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To "instruct" the machine, Babbage borrowed an idea that had just revolutionized the weaving industry. Using a string of cards with strategically placed holes in them, like those in a piano roll, the Frenchman Joseph Marie Jacquard automatically controlled which threads of the warp would be passed over or under with each pass of the shuttle. Babbage planned to use the same technique to program his machine; instead of the positions of threads, the holes in his cards would represent the mathematical commands to the machine. Wrote Babbage's mathematically knowledgeable friend Lady Lovelace, daughter of the poet Lord Byron: "We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves."
Babbage's loom, alas, never wove anything. By the time the eccentric genius died in 1871, he had managed to put together just a few small parts; only his elaborate drawings provide a clue to his visionary machine. Indeed, when Harvard and IBM scientists rediscovered Babbage's work in the 1940s while they were building a pioneering electromechanical digital computer called Mark I, they were astonished by his foresight. Said the team leader, Howard Aiken: "If Babbage had lived 75 years later, I would have been out of a job."
The Harvard machine occupied a large room and sounded, in the words of Physicist-Author Jeremy Bernstein, "like a roomful of ladies knitting." The noise came from the rapid opening and closing of thousands of little switches, and it represented an enormous information flow and extremely long calculations for the time. In less than five seconds, Mark I could multiply two 23-digit numbers, a record that lasted until ENIAC'S debut two years later. But how? In part, the answer lies in a beguilingly simple form of arithmetic: the binary system. Instead of the ten digits (0 through 9) of the familiar decimal system, the computer uses just the binary's two symbols (1 and 0). And with enough Is and 0s any quantity can be represented.
In the decimal system, each digit of a number read from right to left is understood to be multiplied by a progressively higher power of 10. Thus the number 4,932 consists of 2 multiplied by 1, plus 3 multiplied by 10, plus 9 multiplied by 10 X 10, plus 4 multiplied by 10 x 10 X 10. In the binary system, each digit of a number, again read from right to left, is multiplied by a progressively higher power of 2. Thus the binary number 11010 equals 0 times 1, plus 1 times 2, plus 0 times 2X2, plus 1 times 2X2X2, plus 1 times 2X2X2X2 —for a total of 26 (see chart).
Working with long strings of Is and 0s would be cumbersome for humans—but it is a snap for a digital computer. Composed mostly of parts that are essentially on-off switches, the machines are perfectly suited for binary computation. When a switch is open, it corresponds to the binary digit 0; when it is closed, it stands for the digit 1. Indeed, the first modern digital computer completed by Bell Labs scientists in 1939 employed electromechanical switches called relays, which opened and closed like an old-fashioned Morse telegraph key. Vacuum tubes and transistors can also be used as switching devices and can be turned off and on at a much faster pace.