DC2 - systems having two possible states(on/off 0/1(is this...

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Digital circuits II – what’s so special? Digital electronics, we are breathlessly informed (almost daily, it seems) are about to take over our world, or are already doing so, or have done already. Why is this? There are two basic reasons: 1. Noise tolerance from nonlinearity Look at the Schmitt Trigger (compare response to open-loop op-amp). e0 ei 0.7 2.5 5 0 Switch Logic Voltage (V) ON 1 5 OFF 0 0 Since e 0 is almost always saturated, it is either always in one or another of two positions, and can act like a logic switch. We get the following properties: -- very good noise tolerance -- complex circuits can be built from large numbers of simple elements -- i/o characteristics are very precise 1
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2 2. Exact, not approximate, repetition, duplication First, a brief look at numbers and counting in the digital world. Binary logic, representation, counting and number systems The bistable latch, and Schmitt trigger properties can be conveniently described as binary
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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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DC2 - systems having two possible states(on/off 0/1(is this...

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