, and ultimately the British government withdrew its funding for the project.

During this project, he realized that a much more general design, the Analytical Engine, was possible. The input (programs and data) was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixed-point arithmetic.

There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits each (ca. 16.7 kB). An arithmetical unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side. (Later drawings depict a regularized grid layout.) Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.

The programming language to be employed by users was akin to modern day assembly languages. Loops and conditional branching were possible, and so the language as conceived would have been Turing-complete as later defined by Alan Turing. Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards.

In 1842, the Italian mathematician Luigi Menabrea, whom Babbage had met while travelling in Italy, wrote a description of the engine in French. In 1843, the description was translated into English and extensively annotated by Ada King (nйe Byron), Countess of Lovelace, who had become interested in the engine eight years earlier. In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine, she has been described as the first computer programmer. The modern computer programming language Ada is named in her honor.

Influence

Predicted influence

Babbage understood that the existence of an automatic computer would kindle interest in the field now known as algorithmic efficiency, writing in his Passages from the Life of a Philosopher, "As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise--by what course of calculation can these results be arrived at by the machine in the shortest time"

Computer science

Swedish engineers Georg and Edvard Sheutz, inspired by a description of the difference engine, created a mechanical calculation device based on the design in 1853. Table-sized instead of room-sized, the device was capable of calculating tables, but imperfectly.

From 1872 Henry continued diligently with his father's work and then intermittently in retirement in 1875. Percy Ludgate wrote about the engine in 1915 and even designed his own Analytical Engine (it was drawn up in detail, but never built). Ludgate's engine would be much smaller than Babbage's of about 8 cubic feet (230 L), and hypothetically would be capable of multiplying two 20-decimal-digit numbers in about six seconds.

Despite this ground work, Babbage's work fell into historical obscurity, and the Analytical Engine was unknown to builders of electro-mechanical and electronic computing machines in the 1930s and 1940s when they began their work, resulting in the need to re-invent many of the architectural innovations Babbage had proposed. Howard Aiken, who built the quickly-obsoleted electromechanical calculator, the Harvard Mark I, between 1937 and 1945, praised Babbage's work likely as a way of enhancing his own stature, but knew nothing of the Analytical Engine's architecture during the construction of the Mark I, and considered his visit to the constructed portion of the Analytical Engine "the greatest disappointment of my life". The Mark I showed no influence from the Analytical Engine and lacked the Analytical Engine's most prescient architectural feature, conditional branching. J. Presper Eckert and John W. Mauchly similarly were not aware of the details of Babbage's Analytical Engine work prior to the completion of their design for the first electronic general-purpose computer, the ENIAC.

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