CS2110-2 Homework 2-Digital Logic and the ALU Solution

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 four 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. Apply DeMorgan’s Law to convert a provided circuit to one without any OR Gates
3. Create an 8-input multiplexer and an 8-output decoder
4. Use multiplexers to create a circuit that evaluates the sign of a number
5. Create a 1-bit full adder
6. Create an 8-bit full adder using the 1-bit full adder
7. Use your 8-bit full adder and other components to construct an 8-bit ALU
1.3 Criteria
You will submit four Circuitsim files that you produce to Gradescope: gates.sim, demorgan.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.
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
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.
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.
3.3 Part 2: DeMorgan’s Law
ALLOWED COMPONENTS: Wiring Tab and Gates Tab
BANNED COMPONENTS: OR Gate, NOR Gate, XOR Gate, XNOR Gate
The circuits in this file are in the demorgan.sim file.
De Morgan’s laws help relate conjunctions (AND) and disjunctions (OR) of propositions with negation.
In this file, you will be creating a circuit that is an alternative to the circuit that is provided in the Provided subcircuit (first tab). Your work will be done in the Student subcircuit (second tab).
3.3.1 Provided
3.3.2 Student
This circuit needs to be directly equivalent to the circuit provided in the Provided subcircuit, meaning the same inputs should lead to the same outputs.
Here’s the catch: There should be ZERO OR gates in your circuit!
3.4 Part 3: Plexers
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, and Gates Tab
All of the circuits in this file are in the plexers.sim file.
3.4.1 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
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
3.4.2 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
3.4.3 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!
3.5 Part 4: Adders & ALUs
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, and Gates Tab
All of the circuits in this file are in the alu.sim file.
3.5.1 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.
3.5.2 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.
3.5.3 Basic 8-Bit ALU
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, Gates Tab, and Plexer Tab
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.
3.5.4 Intermediate 8-Bit ALU
ALLOWED COMPONENTS: Wiring Tab, Circuits Tab, Gates Tab, and Plexer Tab
You will next create a different 8-bit ALU, with identical structure as the previous, but more complex operations as outlined below:
00. isDouble [A == 2 * B]
01. isMultipleOf32 [A % 32 == 0]
10. multiplyBy10 [A * 10]
11. maximum [max(A, B)]
Notice that multiplyBy10 and isMultipleOf32 only operate on the A input. They should NOT rely on B being a particular value.
For the multiplyBy10 and isDouble operations, although there is potential for overflow, we don’t need to worry about it in this homework.
For the isDouble and isMultipleOf32 operations, return 00000001 if the condition is true, and 00000000 otherwise.
1. If A and B are both positive
2. If A and B are both negative
3. If A and B are different signs (e.g A is positive and B is negative)
The provided autograder will check the op-codes according to the order listed above (isDouble (00), isMultipleOf32 (01), multiplyBy10 (10), maximum (11)) and thus it is important that the operations are in this exact order.
3.6 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. demorgan.sim Provided, Student
3. plexers.sim Decoder, MUX, Sign Evaluation
4. alu.sim 1-Bit Adder, 8-Bit Adder, Basic 8-Bit ALU, Intermediate 8-Bit ALU
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”

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

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.
3. Please read the assignment in its entirety before asking 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.
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
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.
6.4 Syllabus Excerpt on Academic Misconduct
Academic misconduct is taken very seriously in this class. Quizzes, timed labs and the final examination are individual work.
Homework assignments are collaborative, In addition many if not all homework assignments will be evaluated via demo or code review. During this evaluation, you will be expected to be able to explain every aspect of your submission. Homework assignments will also be examined using computer programs to find evidence of unauthorized collaboration.
You are expressly forbidden to supply a copy of your homework to another student via electronic means. This includes simply e-mailing it to them so they can look at it. If you supply an electronic copy of your homework to another student and they are charged with copying, you will also be charged. This includes storing your code on any site which would allow other parties to obtain your code such as but not limited to public repositories (Github), pastebin, etc. If you would like to use version control, use github.gatech.edu
6.5 Is collaboration allowed?

Figure 1: Collaboration rules, explained colorfully