digital design

Discussion in 'General Electronics Chat' started by Anne Rachel, Jan 27, 2013.

  1. Anne Rachel

    Thread Starter New Member

    Jan 22, 2013
    I have a question regarding digital design.

    Let x (1), x (2)… x (n) be binary variables. A function f(x(1),x(2),….x(n)) is called a threshold
    switching function iff,
    f(x(1),x(2),…x(n)) = 1 if x(1)a(1)+x(2)a(2) +….. x(n)a(n) > T
    = 0 if x(1)a(1)+x(2)a(2) +….. x(n)a(n) <= T
    Where a (1), a (2) … a (n) and T are real numbers called weights and threshold (T). Show that threshold switching functions can be used to realize any combinational switching function.

    The question seems to be unclear for me.

    thanks in advance for your help
  2. Salaja

    New Member

    Jan 27, 2013
    this kind of reminds me of neural networks.

    each neuron takes inputs, puts a weight on them, and adds them together. if the end result is greater then a threshold, then the output is 1, if it is less, the output is 0.

    and yes, you can emulate any logical circuit with enough of them.

    try proving that each logic gate can be created, and if you can prove that any "combinational switching function" (whatever that is) can be created from logic gates, then you are done.

    eg: AND gate: 2 inputs, weights: 0.75 and 0.75, threshold = 1. the only way to meet the threshold is if both inputs are 1's.

    that said, the question is confusing and i may have misinterpreted it.
  3. Anne Rachel

    Thread Starter New Member

    Jan 22, 2013
    thanks a lot :) It was useful!!