# A density lemma

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Figure 2-3 were marked in a manner similar to the mu lti­ plication tables used today. This apparatus re­ duced multipl ication and division into simpler calculations of addition and subtraction (Figure 2-2). In 1 620, using the principles o f Napier's Bones, Edmund Gunter developed the first slide rule (Figure 2 - 3 ) . Since then the slide rule has been widely used by scientists, mathematicians, and businesspeople for performing rapid calculations. After 350 years of reliable service, the slide rule was made extinct almost overnight by the intro­ duction of the electronic pocket calculator in the early 1 970s.

FfiE 40 I ntroduction Supercomputers: A Special Breed Control Data Corporation has maintained its repu­ tation as an industry leader 1n the field of super­ computers since the second generation. When the CDC 6600 was fi rst announced. its rated speed of approximately 3 million operations per second was astonishing. Then the 6600 was replaced by the 7600, which cou ld perform 36 million operations per second, a n umber thought incredible at the time. During the fou rth generation, CDC an­ nounced the STAR- 1 00.

The machine was completely electronic, consisting of 1 9,000 vacuum tubes and tens of thousands of other electronic components. It had 500,000 sol­ dered joints and no moving parts. Unlike the ABC and today's binary computers, the EN IAC used decimal arithmetic. Every digit in the machine could contain any of the decimal digits from zero to nine. Counting proceeded from 0, 1 , 2, 3, 4, 5, 6, 7 , 8 , 9 and then to "O carry the 1 " to form the n u mber 1 0. In binary, only the digits zero and one are used, and n umbers are carried on every second count.