Understanding Shannon's Expansion Theory

  • Thread starter Thread starter Sinister
  • Start date Start date
  • Tags Tags
    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.
Sinister
Messages
32
Reaction score
0
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
 
Engineering news on Phys.org
anyone?
 

Thread 'How might electronics be different if AC voltage was 72V at 45 Hz?'

Hey guys. I have a question related to electricity and alternating current. Say an alien fictional society developed electricity, and settled on a standard like 73V AC current at 46 Hz. How would appliances be designed, and what impact would the lower frequency and voltage have on transformers, wiring, TVs, computers, LEDs, motors, and heating, assuming the laws of physics and technology are the same as on Earth?
View full post »

Thread 'What happens if shielded cable has a short to the shield?'

While I was rolling out a shielded cable, a though came to my mind - what happens to the current flow in the cable if there came a short between the wire and the shield in both ends of the cable? For simplicity, lets assume a 1-wire copper wire wrapped in an aluminum shield. The wire and the shield has the same cross section area. There are insulating material between them, and in both ends there is a short between them. My first thought, the total resistance of the cable would be reduced...
View full post »

Thread 'Why does the amperage go real high if there is a low voltage short?'

I used to be an HVAC technician. One time I had a service call in which there was no power to the thermostat. The thermostat did not have power because the fuse in the air handler was blown. The fuse in the air handler was blown because there was a low voltage short. The rubber coating on one of the thermostat wires was chewed off by a rodent. The exposed metal in the thermostat wire was touching the metal cabinet of the air handler. This was a low voltage short. This low voltage...
View full post »

Similar threads

MHB Synthesizing Functions using K-maps
Replies
3
Views
3K
I How deep does it need to go for a physics theory to be consistent?
2
Replies
50
Views
3K
Taylor Expansion/Equilibrium/Dependence of variables
Replies
1
Views
2K
I Is Hooke's law really not working, or is it me being dummy?
Replies
13
Views
2K
MHB Applying Shannons Expansion Theorem
Replies
3
Views
3K
Help understanding Shannon entropy
Replies
9
Views
4K
Help understanding closed line integrals
Replies
5
Views
3K
I How is a binomial expansion done?
Replies
4
Views
2K
MHB Partial Derivatives of Matrix/Vector Function: An Easier Way?
Replies
1
Views
2K
Understanding the Variables of the FT and DTFT: Intuition and Differences
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top