Homework 2 Digital Logic and the ALU

CS 2110 Homework 2
Digital Logic and the ALU

Contents
1 Overview 3
1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Optional Tutorial 4
2.1 Part 1 — Read Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Part 2 — Complete Tutorial 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Part 3 — Complete Tutorial 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Instructions 4
3.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.2 Part 1: 1-Bit Logic Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.3 Part 2: Plexers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.1 Multiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.2 Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3.3 Sign Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4 Part 3: Adders & ALUs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.1 1-Bit Adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.2 8-Bit Adder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4.3 Basic 8-Bit ALU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.4.4 Intermediate 8-Bit ALU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.5 Running the Autograder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Deliverables 10
5 Sub-Circuit Tutorial 10
6 Rules and Regulations 12
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6.1 General Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.2 Submission Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.3 Submission Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.4 Syllabus Excerpt on Academic Misconduct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.5 Is collaboration allowed? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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1 Overview
1.1 Purpose
You have learned about digital logic, including transistors, gates, and combinational logic. Gates (AND,
OR, etc.) can be built using transistors, and Combinational Logic circuits (decoder, MUX, etc.) can be
built using gates. Note how the concepts build up from transistors to gates to combinational logic. We have
provided you with a tool called Circuitsim (available through Docker) that allows you to simulate building
circuits, without actually using physical hardware.
The purpose of this assignment is for you to become proficient building gates out of transistors, and combinational logic circuits out of gates, using Circuitsim. You will put these components together to create
an ALU (arithmetic logic unit) circuit, which will allow you to perform several specified math and logic
operations using digital logic.
1.2 Task
You will complete three Circuitsim files, and build an ALU from the ground up, starting with transistors,
and then gates, and then the remainder of your combinational logic. Please read this entire document for
detailed instructions, including which digital logic components you are allowed to use or prohibited from
using for each part of the assignment.
This document also contains tutorials on using Circuitsim and creating subcircuits, among other topics.
The steps to complete this assignment include:
1. Create the standard logic gates (NAND, NOR, NOT, AND, OR)
2. Create an 8-input multiplexer and an 8-output decoder
3. Use multiplexers to create a circuit that evaluates the sign of a number
4. Create a 1-bit full adder
5. Create an 8-bit full adder using the 1-bit full adder
6. Use your 8-bit full adder and other components to construct an 8-bit ALU
1.3 Criteria
You will submit three Circuitsim files that you produce to Gradescope: gates.sim, plexers.sim, and alu.sim.
Your circuits must work properly and produce the desired results in order to receive credit. For the ALU
portion, we will give partial credit for each operation that works properly.
Be sure to avoid using components that are disallowed for each phase of this assignment.
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2 Optional Tutorial
Note: This tutorial is optional and to help you get acquainted with CircuitSim before you
start this homework. If you’re comfortable with this software, feel free to skip to section 2.
CircuitSim is an interactive circuit simulation package. We will be using this program for the next couple
of homework assignments. This is a tutorial to help you get acquainted with the software. CircuitSim is
a powerful simulation tool designed for educational use. This gives it the advantage of being a little more
forgiving than some of the more commercial simulators. However, it still requires some time and effort to be
able to use the program efficiently. With this in mind, we present you with the following assignment:
2.1 Part 1 — Read Resources
Read through the following resources
• CircuitSim Wires Documentation https://ra4king.github.io/CircuitSim/docs/wires/
• Tutorial 1: My First Circuit https://ra4king.github.io/CircuitSim/tutorial/tut-1-beginner
2.2 Part 2 — Complete Tutorial 2
Complete Tutorial 2 https://ra4king.github.io/CircuitSim/tutorial/tut-2-xor
Instead of saving your file as xor.sim, save your file as part1.sim. As well, make sure you label your two
inputs a and b, and your output as c, as well as rename your subcircuit to xor.
2.3 Part 3 — Complete Tutorial 3
Complete Tutorial 3 https://ra4king.github.io/CircuitSim/tutorial/tut-3-tunnels-splitters
Name the subcircuit umbrella, the input in, and the output out. Save your file as part2.sim.
3 Instructions
For this assignment, you will be using CircuitSim. The version is included in the 2110 Docker
container. If you are having issues with Docker, it can also be found on canvas under Files ->
Tools -> CircuitSim.jar.
3.1 Requirements
For the first part of this assignment (the logic gates), you may use only those components found in
the Wiring tab (being the input/output pins, constants, probes, clocks, splitters, tunnels, and transistors),
along with any of the sub-circuits that you create or that already exist.
For the second part of this assignment (the multiplexer and decoder), you may use only those components
found in the Wiring and Gates tabs along with any of the sub-circuits that you create or that already
exist, except in the sign evaluation circuit where you may use the Plexer Tab as well.
For the last part of this assignment, you may use only those components found in the Wiring and Gates
tabs (except for the XOR/XNOR gates) as well as any of the sub-circuits that you create or that
already exist. The term sub-circuit refers to any circuits that you have constructed in this part of the
homework. If you’re unsure on how to utilize a sub-circuit, check out Section 5. For the ALU portion
specifically, you may use the Plexer Tab as well.
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Use of anything not listed above will result in heavy deductions. Your need to have everything in
their correctly named sub-circuit. More information on sub-circuits is given below.
Use tunnels where necessary to make your designs more readable, but do not overdo it! For gates, muxes,
adders and decoders you can often get clean circuits just by placing your components well rather than using
tunnels everywhere.
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3.2 Part 1: 1-Bit Logic Gates
ALLOWED COMPONENTS: Wiring Tab and Circuits Tab
All of the circuits in this file are in the gates.sim file.
For this part of the assignment, you will create a transistor-level implementation of the NAND, NOT, NOR,
AND, and OR logic gates.
Remember for this section that you are only allowed to use the components listed in the Wiring section,
along with any of the logic gates you are implementing in CircuitSim. For example, once you implement the
NOT gate you are free to use that subcircuit in implementing other logic gates. Implementing the gates in
the order of the subcircuit tabs can be the easiest option.
As a brief summary of the behavior of each logic gate:
NAND (Inputs: A, B - Output: OUT)
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0
NOR (Inputs: A, B - Output: OUT)
A B A NOR B
0 0 1
0 1 0
1 0 0
1 1 0
AND (Inputs: A, B - Output: OUT)
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1
OR (Inputs: A, B - Output: OUT)
A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1
NOT (Input: IN - Output: OUT)
A NOT A
0 1
1 0
Hint: Start by creating the NAND and NOT gates from transistors. Then use this gate as a subcircuit for
implementing the others.
All of the logic gates must be within their named sub-circuits.
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3.3 Part 2: Plexers
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, and Gates Tab
NOTE: For the sign evaluation circuit, you may use the Plexer tab as well.
All of the circuits in this file are in the plexers.sim file.
3.3.1 Multiplexer
The multiplexer you will be creating has 8 1-bit inputs (labeled appropriately as A, B, C, ..., H), a single 3-bit
selection input (SEL), and one 1-bit output (OUT). The multiplexer uses the SEL input to choose a specific
input line for forwarding to the output.
For example:
SEL = 000 ==> OUT = A
SEL = 001 ==> OUT = B
SEL = 010 ==> OUT = C
SEL = 011 ==> OUT = D
SEL = 100 ==> OUT = E
SEL = 101 ==> OUT = F
SEL = 110 ==> OUT = G
SEL = 111 ==> OUT = H
3.3.2 Decoder
The decoder you will be creating has a single 3-bit selection input (SEL), and eight 1-bit outputs (labeled A,
B, C, ..., H). The decoder uses the SEL input to raise a specific output line, as seen below.
For example:
SEL = 000 ==> A = 1, BCDEFGH = 0
SEL = 001 ==> B = 1, ACDEFGH = 0
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SEL = 010 ==> C = 1, ABDEFGH = 0
SEL = 011 ==> D = 1, ABCEFGH = 0
SEL = 100 ==> E = 1, ABCDFGH = 0
SEL = 101 ==> F = 1, ABCDEGH = 0
SEL = 110 ==> G = 1, ABCDEFH = 0
SEL = 111 ==> H = 1, ABCDEFG = 0
3.3.3 Sign Evaluation
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, Gates Tab, and Plexer Tab
In this step, you will construct a circuit that takes an 8-bit two’s complement input and evaluates whether
the input is negative, zero, or positive. Based on this, this circuit will output a 3-bit bit-vector called NZP
where the most significant bit is 1 iff the input is negative, the middle bit is 1 iff the input is zero, and the
least significant bit is 1 iff the input is positive. Only 1 bit of the output should be set at any given time.
Zero is not considered a positive number. For example, if the input to this circuit is positive, then
it will output 001
With that in mind, set the correct bit and implement this circuit in the Sign Evaluation subcircuit
Hint: Recall that in two’s complement, the most significant bit can be used to determine the sign of a
number!
3.4 Part 3: Adders & ALUs
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, and Gates Tab
BANNED COMPONENTS: XOR Gate, XNOR Gate
NOTE: For the ALU specifically, you may use the Plexer tab as well.
All of the circuits in this file are in the alu.sim file.
3.4.1 1-Bit Adder
The full adder has three 1-bit inputs (A, B, and CIN), and two 1-bit outputs (SUM and COUT). The full adder
adds A + B + CIN and places the sum in SUM and the carry-out in COUT.
For example:
A = 0, B = 1, CIN = 0 ==> SUM = 1, COUT = 0
A = 1, B = 0, CIN = 1 ==> SUM = 0, COUT = 1
A = 1, B = 1, CIN = 1 ==> SUM = 1, COUT = 1
Hint: Making a truth table of the inputs will help you.
3.4.2 8-Bit Adder
For this part of the assignment, you will daisy-chain 8 of your 1-bit full adders together in order to make an
8-bit full adder.
This circuit should have two 8-bit inputs (A and B) for the numbers you’re adding, and one 1-bit input for
CIN. The reason for the CIN has to do with using the adder for purposes other than adding the two inputs.
There should be one 8-bit output for SUM and one 1-bit output for COUT.
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3.4.3 Basic 8-Bit ALU
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, Gates Tab, and Plexer Tab
BANNED COMPONENTS: XOR Gate, XNOR Gate
Note that this rule recursively extends to any component that your ALU uses, so you will
need to ensure that no other part of the ALU uses the XOR or XNOR gates
You will first create a simple 8-bit ALU, using the 8-bit full adder you created previously.
For this ALU, we will be using a multiplexer. This ALU has two 8-bit inputs for A and B and one 2-bit input
for OP, the op-code for the operation in the list below. It has one 8-bit output named OUT. The following 4
operations will be selected from:
00. Addition [A + B]
01. AND [A & B]
10. NOT [NOT A]
11. Pass [PASS A]
NOTE: the Pass operation simply refers to outputting the value of A unchanged.
Notice that NOT and Pass only operate on the A input. They should NOT rely on B being a particular
value.
The provided autograder will check the op-codes according to the order listed above (Addition (00), AND
(01), etc.) and thus it is important that the operations are in this exact order.
3.4.4 Intermediate 8-Bit ALU
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, Gates Tab, and Plexer Tab
BANNED COMPONENTS: XOR Gate, XNOR Gate
Note that this rule recursively extends to any component that your ALU uses, so you will
need to ensure that no other part of the ALU uses the XOR or XNOR gates
You will next create a different 8-bit ALU, with identical structure as the previous, but more complex
operations as outlined below:
00. isEqual [A == B]
01. isMultipleOf8 [A % 8 == 0]
10. MultiplyBy7 [7 * A]
11. Maximum [max(A, B)]
Notice that MultiplyBy7 and isMultipleOf8 only operate on the A input. They should NOT rely on
B being a particular value.
For the MultiplyBy7 operation, although there is potential for overflow, we don’t need to worry about it
in this homework.
For the isMultipleOf8 and isEqual operations, return 00000001 if the condition is true, and 00000000
otherwise.
The provided autograder will check the op-codes according to the order listed above (isEqual (00), isMultipleOf8 (01), etc.) and thus it is important that the operations are in this exact order.
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3.5 Running the Autograder
To run the autograder, type the following command into your terminal while in the homework 2 directory:
java -jar hw02-tester.jar
Make sure all the tests have been passed. Keep in mind that even if you get full credit from the autograder,
we reserve the right to test for more cases. Note: To guarantee that the autograder runs without error, run
it from your Docker container. To do this, either run ./cs2110docker.sh and open the terminal inside the
graphical client, or run ./cs2110docker.sh -it to open a shell directly in your terminal.
4 Deliverables
Please upload the following files onto the assignment on Gradescope:
1. gates.sim NOT, NAND, NOR, AND, OR
2. plexers.sim Decoder, MUX, Sign Evaluation
3. alu.sim 1-Bit Adder, 8-Bit Adder, Basic 8-Bit ALU, Intermediate 8-Bit ALU
Be sure to check your score to see if you submitted the right files, as well as your email
frequently until the due date of the assignment for any potential updates.
No partial credit will be given for incorrect outputs for Part 1, Part 2, and the adder-portion
of Part 3. For the ALUs, partial credit will be awarded on a per-operation basis, wherein each
operation must perform successfully to be awarded credit. Because of this, we urge you to
check your score before the due date.
5 Sub-Circuit Tutorial
As you build circuits that are more and more sophisticated, you will want to build smaller circuits that you
can use multiple times within larger circuits. Sub-circuits behave like classes in Object-Oriented languages.
Any changes made in the design of a sub-circuit are automatically reflected wherever it is used. The direction of the IO pins in the sub-circuit correspond to their locations on the representation of the sub-circuit.
To create a sub-circuit:
1. Go to the “Circuits” menu and choose “New circuit”
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2. Name your circuit by right-clicking on the “New circuit” item and selecting “Rename”
To use a sub-circuit:
1. Click the “Circuits” tab next to the “Misc” tab
2. Select the circuit you wish to use and place it in your design
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6 Rules and Regulations
6.1 General Rules
1. Starting with the assembly homeworks, any code you write must be meaningfully commented. You
should comment your code in terms of the algorithm you are implementing; we all know what each
line of code does.
2. Although you may ask TAs for clarification, you are ultimately responsible for what you submit. This
means that (in the case of demos) you should come prepared to explain to the TA how any piece of
code you submitted works, even if you copied it from the book or read about it on the internet.
3. Please read the assignment in its entirety before asking questions.
4. Please start assignments early, and ask for help early. Do not email us the night the assignment is due
with questions.
5. If you find any problems with the assignment it would be greatly appreciated if you reported them to
the author (which can be found at the top of the assignment). Announcements will be posted if the
assignment changes.
6.2 Submission Conventions
1. All files you submit for assignments in this course should have your name at the top of the file as
a comment for any source code file, and somewhere in the file, near the top, for other files unless
otherwise noted.
2. When preparing your submission you may either submit the files individually to Canvas/Gradescope
or you may submit an archive (zip or tar.gz only please) of the files. You can create an archive by right
clicking on files and selecting the appropriate compress option on your system. Both ways (uploading
raw files or an archive) are exactly equivalent, so choose whichever is most convenient for you.
3. Do not submit compiled files, that is .class files for Java code and .o files for C code. Only submit the
files we ask for in the assignment.
4. Do not submit links to files. The autograder does not understand it, and we will not manually grade
assignments submitted this way as it is easy to change the files after the submission period ends.
6.3 Submission Guidelines
1. You are responsible for turning in assignments on time. This includes allowing for unforeseen circumstances. If you have an emergency let us know IN ADVANCE of the due time supplying documentation (i.e. note from the dean, doctor’s note, etc). Extensions will only be granted to those who contact
us in advance of the deadline and no extensions will be made after the due date.
2. You are also responsible for ensuring that what you turned in is what you meant to turn in. After
submitting you should be sure to download your submission into a brand new folder and test if it
works. No excuses if you submit the wrong files, what you turn in is what we grade. In addition, your
assignment must be turned in via Canvas/Gradescope. Under no circumstances whatsoever we will
accept any email submission of an assignment. Note: if you were granted an extension you will still
turn in the assignment over Canvas/Gradescope.
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6.5 Is collaboration allowed?
Collaboration is allowed on a high level, meaning that you may discuss design points and concepts relevant
to the homework with your peers, share algorithms and pseudo-code, as well as help each other debug code.
What you shouldn’t be doing, however, is pair programming where you collaborate with each other on a
single instance of the code. Furthermore, sending an electronic copy of your homework to another student
for them to look at and figure out what is wrong with their code is not an acceptable way to help them,
because it is frequently the case that the recipient will simply modify the code and submit it as their own.
Figure 1: Collaboration rules, explained colorfully