You will be learning how to use the remaining essential parts of logisim, in particular, splitters to take a subset of bits on a wire, and to rejoin them. In addition, please fill out the course survey and give us some feedback!
Exercise 0: Course survey
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- Show the survey's submission confirmation page to your TA.
Start all Logisim circuits from scratch. Feel free to do each exercise as separate sub-circuits in the same Logisim file.
The following exercises will introduce you to more advanced techniques/concepts in Logisim.
Exercise 1: SplittersThis is the last essential tool you will need in this class. To demonstrate its use you will construct a circuit that manipulates an 8-bit number.
- Create a new subcircuit and name it "Ex1".
- Add an 8-bit input pin to your circuit and label it "In".
- 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. Change bits 1, 2, and 6 to be coming out on fan arm 1 (the middle one). Have all the other bits come out of the default fan arm. 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 Ex1 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: this is an exercise testing your understanding of number representation as well as to show how splitting a bus can give you certain insights about the value on the wire.
Exercise 2: Rotate RightWith your knowledge of splitters and your knowledge and experience with multiplexers from the last lab, 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.
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, like with the envelopes in exercise 5 of lab0?
Tip: If your wiring from a large splitter is getting messy, sometimes chaining splitters can keep things more localized and cleaner. For example, a 1 to 16 split can be achieved by a fan out of 4 connected to 4 more splitters of fan out 4.
- Show your TA your rotr circuit and verify that it works.