CS 3410 Spring 2019
Project Due: February 15, 2019 at 11:59:00pm
Please submit all required documents to CMS.
You must work ALONE for this and all other individual projects. Failure to adhere to this rule will result in an Academic Integrity Violation. You will only be able to work in groups for designated group projects. Updates to this assignment will be posted on the course web page.
In the first four projects you will design a subset of the RISC32 architecture in Logisim, a software logic simulator. The goal of these projects is to move you from designing small special-purpose circuits to building complex, general-purpose CPUs. By the end of the third project, you will have designed a 32-bit pipelined RISC CPU. For these assignments, we will ignore more advanced features, including the RISC coprocessor instructions and traps/exceptions.
In this project, you will design a RISC ALU (arithmetic and logic unit) which performs all of the core computations dictated by the assembly language. You have already seen pieces of the ALU, such as a 32-bit adder circuit, in class. You can also consult section A.5 in your textbook.
We will be using Logisim, a free hardware design and circuit simulation tool. Logisim comes with libraries
containing basic gates, memory chips, multiplexers and decoders, and other simple components. In later
assignments, you will use many of these components to build your final CPU.
However, for this
assignment you may only use the following Logisim elements:
**Important - Use this guideline for designing your circuits to avoid losing points!**
Academic Integrity. As one of the most widely studied architectures, RISC has a wealth of information available on the web and in textbooks. You may consult any RISC documentation available to you in order to learn about the instruction set, what each instruction does, how an ALU works, etc. However, we expect your design to be entirely your own, and your submission should cite any significant sources of information you used. If you are unsure if it is okay to borrow from some other source, just ask the TAs. If you are hesitant to ask the TAs or to cite the source, then it is probably not okay. Plagiarism in any form will not be tolerated. It is also your responsibility to make sure your sources match the material we describe here.
All of the following should be subcircuits in a single Logisim circuit file. To get you started we've provided an ALU_template.circ file with all the appropriate inputs and outputs specified.
You implemented this circuit in Lab 2, but in case your design had issues, we've replicated the specification below. The completed ALU you submit will need this piece to work.
| LeftShift32: | C = (B << Sa) | carrybits |
| Inputs: | B[32], Sa[5], Cin |
| Outputs: | C[32] |
The output C is computed by shifting B to the left Sa bits, and
filling the vacated bits on the right with carrybits, which is just Sa copies of
Cin. The shift amount Sa can be anything from 0 to 31, encoded as an unsigned
integer.
Note: Some inputs and outputs are busses (as noted by the bus width in brackets); the rest are 1-bit wide.
One way to implement such a shifter is to perform the shift as a series of stages: the first stage shifts either 0 or 16 bits, the second stage either 0 or 8 bits, the third stage either 0 or 4 bits, and so on. By enabling different combinations of stages, the circuit can shift any desired amount. Hint: Shifting a value on a 32-bit bus by a constant amount, either left or right, is simply a matter of adding, removing, and renaming the wires on the bus, and so requires no gates at all.
| Add32: | C = A + B + Cin; V = overflow |
| Inputs: | A[32], B[32], Cin |
| Outputs: | C[32], V |
The output C is computed by adding A, B, and Cin. A,
B, and C are signed two's complement numbers. If overflow occurs, the output
V should be asserted. In such cases, the output C should correspond to the value
computed if all overflow errors are ignored. Hint: Use subcomponents to make wiring easier by building
a 1-bit adder, then a 2-bit adder, then a 4-bit adder, and so on up to 32-bits.
There actually isn't a huge difference between signed and unsigned adders. In fact the only difference between the two is the way that overflow is calculated. Below is a 4-bit unsigned adder, like the one you did in Lab 1...
...and here is everything you need to add to it so it can behave like a 4-bit two's complement signed adder.
Not much at all! Also, note that the one-bit adder subcircuits in both the signed and unsigned 4-bit adders are identical (the one-bit adders are all unsigned adders). Use this distinction when building your 32-bit signed adder.
| ALU32: | (C, V) = fOp(A, B, Sa) |
| Inputs: | A[32], B[32], Op[4], Sa[5] |
| Outputs: | C[32], V |
The C and V outputs are computed according the value of the Op input
based on the table of operations below. For the add and subtract operations, the
V output should be set to 1 if and only if the C output could be
incorrect due to a numerical overflow occurring during computation. The value C output in the
presence of overflow should correspond to the value computed if all overflow errors are ignored.
| Op | name | C | V |
|---|---|---|---|
| 0001 | or | C = A | B | V = 0 |
| 0101 | nor | C = ~(A | B) | V = 0 |
| 0011 | and | C = A & B | V = 0 |
| 0111 | xor | C = A ^ B | V = 0 |
| 0010 | eq | C = (A == B) ? 000...0001 : 000...0000 | V = 0 |
| 0000 | ne | C = (A != B) ? 000...0001 : 000...0000 | V = 0 |
| 0100 | le | C = (A ≤ 0) ? 000...0001 : 000...0000 | V = 0 |
| 0110 | gt | C = (A > 0) ? 000...0001 : 000...0000 | V = 0 |
| 100x | add | C = A + B | V = overflow |
| 110x | subtract | C = A - B | V = overflow |
| 101x | shift left logical | C = B << Sa | V = 0 |
| 1110 | shift right logical | C = B >>> Sa | V = 0 |
| 1111 | shift right arithmetic | C = B >> Sa | V = 0 |
An x in the opcode indicates that the circuit should not depend on the value of that bit when
determining the appropriate operation. For example, your circuit should add when the opcode is
either 1000 or 1001.
The expression (test) ? 1 : 0 has a value of 1 if test is true, and 0
otherwise. In both cases, the upper 31 bits of the output are zero. Note the difference between logical right
shift (which fills with zero bits), and arithmetic right shift (which fills the new bits with copies of the
sign bit of B). The logical and (&), or (|), xor (^),
nor, and complement (~) operators are all bit-wise operations.
Your ALU should use your adder and left shifter as components. But, as in class, your ALU should only use a single 32-bit adder component to implement both addition and subtraction. Similarly, your ALU should use only a single 32-bit left shifter component to implement all of the shift operations. For instance, right shifting can be accomplished by transforming the inputs and outputs to your left shifter. You will be penalized if your final ALU circuit uses more than one 32-bit adder or left shifter. Of course, always strive to make your implementation clear, but do not duplicate components in an effort to do so.
Your ALU will need to be able to select the appropriate output from your components. Do not use a large mux as a way to select between your operations. Foremost, some of the inputs to this large mux would be unused or duplicated which is poor design. Additionally, larger muxes add much more complexity and gates, further increasing the critical path. Likewise, do not use a large decoder in your design. Take some time to break this logic into smaller, concise stages. You will be penalized if your final ALU circuit uses a large mux (16 to 1) or decoder (4 to 16).
It is important that your implementation of the three circuits described above adhere to the specification in this document. Adhering to specification is important in most all design processes, and it will also have a more immediate effect on your grade for this lab. Automated grading will expect that the three circuits above (and their inputs and outputs) are named exactly as specified (case-sensitive!) and behave exactly as specified.
Also recall that when the specification denotes a pin as A[32], the pin should be named "A"
and be 32 bits wide. The pin should not be named "A[32]".
The design document should include a diagram showing all the major components in the ALU (adder, shifter, etc.), and the datapath connections between them. For a well-designed design document, a screenshot of the Logisim circuit itself can serve as a diagram; otherwise, use the documentation to clarify and explain any parts of your circuit we might find confusing. You should provide an explanation for any more complex parts/subcomponents of your ALU.
Also include a description of your control and instruction decoding logic. For each control logic signal (or group of related control logic signals) you should provide (a) a brief description of what the signal does, e.g. what the values of the control signal mean; and (b) a truth table showing what value the signal takes for each possible opcode.
You will need to submit a design document along with your Logism project files and README via CMS.Essentially, documentation provides you with another avenue of communicating your intended design and implementation in case your circuit has mistakes. For more help on the documentation, see example design doc provided here (LaTeX source provided here).
In addition to the a design document, you are required to submit a short README. The README includes the following:
In synchronous logic (logic that is driven by a clock signal), the critical path is the slowest logic path in the circuit. We have assumed that the operation of the ALU completes in one clock cycle. In order to determine how long the clock cycle is, you need to figure out which path in your circuit is the longest path for the input signals to propagate through. This particular path is called the critical path. The amount of time for the input signals to propagate through the critial path is the minimum length of one clock cycle. The reciprocal of the clock period gives the maximum frequency of the input clock signal. You may express your critical path in terms of the number of gates in the path. To determine the critical path you should use the following simplifying assumptions:
In microprocessor design, gate count refers to the number of transistor switches, or gates, that are needed to implement a design. Even with today's process technology providing what was formerly considered impossible numbers of gates on a single chip, gate counts remain one of the most important overall factors in the end price of a chip. Designs with fewer gates will typically cost less, and for this reason gate count remains a commonly used metric in the industry. To determine the gate count you should use the following assumptions:
Extensively testing your circuit is important to ensure correctness. Logisim, luckily, allows the use of test vectors for automated testing of circuits.
While it is not feasible to test every possible input tuple, it is feasible in Logisim to test up to several
thousand input tuples. For serious testing, you will want to write programs (e.g. in Perl, Python, Java,
Bash, etc.) to generate the test vectors. You should strive to include enough tuples, and to choose the
tuples strategically enough, so as to exercise the complete functionality of your circuits. Some of your
tuples might be written by hand to test corner cases (e.g. adding combinations of zero, +1, -1, max_int,
min_int, etc.). Some might be generated systematically (e.g. testing every possible shift amount, and every
possible Op), and others might be generated randomly (to catch cases you didn't think of).
Testing is a significant part of this project and will be graded accordingly.
For this lab, you should create three ASCII text test vector files, one for each of the Left Shifter, Adder, and ALU circuits. These files should be formatted as Logisim test vectors (see Logisim's in-program help for the format). A brief comment at the top of each file should indicate how the test vectors were chosen/generated.
Getting started: Design your circuits on paper before building them in Logisim. Design, then build and
test the left shifter circuit first. Next, design, build, and test a left/right shifting unit to be used in
the ALU. Think of the left/right shifter as miniature ALUs: it will have its own opcode-like control input of
your choice that selects between its different sub-operations. Repeat the same steps for circuit 2: design,
build, and test an adder/subtractor unit for use in your ALU. Then design a comparator unit that can perform
the four comparison operations by processing the output of the adder/subtractor or other subcomponents.
Finally, design, build, and test the complete ALU for circuit 3. The overall idea is to compute several
potentially needed values of the output C using the pieces you have already built and then to
select the appropriate one using a multiplexer.
Decoding logic: Your circuit will compute several values in parallel, but it will ultimately select only one for output. Your decoding logic can often be simplified if you note that you only need the output of a sub-component to be correct (i.e. for it to receive the correct inputs) if you know ultimately that it will be selected for output. In short, try to find the cases where you really don't care about the inputs to, or outputs from, a sub-component.
Is optimal always best? We want you to build a good working circuit. What does good mean? It could mean speed, readability, compactness, etc. Eventually, in later assignments, you will be asked to document your goals and justify the choices you made. However, even if you opt for highly optimized circuits, you should make sure all of your designs are clear and easy to follow. They should be annotated (with text labels on the circuits) for any unusual or difficult parts of the circuit. Think and design before you implement. Laying down a very complicated circuit for relatively simple functionality will not work in your favor during grading.
Logisim combinational analysis: Take advantage of Logisim's combinational analysis window (found under Project > Analyze Circuit), which can automatically generate near-optimal circuits given a truth table. This only works for circuits with a few inputs, but is very well suited to control logic.
How to use Logisim: Take advantage of our courses many informational design and style guides. We also have a Tips and Tricks page to make your first logisim project a breeze.
Getting help: Ask the course staff for help. We are always available on Piazza.
Although the ripple-carry adder that we designed in Lab 1 and covered in lecture is easy to teach and reason about, in practice it is far too slow to be used in a real processor. A much faster and more effective design is the carry-lookahead adder which trades off a high gate count for a vastly lower critical path. There are a number of excellent online resources on the topic. Section A.6 in your textbook is another good resource.
Particularly adventurous students who endeavour to optimize their critical path by building a carry-lookahead adder of one sort or another will be rewarded with extra credit. Please note, however, that it is essential that your design must work. Building a working CLA is significantly more difficult than building a working ripple adder, and every term, a few students set out to do it and end up with no working adder at all. Don't let this happen to you!
Let's get this straight. To verify the correctness of your ALU, you are going to log the output of your ALU for a few inputs, and then you are going to verify that your ALU gives the same output when given those same inputs?
This is basically asking "does your ALU produce the same outputs as your ALU?"
The first rule of tautology club is the first rule of tautology club.