L08_digital_abstraction

L08_digital_abstraction - The Digital Abstraction ! Analog...

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The Digital Abstraction Analog Signaling & Noise Digital Signaling, Noise Margins Sampling Theorem Quantization Noise 6.02 Spring 2008 The Digital Abstraction, Slide 1 Representing information with voltage Representation of each point (x, y) on a B&W Picture: 0 volts: BLACK 1 volt: WHITE 0.37 volts: 37% Gray etc. Representation of a picture: Scan points in some prescribed raster order… generate continuous voltage waveform 6.02 Spring 2008 The Digital Abstraction, Slide 2
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Information Processing in the Analog Domain First let’s introduce some processing blocks: v Copy v INV v 1-v 6.02 Spring 2008 The Digital Abstraction, Slide 3 Why have processing blocks? The goal of modular design: ABSTRACTION What does that mean anyway? Rules simple enough for a 6-3 to follow… Understanding BEHAVIOR without knowing IMPLEMENTATION Predictable composition of functions Tinker-toy assembly Guaranteed behavior under REAL WORLD circumstances 6.02 Spring 2008 The Digital Abstraction, Slide 4
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? Let’s build a system! Copy INV Copy INV Copy INV Copy INV output (Reality) input 6.02 Spring 2008 The Digital Abstraction, Slide 5 Why did our system fail? Why doesn’t reality match theory? 1. COPY Operator doesn’t work right 2. INVERSION Operator doesn’t work right 3. Theory is imperfect 4. Reality is imperfect 5. Our system architecture stinks ANSWER: all of the above! Noise and inaccuracy are inevitable; we can’t reliably engineer perfect components – we must design our system to tolerate some amount of error if it is to process information reliably. 6.02 Spring 2008 The Digital Abstraction, Slide 6
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The Key to System Design A system is a structure that is guaranteed to exhibit a specified behavior, assuming all of its components obey their specified behaviors. How is this achieved? Contracts! Every system component will have clear obligations and responsibilities. If these are maintained we have every right to expect the system to behave as planned. If contracts are violated all bets are off. 6.02 Spring 2008 The Digital Abstraction, Slide 7 The Digital Abstraction Real World “Ideal” Abstract World Volts or Electrons or Ergs or Gallons Bits 0/1 Noise Manufacturing Variations Keep in mind that the world is not digital, we would simply like to engineer it to behave that way. Furthermore, we must use real physical phenomena to implement digital designs!
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L08_digital_abstraction - The Digital Abstraction ! Analog...

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