Understanding Shannon's Expansion Theory

Thread starter Sinister
Start date Oct 10, 2011
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Expansion

AI Thread Summary

Shannon's Expansion Theorem allows for the decomposition of Boolean functions based on a chosen variable, simplifying circuit design. The theorem states that any Boolean function can be expressed as a combination of two sub-functions, depending on whether the variable is true or false. In the context of a 2-1 multiplexer, x1 serves as the control signal, determining which of the two inputs is passed to the output. By applying the theorem, one can break down complex functions into simpler components, making it easier to implement in digital circuits. Understanding this foundational concept is crucial for effective digital design and optimization.

Oct 10, 2011

Sinister

I'm so confused on how Shannon's expansion theorm 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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Oct 11, 2011

Sinister

anyone?

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