Build Instructions

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• 1

  ▇▇▇▇ Get Familiar with the Simulator ▇▇▇▇

  We are going to use an online simulator to develop logic circuits called the Falstad simulator. It is actually very handy as it can simulate lots of different kinds of circuits, but we are only going to use some of its features.

  When you go directly to the simulator, you'll see this screen:

  Starting Fresh

  Usually, I'll give you a link to a circuit that's already built. However, it is good to know how to operate the simulator directly. As you can see, there's always a simple analog circuit when you open the page. First thing to do is get rid of it. Click on Circuits and then Blank Circuit.

  Now you have a  blank page to work with. Note how RUN is in upper case and bold?

  That means the circuit is live. If you ever accidentally stop it (the STOP will be upper case and bold) then the circuit won't work until you press run. You might use that button to pause a simulation, but usually just leaving things running is fine.

  By the way, if you click on a link to view a simulation I've already set up for you the simulator may show the circuit off to one side of your screen or perhaps even entirely off your screen. To correct this, select Edit | Center Circuit from the simulator's menu.)

  Adding I/O

  A blank page isn't very interesting. Right click anywhere in the black area (by the way, the Options menu will let you pick a white background if you prefer). You will see a menu appear that will let you pick components to place. We will mostly be interested in Logic Gates, Input and Output along with Digital Chips.

  For now select Logic Gates, Input and Output and pick "Add Logic Input." 

  Then use your mouse to click and drag. Where you click will become a terminal and the far end of the drag will say L. Make the length as you please and let go of the mouse button. The whole thing should look something like this:

  The L stands for low which is another way of saying 0 -- one of the two logic states. If you click on the L, it will turn to an H which stands for high -- a logic 1. Each time you click, the input will change from L to H or H to L. In addition -- if you don't change the options -- a wire carrying a high logic level will appear green. A logic low wire will appear gray. Put another input down next to the first one like this:
  

  You shouldn't have to select the menu again. Just click and drag. You can make as many inputs as you want until you pick another component type from the menu.
  

  You might have noticed on the menu that next to the text "Add Logic Input" there was an "i." That's the keyboard shortcut. The shortcut for "Add Logic Output" is an "o." Try adding two outputs that line up with the inputs. Instead of selecting the menu, just press "o" and then click and drag. But before you do, let's think about where to put them. You'll want to click somewhere near the inputs and then drag away (to the right). See the next section if you want to know where to click or try it and then you can always delete anything you want to change after you read the next section.

  Wiring

  If you click directly on the terminal, the output will automatically connect to the input. Normally that isn't what you want, but in this case we do. Try drawing one connected output by clicking right on an input terminal and dragging. Then create the second output near the second input but not connected (like in the figure above). Here's what it should look like:

  To connect the input and output terminals you need a wire. You can select "Add Wire" off the right click menu or you can press its shortcut "w." Once you've picked the wire you can click on one terminal and drag to the other.
  

  If you make a mistake, just click on the element you want to remove and use the Delete key. Control+Z will undo your last action, too. The Edit menu has the usual entries like cut and undo, as well.

  Once you have connections made, you can click on the inputs and you'll see the corresponding outputs will change. When you make an input H you will see the entire wire will turn green. If not, you probably didn't make the connection the way you thought.

  You should wind up with something that looks like this link (the final image in the animation above). Obviously, you might have your positions and lengths a little different and that's OK.

  By the way, sometimes you want your diagrams to show 1 and 0 instead of H and L. You can right click on the input and select Edit and check the numeric box if you want that effect. It doesn't change the operation of the circuit, though.

  Next Steps

  Having an input tied to an output is not much of a logic circuit! In the next step we will do something more interesting. You can go ahead and select Blank Circuit from the Circuits menu to get ready for that.

  By the way, because the simulator totally in your browser, it is hard to save your work. If you look on the File menu, you can see there are several options to export your circuit as a link, in a file, or as text. You can also import text or a file. In the case of the link, just clicking on it loads the circuit which is what I use for the example links in this bootcamp.

• 2

  ▇▇▇▇ Understanding Basic Logic Gates ▇▇▇▇

  Open the simulator using this link and you'll see the three fundamental logic gates that will build up just about all kinds of logic. To the left are two logic inputs and each gate has its own output. Remember, you can click on the inputs to change from 0 (L) to 1 (H) and see the results.

  You can experiment and find the truth table -- a table that shows the outputs for all possible inputs -- for each gate. I'll call the top input "A" and the bottom input "B":

  Inverter:

  A	Output
  0/L	1/H
  1/H	0/L

  The inverter or NOT gate just flips the input to the opposite state.

  AND:

  A	B	Output
  0	0	0
  0	1	0
  1	0	0
  1	1	1

  In English, this gate says that the output will be true (or high) only if A AND B are 

  both true.

  OR:

  A	B	Output
  0	0	0
  0	1	1
  1	0	1
  1	1	1

  In English, this gate says the output will be true if either A or B is true.

  Multiple Inputs

  The inverter always has one input, but an AND or OR gate can have as many as you like as long as there are at least two. In the simulator, if you double click a gate that can have more inputs, you will see a dialog that lets you set the number of inputs you want. 

  In the case of an AND gate, all inputs -- no matter how many -- have to be high/true/1 for the output to go high. For an OR gate, any input high will set the output, no matter how many inputs there are.

  Assertions

  In general, you'll hear people use the words 1 and high used interchangeably to mean a logic 1. However, there is another phrase you'll often hear: asserted. This phrase is a bit tricky. Suppose I have a door open sensor that is a pull up resistor and a normally open switch to ground. When the door is closed, the switch will engage and the output will be low.

  Note the bar over the signal name "Door Closed"? That means the signal is inverted. So a low means the door is closed and a high means it is not. We would often say a signal is "asserted" and in this case that would mean the door IS closed, which is a low. You might also hear the signal is "true" when it it low, although you can't always be sure as sometimes people will say "true" meaning 1. 

  Notice this is all in how I choose to name things. If I called the signal "Door Open" it wouldn't need a bar and asserted would then be high even though the circuit didn't change at all. 

  Because it it hard to draw bars over things when typing, you'll sometimes see other ways to indicate a negative true signal:

  • a leading slash (/Q)
  • a lower-case n prefix or suffix (nQ or Q_n)
  • a trailing  # (Q#)
  • an "_B" or "_L" suffix (Q_B or Q_L)

  A Practical Design Experiment

  Suppose you had a black box that connected to the door sensor that chimes when the door is open (that is, the sensor output is high). We have a requirement to add a second door. What logic gate would you use to make the chime sound if either door opens?

  Your answer should be an OR gate. If either sensor goes high, the output goes high and, thus, the chime sounds.

  Now, suppose the black box chimes when the signal is low (that is, the door is closed). We want to chime (low input to black box) if either door is closed). An OR gate won't do it now because the logic is reversed.

  The truth table for our function is:

  Door 1#	Door 2#	Chime#
  0	0	0
  0	1	0
  1	0	0
  1	1	1

  If you look back in the next section, you'll see that this is an AND gate. In fact, for inverted inputs, and AND gate will act like an OR gate and -- you can probably guess -- an OR gate acts like an AND gate.

  You don't need to remember the name, but this is Demorgan's theorem. You could have got the same effect by inverting the inputs and then using the gate you'd expect (that is, an OR gate). Then you'd have to invert the output to send to the black box. So now you'd have 4 gates where 1 would do the job.

  Minimizing logic like this used to be a big part of digital design. Now (in future bootcamps) we will describe what we want and the computer will figure out the most efficient way to implement it.

• 3

  ▇▇▇▇ More Advanced Logic Gates ▇▇▇▇

  This circuit is similar to the previous one, but it show two new gates: NAND and NOR. These are simply an AND gate and an OR gate with an inverter at the output. So where an AND gate will output a 1, a NAND gate will output a 0. Obviously, you can make these with two gates and the symbol suggests this (an AND or OR gate with a little circle at the output). However, these can often be implemented as a single gate, so it is handy to have symbols for them.

  Here's another circuit with a different composite gate.

  See the bottom gate that looks like an OR gate with an extra line? This is a two input gate that has a high output if either input is high, but not both. The three gates at the top (an OR, a NAND, and an AND) implement the same function. That proves that you don't have to have an XOR gate, but it is so useful that it is handy to have a single symbol for it.

  This kind of gate is called an exclusive OR or XOR gate. There are two things that make it very useful. 

  First, look at the XOR truth table:

  A	B	Output
  0	0	0
  0	1	1
  1	0	1
  1	1	0

  You might make two observations. If A is 0, then the output is a copy of B (or, if you prefer, if B is 0, then the output is a copy of A). But if A is 1, the output is the inverts of B (and the same holds true if B is 1, the output is the inverse of A). This makes the XOR gate a sort of programmable inverter.

  The other thing to note is that using binary addition, the output is the sum of A+B. You might wonder how 1+1=0. Well, if you answer is a single bit that's correct, but there is an extra carry bit. This circuit doesn't compute the carry bit, but it does compute the sum. In a future bootcamp, you'll see how the XOR and some other logic can add numbers together in a configuration called a half adder or a full adder.

  By the way, the top set of gates is one way to create an XOR gate. You can actually make one using several other methods (for example, using all NAND or NOR gates). So if you see a different schematic for the inside of an XOR gate, that's OK. There's more than one way to do it.

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