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Showing posts with label logic gates NOT OR AND inverter. Show all posts
Showing posts with label logic gates NOT OR AND inverter. Show all posts

09 April 2008

LOGIC GATE PIZZAQ was WRONG!!!!!!! I was Not Perfect! Now I'm perfect, and the prize now also includes small antipasto

I WAS NOT PERFECT.
I MADE A MISTAKE.
I HATE THAT.

Okay, much gratitude to Mike, who (a.) usually is the only guy in C-space with the guts to try to answer these math nerd PizzaQs and (b.) is usually right.

In my first post about Logic Gates, I got the shapes of the AND and the OR gates right.

But when I asked the PizzaQ, I screwed the pooch and switched the shapes around (and left out the text inside the gates).

Thanks to Mike, the PizzaQ is now fixed.

You can trust this diagram. Really. It works now.

Mike, you got to fill in the table again, sorry. Obviously this is a different circuit from the one you tried to solve.

As expiation for my skroo-up, we are upping the prize to the 7 slices PLUS a small antipasto.

In private e-mail, Mike emphasized how rusty he was with all this, but I think I trumped him on rusty. The last time I had to know this crap for tests was maybe 1967.

My Logic textbook was Irving Copi's 5th Edition, which began with a preface that explained that a week after he published 10,000 copies of the 4th edition, some nice fellow wrote him a letter to tell him that 10 of his Quantification Rules were Wrong. So yeah, I screwed the pooch on this PizzaQ. But it could have been worse.

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 .