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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 contemporaty 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 contructing a table, even to the point of setting up type for pinting. 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 an even better idea. If was called the Analytical Engine, and through repeated design and redesign (with a few small models and parts of it actually built) it consumed Babbage off and on until his death. The Analytical Eginge is the closest thing to a computer the nineteenth century has to offer. In Babbage's design, it had a store (comparable to our concept of memory) and a mill (the arithmetic unit). Multiplication could be handled by repeated addition, and division by repeated substraction.
What's most intriguing about the Analytical Engine is that it could be programmed using cards that were adapted from the crds used in the Jacquard pattern-weaving loom. As Augusta Ada Byron, Countess of Lovelac (1815-1852), put it (in notes to her translation of an article written by an Italian mathematician about Babbage's Analytical Engine), "We may say that the Analytical Engine weaves algebrical patterns just as the Jacquard-loom weaves flowers and leaves."
Babbage seems to be the first person to understand the importance of a conditionnal jump in computers. here's Ada Byron again : "A cycle of operations, then, must be understood to signify any set fo operations which is repeated more than once. It is equally a cycle, whether it be repeated twice only, or an indefinite number of times ; for it is the fact of a repetition occuring at all that constitutes it such. In many cases of analysis there is a recurring group of one or more cycles ; that is, a cycle of cycle, or a cycle of cycles."

Historically, the most important operating system for 8-bit microprocessors was CP/M (Control Program for Micros), written in the mid-1970s for the Intel 8080 microprocessor by Gary Kildall (born in 1942), who later founded Digital Research Incorporated (DRI).
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CP/M was once a very popular operating system for the 8080 and remains historically important. CP/M was the major influence behind a 16-bit operating system named QDOS (Quick and Dirty Operating System) written by Tim Paterson of Seattle Computer Products for Intel's 16-bit 8086 and 8088 chips. QDOS was eventually renamed 86-DOS and licensed by Microsoft Corporation. Under the name MS-DOS (Microsoft Disk Operating System, pronounced em ess dahs, like the German article das), the operating system was licensed to IBM for the first IBM Personal Computer, introduced in 1981. Although a 16-bit version of CP/M (called CP/M-86) was also available for the IBM PC, MS-DOS quickly became the standard. MS-DOS (called PC-DOS on IBM's computers) was also licensed to other manufacturers who created computers compatible with the IBM PC.
MS-DOS didn't retain CP/M's file system. The file system in MS-DOS instead used a scheme called the File Allocation Table, or FAT, which had been originally invented at Microsoft in 1977.

Sometimes people squabble over whether programming is an art or a science. On the one hand, you have college curricula in Computer Science, and on the other hand, you have books such as Donald Knuth's famous The Art of Computer Programming series. "Rather", wrote physicist Richard Feynman, "computer science is like ingineering - it is all about getting something to do something."
If you ask 100 different people to write a program that prints out prime numbers, you'll get 100 different solutions. Even those programmers whose the Sieve of Eratosthenes won't implement it in precisely the same way that I did. If programming truly were a science, there wouldn't be so many possible solutions, and incorrect solutions would be more obvious. Occasionally, a programming problem incites flashes of creativity and insight, and that's the "art" part. But programming is mostly a designing and building process not unlike erecting a bridge.