Hello! I've been wanting to begin my adventure with electronics for a long time, and without thinking that much about it, i kickstarted it by choosing to build an ALU for mu project on physics. Its nothing to complicated, the logical part is allready done, but i didn't predict electronics would be this confusing.

I've been reading quite a lot about it but there are some things that i can't understand, and sadly my teacher doesn't know much besides what she is supposed to know, so i have nobody to ask.

To begin with i read this article:
http://www.dummies.com/how-to/content/electronics-projects-how-to-create-a-transistor-no.html
and i dont understand one thing. When the base of the transistor goes HIGH, it allows the current to flow through the transistor. This ground path through the transistor creates a shortcut that bypasses the output, which causes the output to go LOW.But what is the definition of a shortcut in this case? There are 2 available paths for the current, why doesn't it take the path with the diode or split between 2 paths?

I know this question may seem stiupid to you, but im completely new to electronics. All i know are basics of electricity, which is ohms law and couple others.
Reference image:

If we assume there's some impedance on the output, current flows through the transistor because it's effectively a short circuit to ground (the BJT looks like a short circuit when the base is high, and an open circuit when the base is low, in a simplified model).

Because we assume the transistor is driving something with nonzero impedance (resistance) on the output, current flows through the zero-impedance path rather than go anywhere else. This is why there's a resistor between the supply rail (VCC) and the transistor-- if there weren't, there would effectively be unlimited current flowing through the transistor when on, because there would be a dead short between VCC and GND.
Thank you! Its all much clearer now.
Okay, so i have made a XOR gate using 4 NAND gates. Here is the simulator applet i used:
http://www.falstad.com/circuit/
And here is the circut. Click on File then Import and paste this:

Code:
$ 1 5.0E-6 10.20027730826997 50 5.0 43
t 160 160 208 160 0 1 0.6262009277122044 0.6381821463329849 100.0
t 160 208 208 208 0 1 0.16587646797966293 0.6291679244752422 100.0
t 336 96 384 96 0 1 0.37195528387207766 0.47520789187434687 100.0
t 336 144 384 144 0 1 -0.15101088839286564 0.4752548225613516 100.0
t 336 240 384 240 0 1 -0.20325125170483377 0.47495334370951003 100.0
t 336 288 384 288 0 1 0.6288662316295033 0.6291679244752422 100.0
t 496 144 544 144 0 1 0.6256125758423393 0.6766801708579545 100.0
t 496 192 544 192 0 1 0.6256681401615507 0.6785062882600826 100.0
w 544 160 544 176 0
w 384 112 384 128 0
w 384 256 384 272 0
w 208 176 208 192 0
s 160 160 112 160 0 0 false
s 160 208 112 208 0 0 false
g 208 224 208 272 0
g 384 160 384 192 0
g 384 304 384 336 0
g 544 208 544 224 0
w 160 160 160 96 0
w 160 96 336 96 0
w 336 288 160 288 0
w 160 208 160 288 0
w 384 80 496 80 0
w 496 80 496 144 0
w 384 224 496 224 0
w 496 224 496 192 0
162 592 128 592 208 1 2.1024259 1.0 0.0 0.0
w 544 208 592 208 0
r 544 128 544 80 0 100.0
w 544 128 592 128 0
r 384 224 432 176 0 1000.0
r 384 80 416 48 0 1000.0
r 208 144 208 80 0 1000.0
r 64 160 112 160 0 1000.0
r 64 208 112 208 0 1000.0
w 208 144 272 144 0
w 272 144 272 240 0
r 272 144 336 144 0 100.0
r 272 240 336 240 0 100.0
w 64 160 64 208 0
R 64 32 32 32 0 0 40.0 5.0 0.0 0.0 0.5
w 64 32 64 160 0
w 208 80 208 32 0
w 208 32 64 32 0
w 432 176 432 32 0
w 416 48 416 32 0
w 544 80 544 32 0
w 544 32 432 32 0
w 432 32 416 32 0
w 416 32 208 32 0


Now i have a 1000 holes in my breadboard so i have to do my best to have as few components as possible if i want to make an alu on it. In the worst case im only going to implement 4 basic logic functions and addition, so that it may be called for an ALU.

Anyway my question is if you see any way to optimize this circut? I mailnly mean resistors, but if there is a better way to combine gates than 4 NANDs then it could help as well.[/url]
  
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