Understanding Shannon's Expansion Theory

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SUMMARY

Shannon's Expansion Theorem provides a method for simplifying Boolean functions by expressing them in terms of a chosen variable. In the discussion, the function f is represented as f = x1'x2'x3' + x1x2'x3' + x1x2x3' + x1x2x3. The user seeks clarification on applying this theorem to design a 2-to-1 multiplexer, where x1 serves as the control input. Understanding this theorem is crucial for digital circuit design and optimization.

PREREQUISITES
  • Boolean algebra fundamentals
  • Knowledge of multiplexers and their functionality
  • Familiarity with digital circuit design concepts
  • Understanding of Shannon's Expansion Theorem
NEXT STEPS
  • Study the application of Shannon's Expansion Theorem in digital circuit design
  • Learn about the design and implementation of multiplexers
  • Explore Boolean function simplification techniques
  • Investigate practical examples of using Shannon's theorem in circuit optimization
USEFUL FOR

Students and professionals in electrical engineering, digital circuit designers, and anyone interested in mastering Boolean functions and multiplexer design.

Sinister
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I'm so confused on how Shannon's expansion theorem works. I'm wondering if someone could dummy it down for me.

For example:
f= x1'x2'x3' + x1x2'x3' + x1x2x3' + x1x2x3

and let's say I want a 2-1 multiplexer with x1 being the control
 
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anyone?
 
Most likely this can only be answered by an "old timer". I am making measurements on an uA709 op amp (metal can). I would like to calculate the frequency rolloff curves (I can measure them). I assume the compensation is via the miller effect. To do the calculations I would need to know the gain of the transistors and the effective resistance seen at the compensation terminals, not including the values I put there. Anyone know those values?

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