## Lab 6

Computer Architecture I ShanghaiTech University
Lab 5 Lab 6 Lab 7

### Goals

There are three parts to this lab. In the first part, 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 the second part, you will prepare for your project 2 by designing a basic ALU.

### Setup

For part 1 and 2, start all Logisim circuits from scratch. Feel free to do each exercise as separate sub-circuits in the same Logisim file.

For part 3, we provided you with a starter Logisim circuit below.

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

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.

### Tunnels

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.

### Extenders

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 1: Practice with Splitters

We're going to construct a circuit that manipulates an 8-bit number.

1. Create a new subcircuit and name it "Ex1".
2. Add an 8-bit input pin to your circuit and label it "In1".
3. Add a 1-bit output pin labeled "Out1" and an 8-bit output pin labeled "Out2" to your circuit.
4. 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.
5. 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:
6. 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.
8. 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.
9. 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.
10. 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.

#### Checkoff [1/3]

• 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 2: Rotate Right

With 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,B` will "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?)
The output should be A rotated right by B bit positions, as outlined above. You are NOT allowed to use Logisim shifters in your solution, though all other combinational logic (MUXes, constants, gates, adders, etc.) is allowed. Logisim's built-in MUXes (find them under the Plexers menu) might be especialy helpful. Show off your `rotr` subcircuit 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?

#### Checkoff [2/3]

• Show your TA your rotr circuit and verify that it works.

### Part 3: Logisim ALU

For this part, we've provided you with a starter Logisim circuit to start out.

In this exercise, you will first implement a 32 bit ALU in Logisim.

As a reminder, recall that ALU stands for Arithmetic Logic Unit. An ALU is a fundamental building block of a CPU (central processing unit) and it performs integer arithmetic and logical (bitwise) operations. The function that the ALU performs (e.g. add, xor) is determined by the control of our datapath, which is determined by the instruction the processor is executing.

This lab assignment is similar to the CPU design project (it is essentially a slightly simpler version of Project 2's ALU). Hopefully by getting a headstart here in lab, Project 2 will go a bit more smoothly!

The 8 functions that you will implement are: shift left logical, shift right logical, shift right arithmetic, rotate left, rotate right, and, or, and xor. The ALU will perform a desired function on 2 32-bit inputs and output the result. The selected function will be determined by the value of the control signal, as listed below.

Here's what occurs for each operation:

Control Operation
000 Shift Left Logical
001 Shift Right Logical
010 Shift Right Arithmetic
011 Rotate Left
100 Rotate Right
101 And
110 Inclusive Or
111 Exclusive Or

#### Checkoff [3/3]

• Set two inputs to your ALU. Toggle the control bits to change the function being performed on the output and verify with your TA that the output is correct.