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Unformatted text preview: systems having two possible states (on/off, 0/1). (is this necessary? why not more discrete states?). Now one can perform logical operations with Boolean algebra (as we have already seen), and one can count in a base-2 number system. (How about other counting systems that we encountered in the very first lectures? Evolution of counting and numbers ) A line of n switches (latches), can be interpreted as an n-length binary number string, which therefore has 2 n possible values: Bit position 7 6 5 4 3 2 1 0 Decimal value 128 64 32 16 8 4 2 1 Example 0 0 0 1 0 1 0 1 There are 2 n numbers, from 0 2 n 1 Bit# n has value 2 n e.g. 10101 2 = 15 h = 21 10 Now, a copy of 10101 is 10101. It is indistinguishable from the original. Once a value in the real world has been approximated or encoded in this form, copies can be made that are not close to the real thing, but are exact ....
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- Fall '07