# boolean logic diagramn

• May 29th 2011, 09:19 PM
fran1942
boolean logic diagramn
Hello I cannot figure out how the path that I have labelled with the arrow works.
Apparently it is feeding the output back into the input, but how can you generate this output before your input is known ?

Can someone please help me understand how this works and how you would draw up a truth table to express it.

http://bphprint.co.nz/circ.jpg

Thanks kindly for any help.
• May 30th 2011, 01:09 AM
bryangoodrich
If I understand the gates (i.e., A connected to an OR-gate and B connected to an AND-gate) and connections correctly, we might express it as a statement:

Q = min(max(A, X), B')

Where B' = 1-B, X is unknown, and true inputs are 1, false inputs 0. There are four possible cases.

Spoiler:
Let A = B = 0 (B' = 1).
Q = min(max(0, X), 1)
Q = X

Let A = B = 1 (B' = 0)
Q = min(max(1, X), 0)
Q = 0

Let A = 0, B = 1 (B' = 0)
Q = min(max(0, X), 0)
Q = 0

Let A = 1, B = 0, (B' = 1)
Q = min(max(1, X), 1)
Q = 1

In three of the cases the output is wholly determined by the values of A and B, regardless of what X is. The one case that is mysterious is whenever A and B are both false. But if I think of this in terms of electric circuits, then if both A and B have no current, then there is no possible way for X to have current. Therefore, we can just define X = 0 there. I don't know if that is the current assessment, but I find that diagram a bit odd. These were my thoughts on it.

I noticed a second thought just now. By what I said above, X = A will produce the same results. Redefine the diagram in those terms and see what you think.