digital-logic
I'm having a bit of trouble figuring out how the truth table was filled in. I understand how to draw the diagram from the first table and I understand the boolean expression given from the truth table but I can't quite grasp how the truth table was filled in. Could anyone do me a favor and explain it for me?
The answer is the inverse of X0
i.e. \$Y = \bar{X_0}\$
It's clearly this because if \$X_0\$ is 1 then the number is an odd number. Sometimes you've just got to look at the truth table without thinking much about boolean algebra.
I entered your truth table into Logisim's combinational analysis window and got this. Is that what you're looking for?
As far as having two bits of state, it doesn't really matter so long as the outcome is the same. I just used S0 and S1 for the old state and BCar and CCar for the Input. New0 and New1 are the new output state.
Best Answer
The way the truth table was filled is the following: You make a list of all the possible states and inputs, in this case A-D in with their respective mapping and X either 0 or 1 for this case. This should cover columns y1,y2 and X. Then we reference the first table, Which tells me that for State A[y1=0,y2=0]and X=0, my next state should be D[Y1=1,Y2=1] and my output Z, and so on and so forth until you go through all the possible states and input combinations