Charles Babbage's Analytical Engine was a mechanical computing device. Its design included a section for storing numbers, another for performing calculations, and punched cards for entering instructions.
The 19th-century design embodied ideas of general-purpose computation, but Babbage did not complete the full machine during his lifetime. It holds an important place in computing history.
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, Babbage realised that a much more general design, the analytical engine, was possible. The work on the design of the analytical engine started around 1833.
The input, consisting of programs ("formulae") 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. 16.6 kB). An arithmetic unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially (1838) 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 (1858) depict a regularised grid layout. Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, roughly equivalent to microcode in modern CPUs, 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. Babbage developed some two dozen programs for the analytical engine between 1837 and 1840, and one program later. These programs treat polynomials, iterative formulas, Gaussian elimination, and Bernoulli numbers.
Construction
Late in his life, Babbage sought ways to build a simplified version of the machine, and assembled a small part of it before his death in 1871.
In 1878, a committee of the British Association for the Advancement of Science described the analytical engine as "a marvel of mechanical ingenuity", but recommended against constructing it. The committee acknowledged the usefulness and value of the machine, but could not estimate the cost of building it, and were unsure whether the machine would function correctly after being built.
Intermittently from 1880 to 1910, Babbage's son Henry Prevost Babbage was constructing a part of the mill and the printing apparatus. In 1910, it was able to calculate a (faulty) list of multiples of pi. This constituted only a small part of the whole engine; it was not programmable and had no storage. (Popular images of this section have sometimes been mislabelled, implying that it was the entire mill or even the entire engine.) Henry Babbage's "analytical engine mill" is on display at the Science Museum in London. Henry also proposed building a demonstration version of the full engine, with a smaller storage capacity: "perhaps for a first machine ten (columns) would do, with fifteen wheels in each". Such a version could manipulate 20 numbers of 25 digits each, and what it could be told to do with those numbers could still be impressive.