Mba In Mis Essay

4097 words - 17 pages

Given a flip-flop circuit,
Determine how the circuit will behave for a sequence of inputs.
  Be able to use a flip-flop to store a single bit.

Basic Circuit
        Here's a basic circuit that involves just two NAND gates.  There are two inputs to this circuit, X and Y.  Can you generate a truth table for this circuit?

* Note that there is no connection where the two wires running from the output back to the input cross.
        Let's address that issue of the truth table.  Here is a truth table for you to fill in.  (Print this web page if you want to work on it.)
X | Y | P | Q |
0 | 0 |   |   |
0 | 1 |   |   |
1 | 0 |   |   |
1 | 1 |   |   |
        Let's review ...view middle of the document...

  In that situation, X = 0, and Y = 1.
* If X = 0, then P = 1.  We know that if either input to a NAND gate is 0, the output is 1.  That's the same as before.
* Now. try to take advantage of the knowledge that P = 1.  If P = 1 AND Y = 1, then Q = 0.
* That gives us the second entry in the truth table above.  Here's the truth table with what we have figured out so far.
X | Y | P | Q |
0 | 0 | 1 | 1  |
0 | 1 | 1 | 0  |
1 | 0 |   |   |
1 | 1 |   |   |
        Next, let's address the third entry in the truth table.  In that situation, X = 1, and Y = 0.
* If Y = 0, then Q = 1.  We know that if either input to a NAND gate is 0, the output is 1.  That's the same as before.  However, this time, we take advantage of knowing that Y = 0.  Before, it was X that was equal to zero, but X = 1 here and it doesn't help us get started.
* Now. try to take advantage of the knowledge that Q = 1.  If Q = 1 AND X = 1, then P = 0.
* That gives us the third entry in the truth table above.  Here's the truth table with what we have figured out so far.
X | Y | P | Q |
0 | 0 | 1 | 1  |
0 | 1 | 1 | 0  |
1 | 0 | 0 | 1 |
1 | 1 |   |   |
        Finally, we have the case where X = 1 and Y = 1.
* If X = 1, then we need to know Q to determine P.
* If Y = 1, then we need to know P to determine Q.
* We are stuck!  There is no obvious way to proceed!
        There is one way to proceed.  We could just assume that P = 1, for example.  Let's try that.
* If Y = 1, and P = 1, then we know that Q = 0.
* If we know that Q = 0, it is an input  to the top NAND gate, so the output there is 1.  Thus, P = 1.  That's what we assumed to start with, so we don't get a contradiction.
* All is copasetic!  Or is it?
* Here is the truth table.
 
X | Y | P | Q |
0 | 0 | 1 | 1  |
0 | 1 | 1 | 0  |
1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 |
        This is interesting, but we need to note the following.
* This result is not at all intuitive.
* The circuit is symmetric.
* If we have symmetric inputs (X = 1, Y = 1), we should have symmetric outputs.
* Instead, we seem to have shown that P = 1 and Q = 0.  That's not at all symmetric, and it it bothersome.
* We got to the result by making an unsymmetrical assumption.  We assumed P = 1.
        What if we made the opposite assumption?  Let's assume P = 0.
* If P = 0, then Q = 1 since P is an input to the bottom NAND gate.
* If we know that Q = 1, it is an input  to the top NAND gate, so the output there is P = 0 since the other input to the top gate, X, is also 1.
* But, P = 0 is what we assumed to start all this.  Again, we do not get a contradiction, so everything seems OK.
* Here is the truth table for this situation.
 
X | Y | P | Q |
0 | 0 | 1 | 1  |
0 | 1 | 1 | 0  |
1 | 0 | 0 | 1 |
1 | 1 | 0 | 1 |
        Now, we can't have it both ways.  This truth table summarizes what we have found.
 
X | Y | P | Q |
0 | 0...

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