# Two different 3-AND gates: correct implementation?

One of the questions in my textbook (Introduction to Computing Systems) asks to design a 3-input AND gate. The given solution is as follows:

simulate this circuit – Schematic created using CircuitLab

If I am reading this correctly, this is a 3-NAND–NOT combination. I don't understand why you need the NAND–NOT instead of just creating an AND by itself. My proposed schematic is the following:

simulate this circuit

This seems simpler, and uses fewer transistors, so I'm guessing that there's some reason that it won't work (otherwise it would be the example solution!). I don't see any possibilities for short-circuiting: if NAND(A,B,C), then NOT OUT, so there will be no path from power to ground (because it would have to go through OUT). On the other hand, I do think that everything is properly grounded: if NAND(A,B,C), then OUT should have a path to ground through whichever of (A,B,C) is logically false.

What am I missing?

• I'm not quite sure how to use the schematic editor. If someone wants to replace my images, please feel free! – wchargin Dec 14 '14 at 17:55
• You're missing how MOSFETs work and what the gate voltage (Vgs) has to be. – Majenko Dec 14 '14 at 17:59
• – Ignacio Vazquez-Abrams Dec 14 '14 at 18:04

The problem here is that you're misunderstanding (or not having the basic understanding) of how MOSFETs work, in particular the $V_{GS}$.

On an N-channel MOSFET the gate voltage has to rise a certain amount above the source pin. On a P-channel it has to fall a certain amount below the source pin.

In your schematic the N-channel's source is connected to $V_{CC}$ and the P-channel's to GND. If the threshold is, say, 1.2V (a reasonable logic level threshold), then the input logic HIGH would have to be at least 1.2V above $V_{CC}$ and the logic LOW would have to be below -1.2V.

That, as you can see, just isn't practical.

• You're certainly right that I don't understand how these work :) Is $V_{CC}$ just the battery/power voltage? (The bar at the top of my hand-drawn schematic?) And what is $V_{GS}$? – wchargin Dec 14 '14 at 18:13
• Hmm...so is the key that the gate voltage is compared relative to the source voltage, as opposed to, say, $0\,\mathrm{V}$? In that case, would it ever make sense to connect an N-type transistor to power or a P-type transistor to ground? – wchargin Dec 14 '14 at 18:30
• There are times when you would do that, but you generally require a special driving circuit. In normal logic it's never used like that. – Majenko Dec 14 '14 at 19:10
• $V_{GS}$ is the difference in voltage between the gate and the source pins. $V_{CC}$ is the supply voltage (battery voltage). – Majenko Dec 14 '14 at 19:11
• Thanks very much for your help! You've certainly given me some things to think about. – wchargin Dec 14 '14 at 22:14