The majority function is a Boolean function $f(x, y, z)$ that takes the value 1 whenever a majority of the variables $x,y,z$ are 1. In the circuit diagram for the majority function shown below, the logic gates for the boxes labeled P and Q are, respectively,
(D) is the correct choice!
I tried with OR OR and I'm getting f as majority too. Where am I wrong?
why not x¯P+xQ=f
please anyone explain
The simplest method, no need to go for wasting time in k-map.
The function is 1 only when the majority is one, it means in function f(x,y,z) at least two var. must be 1.
now observe from the given mux and the above table:
when x = 1, in order to get f(x,y,z) = 1, there must be OR between y and z.
when x == 0, in order to get f(x,y,z) = 1, there must be AND between y and z.
Here when x=0 we get Q operator and when x=1 we get P operator.
So looking to the truth table in below image:
we can see when x=0 yz do AND operation and when x=1 yz do OR operation.
So P is OR gate and Q is AND gate.