Pull the Lab 10 files from the lab starter repository with
$ git pull starter master
All the work in this lab will be done from the program Logisim Evolution, which is included in the lab starter files. Please use the .jar file we've given you, not the version of Logisim that is downloaded on the lab computers! And a note: Logisim does not save your work as you go along, and it does not automatically create a new .circ file when you open it! Save when you start, and save frequently as you work.
$ java -jar logisim-evolution.jar
Part 0: The Basics (Warm-Up)
We'll begin by creating a very simple circuit just to get the feel for placing gates and wires. Before you start, take note of a useful feature: the zoom function! It's in the bottom left corner, and will make your life much easier for the next couple weeks.
- Start by clicking the "AND gate" button. This will cause the shadow of an AND gate to follow your cursor around. Click once within the main schematic window to place an AND gate.
- Click the "Input Pin" button. Now, place two input pins somewhere to the left of your AND gate.
- Click the "Output Pin" button.
Then place an output pin somewhere to the right of your AND gate. Your
schematic should look something like this at this point:
- Click the "Select tool"
button. Click and drag to connect the input pins to the left side of the AND
gate. This will take several steps, as you can only draw vertical and
horizontal wires. Just draw a wire horizontally, release the mouse button,
then click and drag down starting from the end of the wire to continue
vertically. You can attach the wire to any pin on the AND gate on the left
side. Repeat the same procedure to connect the output (right side) of the
And Gate to the LED. After completing these steps your schematic should look
roughly like this:
You can also change the number of inputs of the "AND gate" by clicking it using the select tool and changing the properties in the bottom left segment of the window. This can also be done before you put down the component.
- Finally, click the "Poke" tool and try clicking on the input pins in your schematic. Observe what happens. Does this match with what you think an AND Gate should do?
Part 1: Sub-Circuits
Just as C programs can contain helper functions, a schematic can contain subcircuits. In this part of the lab, we will create several subcircuits to demonstrate their use.IMPORTANT NOTE: Logisim Evolution guidlines say you cannot name a subcircuit after a keyword (e.g. "NAND"), also circuit names must start with "A-Za-z", so no numbers.
- Create a new schematic (File->New) for your work.
- Create a new subcircuit (Project->Add Circuit ). You will be prompted for a name for the subcircuit; call it NAND1 (note the 1 at the end; because there is a component called NAND, you cannot call it NAND).
- In the new schematic window that you see create a simple NAND circuit with 2 input pins on the left side and an output pin on the right side. Do this without using the built-in NAND gate from the Gates folder (i.e. only use the AND, OR, and NOT gates provided next to the selection tool icon). You can change the labels for the inputs and output by selecting the input/output using the select tool and changing the property "Label" in the bottom left of the window.
- Go back to your "main" schematic by double-clicking "main" in the circuit selector at the left of the screen. Your original (blank) schematic will now be displayed, but your NAND circuit has been stored.
- Now, single click the word "NAND1" in the list. This will tell Logisim that you wish to add your "NAND1" circuit into your "main" circuit.
- Try placing your NAND circuit into the "main" schematic. If you did it correctly, you should see a gate with 2 input pins on the left and one output pin on the right. Try hooking input pins and output pins up to these and see if it works as you expect.
- Repeat these steps to create several more subcircuits: NOR, XOR, 2-to-1 MUX, and 4-to-1 MUX. Do not use any built in gates other than AND, OR, and NOT. However, once you've built a subcircuit, you may use it to build others.
Hint: Try writing a truth table. You might also find the lecture slides useful for a refresher on how to build these. You may want to consider using some of your custom subcircuits when designing the others.
- Show your five circuits (NAND, NOR, XOR, 2-to-1 MUX, and 4-to-1 MUX) to your TA. Make sure you took note of the bolded word in step 3.
Part 2: Storing State
Let's implement the circuit we've been talking about in lecture that increments a value ad infinitum. The difference between this circuit and the circuits you've built for lab so far is that you need some registers. The following will show you how to add registers to your circuit.
- Create a new subcircuit (Project->Add Circuit). Name this new subcircuit, AddMachine.
- Load in the Arithmetic Library if it is not already loaded (go to Project->Load
Library->Built in Library and select "Arithmetic"). This library contains elements
that will perform basic mathematical operations. When you load the library, the circuit
browser at left will have a new "Arithmetic" folder.
- Select the adder subcircuit from the "Arithmetic" library and place the adder into your AddMachine subcircuit.
- Load in the Memory Library if it is not already loaded (go to Project->Load Library->Built in Library and select "Memory"). This library contains memory elements used to keep state in a circuit. A new "Memory" folder will appear in the circuit browser.
- Select the register from the "Memory" folder and place one register into your
subcircuit. Below is an image diagraming the parts of a register.
- Connect a clock to your register. You can find the clock circuit element in the "Wiring" folder in the circuit browser.
Connect the output of the adder to the input of the register and the output of the register to the input of the adder.
You may get a "Incompatible widths" error when you try to connect components. This means that your wire is trying to connect two pins together with different bit widths. If you click on the adder with the "Selection" tool, you will notice that there is a "Data Bit Width" property in the bottom left field of the window. This value determines the number of bits each input and output the adder has. Change this field to 8 and the "Incompatible widths" error should be resolved.
Wire an 8-bit constant 1 to the second input of the adder. You can find the "constant" circuit element in the "Wiring" library.
Add two output pins to your circuit so that you may monitor what comes out of the adder and the register. Make sure the output is 8 bits. Thus, by the end, your circuit should look like as follows:
Now let's see if you built your circuit correctly.
- Go back to the "main" subcircuit by double clicking on "main" in the circuit browser.
- Single click on your "AddMachine" circuit to select it.
- Change the "Facing" property to another direction. Any circuit with the "Facing" property can be rotated to accomodate wires as you need them. This will definitely be useful when you do your project.
- Place your AddMachine subcircuit into the main subcircuit.
- Select the AddMachine subcircuit you just placed into main.
- Connect output pins to the AddMachine subcircuit. Output pins are ordered top to bottom, left to right. Thus, if you followed the schematic above, then the top pin on the right side outputs the value of the adder, and the bottom pin is the output of the register.
Right click on your AddMachine subcircuit, and select "View AddMachine. This is the ONLY method to preserve state (i.e. keep register values at its current value). Double-clicking on the circuit at the circuit browser at left makes logisim think you want to edit the circuit instead of just checking what state the circuit has.
Note: You can use Simulate->Go In To State->*Circuit Name*, but that allows you go into the first circuit of that type. If you placed two Fib8 circuits down, it only takes you to the first Fib8 circuit you put down.
- Initialize the register value to 1. You can do this by first, clicking on the register value with the poke tool. Then, type the hex value in.
- To return to the main circuit while preserving state, go to Simulate->Go Out To State->main. Alternatively, you can hold the Command key (control on windows) and press Up-Arrow.
- Now start running your circuit by going to Simulate->Ticks Enabled (or Command/Control + K). Your circuit should now be outputting a counter in binary form.
- If you want to run your circuit faster, you can change the tick frequency in Simulate->Tick Frequency.
- Show your AddMachine circuit to your TA.
Part 3: FSMs to Digital Logic
Now we're ready to do something really cool; translate a FSM into a digital logic circuit.
For those of you who need a reminder, FSM stands for Finite State Machine. FSM's keep track of inputs given, moves between states based on these inputs, and outputs something everytime something is input.
If you've been paying attention in lecture you've noticed that the circuit we built in part 2 looks eerily similar to the diagram of a general FSM circuit. The skeleton file we give you contains a similar circuit. Modify this circuit to implement the following FSM:
If two ones in a row or two zeroes in a row have ever been seen, output zeros forever. Otherwise, output a one.
Note that the FSM is implemented by the following diagram:
Observe that the following is a truth table for the FSM:
st1 st0 input | next st1 next st0 output 0 0 0 | 0 1 1 0 0 1 | 1 0 1 0 1 0 | 1 1 0 0 1 1 | 1 0 1 1 0 0 | 0 1 1 1 0 1 | 1 1 0 1 1 0 | 1 1 0 1 1 1 | 1 1 0
We've provided you with a starter Logisim circuit to start out in FSM.circ
Note that the top level of the circuit looks almost exactly the same as our previous adder circuit, but now there's a FSMLogic block instead of an adder block. FSMLogic is the combinational logic block for this FSM. We have handled the output bit for you, as it's the most complicated to simplify and implement. You should complete the circuit by completing the StateBitOne and StateBitZero subcircuits, which produces the next state bits.
You could go from the truth table to SOP to a circuit, or you could notice that for each state bit, there are only two situations in which it is zero. This could make your life easier if you think a bit outside the box...
- Show your StateBitZero circuit to your TA and demonstrate that it behaves correctly.
- Show your StateBitOne circuit to your TA and demonstrate that it behaves correctly.
Feel free to do each part as separate sub-circuits in the same Logisim file.
The following parts will introduce you to more advanced techniques/concepts in Logisim.
Here are three Logisim features that should both save you a lot of time and make your circuits look much cleaner.
Splitters allow you to take a multi-bit value and split it up into smaller parts, or (despite the name) combine multiple values that are one or more bits into a single value. Here, we split the 4-bit binary number "1001" into "10" and "01", then recombine it with "11" into the final 6-bit number "111001":
Click on a splitter to get its menu in the sidebar. You can use this menu to determine the number of arms on your splitter and how many bits should go on each arm. For the circuit above, the left splitter's menu looks like this:
While the right splitter's menu looks like this:
Notice that there's an option called "facing". You can use this to rotate your splitter. Above, see that the splitter on the right is facing West while the splitter on the left is facing East.
If you see an error wire that is orange, this means that your bit width in does not match your bit width out. Make sure that if you're connecting two components with a wire, you correctly set the bit width in that component's menu.
A tunnel allows you draw an "invisible wire" to bind two points together. Tunnels are grouped by case-sensitive labels give to a wire. They are used to connect wires like so:
Which has an effect such as the following:
Some care should be taken as to which wires are connected with tunnels to which other wires, such as in this case:
Which in turn has the following effect:
We strongly recommend you use tunnels with Logisim, because they make your circuits much cleaner looking, and therefore easier to debug.
When changing the width of a wire, you should use a bit extender for clarity. For example, consider the following implementation of extending an 8-bit wire into a 16-bit wire:
Whereas the following is much simpler, easier to read, and less error-prone:
Additionally consider the case of throwing out bits. In this example, an 8-bit wire is being converted into a 4-bit wire by throwing out the other bits:
Despite the implications of its name, a bit extender can also do this same operation:
Part 4: Practice with Splitters
We're going to construct a circuit that manipulates an 8-bit number.
- Create a new subcircuit and name it "Ex4".
- Add an 8-bit input pin to your circuit and label it "In1".
- Add a 1-bit output pin labeled "Out1" and an 8-bit output pin labeled "Out2" to your circuit.
- Go to the Wiring folder and select the Splitter circuit. This circuit will take a wire and split it into a set of wires of smaller width. Conversely, it can also take many sets of wires and combine them into a larger bus.
- Before you place your circuit, change the "Bit Width In" property (bus width) to 8, and "Fan Out" property (# of branches) to 3. If you move your cursor over the schematic, your cursor should look as follows:
- Now, select which bits to send out to which part of your fan. The least significant bit is bit 0 and the most significant bit is bit 7. Bit 0 should come out on fan arm 0, bits 1, 2, 3, 4, 5 and 6 should come out on fan arm 1, and bit 7 should come out on fan arm 2. FYI: the "None" option means that the selected bit will not come out on ANY of the fan arms.
- Once you configure your splitter, you can place your splitter into your circuit.
- Route "In" to the splitter. Attach a 2-input AND gate to fan arms 0 and 2 and route the output of the AND gate to Out1.
- Now, interpret the input as a "sign and magnitude" number. Place logic gates and other circuits to make Out2 to be the negative "sign and magnitude" value of the input. Sign and magnitude is an alternate way of representing signed values - like 2s complement, but simpler! The combinational logic should be straight-forward.
- We will need another splitter to recombine the fans into a single 8-bit bus. Place another splitter with the proper properties (Bit Width In: 8, Fan Out: 3, correct fan widths). Play with the Facing and Appearance properties to make your final circuit as clean-looking as possible.
- Show your Ex4 circuit to your TA.
- If we decide to take the input and interpret it as a 2's complement number, what inputs will produce Out1 = 1? Hint: What do the first and last bits of a two's complement number being 1 tell you about the number?
Part 5: Rotate RightWith your knowledge of splitters and your knowledge and experience with multiplexers from way back in Lab 3, you are ready to implement a non-trivial combinational logic block:
rotr, which stands for "Rotate Right". The idea is that
rotr A,Bwill "rotate" the bit pattern of input A to the right by B bits. So, if A were 0b1011010101110011 and B were 0b0101 (5 in decimal), the output of the block would be 0b1001110110101011. Notice that the rightmost 5 bits were rotated off the right end of the value and back onto the left end. In RTL, the operation would be something like "
R = A >> B | A << (16 - B)".
You must implement a subcircuit named "rotr" with the following inputs:
- A, 16 bits, the input to be rotated
- B, 4 bits, the rotation amount (Why 4 bits?)
rotrsubcircuit in the main subcircuit. Your solution shouldn't involve a clock or any clocked elements, like registers.
Hint: Before you start wiring, you should think veeeery carefully about how you might decompose this problem into smaller ones and join them together. You should feel very free to use subcircuits when implementing
rotr. If you don't, expect to regret it.
Hint, the second: Just because we gave you an RTL representation doesn't mean it's the best way to look at this problem. Think about the input bits of B and think about how to effectively use splitters! Can you do something with the binary form? Remember why binary is good for use in computers: a 1 is easy to represent as an "ON" signal, and a 0 is easy to represent as an "OFF" signal. Let's say we want to rotate 9 times. 9 is 1001 in binary, or 1x8 + 0x4 + 0x2 + 1x1. Can you use this to make a cleaner circuit?
- Show your TA your rotr circuit and verify that it works.
Part 6: iClicker Question
- Answer one clicker question from lecture given by your TA. This will cover content from the past M, F, W Lectures 10/22 (State, State Machines), 10/24 (Combinational Logic), and 10/26 (Combinational Logic Blocks). Be prepared to explain the thinking behind your answer!