## 08 April 2008

### PIZZAQ -- what's this network of 6 Logic gates do? How hard can this be? Huh? I showed you how to do it.

Oh sure, click all you want.

Okay, three different Logic Gates have been defined HERE -- the NOT Gate (often called an inverter), the OR Gate, and the AND Gate.

There are other Logic Gates, but you can make digital circuitry do everything it can possibly do with the proper arrangement of just these three: NOT, OR, AND.

(I told you this would be on the Quiz.)

Again, these are just Pure Ideas. You could implement this circuit, and really make it work, with garden hoses and water, with gas and pipes and valves, with LEGO or TinkerToys, or with crank and clockwork.

But this whole thing really took off around 1950 (a little earlier if you count the secret war computers) with electronics: first vacuum tubes (valves), and then transistors, and finally integrated circuits -- teeny-tiny transistor networks manufactured on a single chip. So when most people see a diagram like this, they think of electric voltages and electronic elements.

But notice how completely free it is of any electric or electronic symbols, nothing about volts, nothing about ground/earth, no batteries, no plugs, no resistors or capacitors. To figure out how digital systems work, you don't have to know jack shit about electricity or electronics.

The whole idea is to shove inputs of logical 1 and logical 0
into it, and get specific desired logical outputs out the end.

Okay, this one's worth 7 pizza slices, a different topping on each one.

The inputs are P and Q. Fill in the Truth Table for the outputs R and S.

It's not just an arbitrary kludge of Gates intended to give you a 4-aspirin headache. It's a famous circuit that does something very important. There are gazillions of these in your fancy-schmantzy iPods and cell phones and laptops and pagers and calculators.

Please don't drive while talking on your cell phone. Two people have already rear-ended my truck, which was Not Moving, while they were yakking on their fucking cell phones. One in broad daylight, the other at a very well illuminated intersection. I promise you -- you'll be sorry. On Planet Vleeptron, talking on the cell phone while driving costs you a fine of 430,000 Zlubi and 9 horx in Re-Education, Fitness & Appropriate Socialization Camp.

Oh, I said the NOT Gate is also called an inverter. In electronic circuits, it does another job besides turning 0 into 1 or turning 1 into 0. In large, complicated circuitry, a voltage signal travelling through many stages can grow weak, and if that's not fixed, eventually the Gates will misbehave because they can't clearly figure out what the Logical Value of the input is supposed to be. The inverter boosts the weakening signal back up to its original design level.

In some digital electronic schemes, Logical 0 is represented by 0 volts DC, and Logical 1 is represented by +1 volt DC. If the signal weakens to something around +0.6 volts, gates may confuse the logical values. So designers liberally throw in NOT gates throughout the circuitry. If they really don't want to change the logic value at that stage, they connect 2 NOT gates in a row, because not(not(P)) = P .

Mike said...

It's been a really, REALLY long time since I've done one of these, but this is what I came up with:

RS
--
01
10
10
11

Vleeptron Dude said...

I hope you're happy, you just made me go back to the problem and follow the Boolean Algebra logic through it meticulously gate by gate to make sure I was right.

I was right.

You are not[right].

You ain't using some old perverted Negative Logic convention, are you? For this Pizza,

0 = False = No = 0 volts DC
1 = True = Yes = +1 volt DC

which is the way Real Americans do it. Maybe Eastern Europeans still do that 1 = False kind of thing. Maybe Klaas in Rotterdam is into that sick-o Neg Log stuph.