Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [85]
Napier also invented another multiplication aid, which is composed of strips of numbers usually inscribed on bone, horn, or ivory and hence referred to as Napier's Bones. The earliest mechanical calculator was a somewhat automated version of Napier's bones built around 1620 by Wilhelm Schickard (1592–1635). Other calculators based on interlocking wheels, gears, and levers are almost as old. Two of the more significant builders of mechanical calculators were the mathematicians and philosophers Blaise Pascal (1623–1662) and Gottfried Wilhelm von Leibniz (1646–1716).
You'll no doubt recall what a nuisance the carry bit was in both the original 8-Bit Adder and the computer that (among other things) automated the addition of numbers wider than 8 bits. The carry seems at first to be just a little quirk of addition, but in adding machines, the carry is really the central problem. If you've designed an adding machine that does everything except the carry, you're nowhere close to being finished!
How successfully the carry is dealt with is a key to the evaluation of old calculating machines. For example, Pascal's design of the carry mechanism prohibited the machine from subtracting. To subtract, the nines' complement had to be added the way that I demonstrated in Chapter 13. Successful mechanical calculators that real people could use weren't available until the late nineteenth century.
One curious invention that was to have a later influence on the history of computing—as well as a profound influence on the textile industry—was an automated loom developed by Joseph Marie Jacquard (1752–1834). The Jacquard loom (circa 1801) used metal cards with holes punched in them (much like those of a player piano) to control the weaving of patterns in fabrics. Jacquard's own tour de force was a self-portrait in black and white silk that required about 10,000 cards.
In the eighteenth century (and indeed up to the 1940s), a computer was a person who calculated numbers for hire. Tables of logarithms were always needed, and trigonometric tables were essential for nautical navigation using the stars and planets. If you wanted to publish a new set of tables, you would hire a bunch of computers, set them to work, and then assemble all the results. Errors could creep in at any stage of this process, of course, from the initial calculation to setting up the type to print the final pages.
The desire to eliminate errors from mathematical tables motivated the work of Charles Babbage (1791–1871), a British mathematician and economist who was almost an exact contemporary of Samuel Morse.
At the time, mathematical tables (of logarithms, for example) were not created by calculating an actual logarithm for each and every entry in the table. This would have taken far too long. Instead, the logarithms were calculated for select numbers, and then numbers in between were calculated by interpolation, using what are called differences in relatively simple calculations.
Beginning about 1820, Babbage believed that he could design and build a machine that would automate the process of constructing a table, even to the point of setting up type for printing. This would eliminate errors. He conceived the Difference Engine, and basically it was a big mechanical adding machine. Multidigit decimal numbers were represented by geared wheels that could be in any of 10 positions. Negatives were handled using the ten's complement. Despite some early models that showed Babbage's design to be sound and some grants from the British government (never enough, of course), the Difference Engine was never completed. Babbage abandoned work on it in 1833.
By that time, however, Babbage had