09/19/2006
A student, examining my email writes:
Sorry if I am mistaken but isn't that a NAND gate?
<<name withheld to protect the well-meaning student>>
Yale Patt wrote:
If A=1 and B and C both = 0 then what is the output
of all three at the intersection. (in the squiggly oval)
(The student included a .jpg file with the above question)
Thank you,
<<name withheld ...>>
Good! You have captured exactly the three-input AND gate that I put
on the board last week. Unfortunately, the email program I am using
does not allow me to simply attach the .jpg file you included, so
I will have to draw its essence here:
Rather than take a chance on anyone misunderstanding my message,
I thought I should make it clear. And, I thank the well-meaning
student since others may also be confused by my statement above.
What I said in my earlier email message was that the original writer
had "captured exactly the three-input AND gate that I put on the board
(in class) last week." The .jpg file that the student included was
indeed the AND gate that I put on the board, including the inverter
which I left out of my drawing below. I left it out in the interests
of time, since the output inverter was not relevant to the student's question.
Unfortunately, since it created confusion, I now wish I had left it in.
So, just to be clear, what I have drawn below is a NAND gate. If I add
the output inverter (as I did in class, and is in your notes perhaps),
we have an AND gate.
Got it? Good!
Yale Patt
_______ ________ _______
| | |
_| _| _|
|| || ||
A --o|| B --o|| C --o||
||_ ||_ ||_
| | |
| | |
---------------------------------------- the point in question.
|
_|
||
A --||
||_
|
|
_|
||
B --||
||_
|
|
_|
||
C --||
||_
|
|
---
\ /
Let's apply the 0s and 1s you suggest to the gates of all transistors
and see what we get.
With A=1, the corresponding P-type is an open circuit, and the
corresponding N-type is a closed circuit.
With B=0 (same for C), the P-type is closed and N-type is open.
If I now redraw the circuit, replacing the "opens" with broken connections
and the "closeds" with pieces of wire, I get:
_______ ________ _______
| | |
| | |
| |
1 -- 0 -- | 0 -- |
| |
| | |
| | |
---------------------------------------- the point in question.
|
|
|
1 -- |
|
|
|
|
0 --
|
|
|
0 --
|
|
---
\ /
Finally, we analyze what is going on. From "the point in question," there
are two direct connections (wires) to the power supply (2.9 volts). Also,
from "the point in question," the path to "ground" is broken so there is no
path to ground. Therefore "the point in question" is at 2.9 volts.
Therefore: the value 1.
Got it?
Yale Patt