CS 252 Sim #1 Basics of Binary solution

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1 Purpose
The point of this project is to give you practical experience with how the CPU
works internally; while you’ll be writing code in C and Java, the logic you’ll be
using is essentially the same as the digital logic implemented in hardware.
1.1 What You’ll Be Doing
• You will implement a few individual gates as Java classes; these are not
too complex, and mostly function as an introduction to how this Java
simulation works.
• You will implement a 32-bit adder as another Java class; it will perform
every step of the addition (column by column) using logical statements –
never addition. The purpose of this class is twofold: one, to give you
practice expressing complex conditions as logical statements, and two, to
fully convince you that “dumb” hardware can do everything required to
perform addition.
• You will implement another class, which performs 2’s complement on a 32-
bit input; we’ll require that this uses your NOT class to negate the input
(you can’t do it by hand), and also require that you use your ADD class.
The purpose of this one is to practice with hardware abstractions: that
is, of using simple components as elements in larger pieces of hardware.
• Your last Java class will be a subtractor – which will be built out of your
2’s complement and adder classes.
• You will write a single C function. This function will implement addition,
using the same rules as your Java class (that is, you have to do it with
logic, not with +). But for this function, your inputs and outputs will be
integers (instead of arrays of booleans), and thus you will have to use bit
shifting and masking to read and write individual bits inside integers.
This function will also implement subtraction – but using a more streamlined fashion. Instead of performing 2’s complement and then adding, you
will actually mix the 2’s complement operation and addition into a single
step.
The purpose of this function is twofold: first, to start to build a connection
in your mind between integers and their hardware, bit-wise implementation; and second, to teach you the basics of bit shifting and masking.
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1.2 Languages
This project will use both C and Java. We won’t be doing anything complex in
either language. If you feel a little rusty, feel free to ask questions in class, or
come by Office Hours. There are introductory videos to both languages posted
on Piazza.
You will be implementing the adder twice: once in C, and once in Java. I’m
doing this for several reasons. First, I want you to refresh your knowledge of
both languages, as we’ll be using them in later projects. Second, seeing this in
two different ways (values as integers, or values as arrays of booleans) should
help you understand the link between the “values” we see as programmers, and
the electrical wires that carry the bits.
2 Tasks
You must implement a total of 6 different Java classes and 1 C file, representing
a gradually increasing level of complexity. I encourage you to implement them
in the order listed, so that you can gradually build on your understanding.
For each of the required files, I’ve provided a skeleton file to get you started.
Pay attention to the comments I’ve left, as well as any example code I provide.
Don’t leave the C function to the last minute. While it is a repetition of
the adder that you already implemented in Java (with a few extra features),
students often find it more challenging than they would have guessed – since
few of you are already familiar with how to read and write individual bits inside
an integer.
2.1 You Can’t Do Addition!
None of the code that you write for this project may use the ordinary addition
operator – in fact, our grading script will scan your program for that operator,
and will cut your grade in half if it finds any! (++ is OK for your for() loops –
but += is not.)
Instead, you must implement your code entirely with logical operators. For
the Java program, the key operators will be:
• && (boolean AND)
• || (boolean OR)
• != (boolean XOR)
For the C program, you will need to extract bits from the inputs, and then
assemble them back together for the outputs. In addition to the operators
above, you will find the following operators useful (later in this spec, I have
written up some reminders about how to use them):
• >> (right shift)
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• << (left shift)
• & (bitwise AND – useful for extracting bits out)
• | (bitwise OR – useful for adding bits in)
2.1.1 Can You Please Regrade My Code?
Sometimes, students think that the grading script is unfair. It will mark them
down for uses of + that they didn’t think should be a problem, and they ask us
to overrule the grading script by hand.
There are two common scenarios where this happens. Pay attention to
what I’m about to say here.
• In Comments
The grading script is not smart enough to parse your code and realize that
your + is inside a comment. So, even though you’re not using it in your
code, you get marked down.
ANSWER: No, I won’t fix this.
You have the grading script. Run it before you turn in your code! If your
comment has a problem, then change the comment before you turn it in.
• In Array Indexing
Some students write their code in such a way that they need to access element [i+1] or [i-1] while they iterate through the array. To change this
would require that they rethink their algorithm in a non-trivial manner.
ANSWER: Yes, I’ll fix this. But I wish I didn’t have to.
Do your best to devise an algorithm, from the beginning, that doesn’t
need to do this. But if this is your best answer, I’ll allow it.
2.2 Base Code
Download all of the files from the Sim1 zip file posted on Piazza.
You should start by looking at:
• Sim1 XOR.java
This is an example, which has lots and lots of comments to explain what’s
going on in the Java simulation.
• sim1.h
This is the “header” file for the C part of the project. You must not
modify this file – but you should read it, to understand what sorts of
inputs I will provide to you, and what sorts of outputs you must produce.
You should fill in the TODO marks in the following files:
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• Sim*.java (except for XOR)
These represent the various features you must implement. (XOR is an
example of how to do composition, you don’t have to change that.)
Start with AND/OR/NOT. Then implement ADD. Do 2sComplement next,
followed by SUB.
Make sure that you read the entire spec – some of these classes have extra
restrictions about how you will implement them.
• sim1.c
This contains one function to implement, which performs ADD. (And,
when a certain flag is turned on, it also performs SUB – but you will find
out that the two are very similar.)
Do this one last, but don’t leave it to the last minute. Leave some extra
time to complete it.
You should not modify the following files:
• grade sim1
This is the grading script that I’ve provided, for testing your code. It
should work well on CS department machines; it’s also possible (no guarantees) that it might work well on your personal Mac or Linux machine.
(The command timeout, which is used by the grading script, is missing
from most Macs. But you can Google to find out how to get it installed.)
• RussWire.java
This implements RussWire, a necessary utility class for all of the other
Java classes (see below).
• Test*.java
test*.c
These are the source files for the testcases.
• *.out
These show the expected output from each testcase.
• sim1.h
This is the header which your C code will use to communicate with each
testcase.
3 The RussWire Class
In hardware, it is never possible for the same wire to carry two different signals
during the same “clock cycle” – that is, during the same unit of time. In this
project, every time we run a testcase, we are simulating a single clock cycle –
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which means that every input and output, from every different object, can only
have one value, forever. (Of course, if you create multiple instances of the same
object, each instance can have different values.)
However, we don’t know all of the values at once. Instead, information must
flow from our inputs, into some components, which calculate some tiny part of
the answer; that is fed forward, to other components, which calculate a little
more, and on through the network, until we finally determine our output. In
hardware, this all happens naturally; we just energize the circuits, wait a few
picoseconds, and the correct value arrives at the output.
Unfortunately, when we simulate this with code, we have to be a little more
careful. We must be careful to execute all of our components in a specific order,
and make sure that we set each “wire” within our simulation no more than once.
We also need to sanity-check our code, and ensure that we never read a “wire”
before it’s been set by something else.
The RussWire class does this for you. It basically is just a wrapper around
a boolean, along with a flag that indicates whether or not the flag has been set
yet. It has two basic rules:
• If you try to read it before it has been set, it throws an exception. (Sorry,
no default values here!)
• If you try to set it a second time, it throws an exception. (No changing
the value after you’ve set it.)
Basically, if you see an exception from this class, it means that your simulation
has a bug that needs to get fixed.
3.1 Irritations of the RussWire Class
All of the inputs and outputs of your classes must be RussWire classes (or
arrays of such classes). Unfortunately, this means that things will be slightly
more annoying.
First, the constructor for every class must create a RussWire object for every
bit of input or output. You must also declare these variables as public fields of
your class:
public class Example
{
public void execute() { … }
public RussWire in, out;
public Example()
{
in = new RussWire();
out = new RussWire();
}
}
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When you need an array of bits, you need to create the array object first, then
fill it in with individual wire objects:
RussWire[] arr = new RussWire[32];
for (int i=0; i<32; i++)
arr[i] = new RussWire();
(If you have an array of inputs or outputs, remember that you need to declare
the variable in the class, NOT inside the constructor function – or else it won’t
be publicly visible to other objects!)
Finally, the most annoying part: you cannot use = to assign values. Instead,
call get() to read a value from one wire, and set() to write to another. (If you
need to hard-code a value, you can simply call set() with a boolean constant.)
boolean value = input_wire.get();
output_wire.set(value);
other_hardcoded_output_wire.set(true);
4 Rules for Simulating Hardware
Since you are simulating hardware, there are a number of rules about what you
can and can’t do in execute(). I know, these rules sound silly, and if this was
just a program, you’d be right. But the whole idea is that we are pretending
that we are actually wiring little components together with physical wires. These
limitations represent the real limitations of hardware.
In the execute() method, you MUST NOT:
• Create any new objects. (You must do this in the constructor.)
(Creating and using Java primitives – such as boolean – is OK. Basically,
just don’t use the keyword new.)
• Ever perform addition or any other mathematical operation – except for
the ++ operator which is required for a for() loop.
(Remember, logical operators are allowed.)
In the constructor for a Java class, you may create new objects – but save
them as public variables of the object, so that you can use them later. (See my
XOR code for an example.)
5 Required Functions
Each Java class implements some inputs, an execute() method, and some outputs. My skeleton code has already defined the inputs and outputs, and provided
an (empty) execute() method; you must write the body of execute().
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For most classes, you will also need to fill in the constructor for the class – use
that to create the RussWire objects that you need, or any other sub-components.
For some of the classes, in addition to the input and output wires that I’ve
defined, you will also need to add some more variables (for sub-components).
Feel free to add these – just make sure that you initialize them properly in your
constructor as well.
The following classes have special limitations you should pay attention to:
5.1 Sim1 ADD
This class has two 32-bit inputs, and several outputs. The primary output,
sum, is a 32-bit array, and it should contain the output from the addition. The
carryOut wire should indicate whether or not there was carry-out from the
MSB, and the overflow wire should indicate whether or not overflow occurred.
You should treat both inputs (and the output) as 32-bit signed integers.
Remember, the fact that they are signed won’t affect how you perform addition,
but it will affect how you determine whether or not overflow occured.
Element [0] in each array is the least significiant bit, and element [31] is
the most.1
5.1.1 Challenge: Elegance
Lots of students implement ADD with a long series of if/else statements, and
that’s fine; it will earn full functionality credit if it’s correct.
However, challenge yourself to find elegant, one line solutions to key steps.
In particular, it is possible (using only AND, OR, NOT, and XOR) to perform
each of the following steps in one line of code:
• Calculate the sum bit, for one column, using the a,b and carry-in values
for that column.
• Calculate the carry-out, for one column, using the a,b and carry-in values
for that column.
• Calculate the carryOut output from the entire adder.
• Calculate the overflow output from the entire adder.
(This one is the hardest one, but the one most worth working at. It’s
shocking how simple it is, once you get your head around it.)
1Here is an example of the big-endian vs. little-endian debate. I said that [0] is the LSB,
which makes sense to me because the LSB is worth 20
. But if we drew the array as a picture,
[0] would be the leftmost element in the array!
That’s why having precise terminology like LSB/MSB is so useful.
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5.2 Sim1 2sComplement
This Java class simply calculates the 2’s complement of a 32-bit input. However,
it must not do the addition inside its own execute() method! Instead, it must
have sub-components inside it (see my XOR code for an example), and must
use those components to actually perform the calculations.
In other words, this execute() method must:
• Use your NOT class to negate the inputs (but you’ll need to negate 32 items
– how will you do that?
• Use your ADD class to add 1 to the negated values.
5.3 Sim1 SUB
This must perform subtraction. It has (almost) the same inputs and outputs
as the ADD class – the only difference being that it doesn’t have carryOut or
overflow outputs.
However, like your 2sComplement class, this must not do the work itself.
Instead, compose it from the 2sComplement and ADD classes.
5.4 C Code: execute add(Sim1Data *obj)
Your C code must implement only a single function, which performs 32-bit
signed addition, much like the Sim1 ADD class in Java; however, it has a few
additional features.
Since C doesn’t have classes, the inputs and outputs for this function are all
stored in a struct which is passed (by pointer) to your C code.
More importantly, the inputs and outputs are not arrays. Instead, they are
actual 32-bit integers. You must not use the C addition operator to calculate
the result. Instead, you must perform bitwise addition, just like the Java class.
To do this, you will need a for() loop which iterates over the 32 bits; for
each bit, it should perform 4 basic tasks:
• Use bit shifting and masking (see below) to extract one bit from input a,
and one bit from input b.
• Figure out what the sum and carry bits are for the current column.
• Save the carry into a temporary variable of some sort (for use in the next
iteration of this loop).
• Write the sum-bit to the output – again, using bit shifting and masking.
5.4.1 Other Flags
The output struct has three additional flags which are not present in the Java
version (see sim1.h). The fields aNonNeg,bNonNeg,sumNonNeg indicate whether
or not the two inputs (and the sum) are non-negative2
. To calculate these values,
2Remember, “non-negative” means “positive or zero.”
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you must not use greater than/less than operators. Instead, you must extract
the MSB from each of the three numbers, and then set the three NonNeg fields
appropriately.
NOTE: When you set the bNonNeg field in execute add(), you should set it
based on the original (not negated) value of the b input – even if we are performing subtraction!
5.4.2 Subtraction
As you know, subtraction in a computer is simply a 2’s complement of the 2nd
term, and then addition. In our Java version of the program, we use your NOT
and ADD classes to perform 2’s complement, and then use the ordinary ADD class
to add the values together.
However, you will be using another method in execute add() – one which
is more true to how it works in hardware. We will see that, inside a computer,
we don’t perform the 2’s complement and add as two separate steps. Instead,
we simply perform (bitwise) negation of the 2nd input – and we also set the
“carry-in” to 1.
The “carry-in” bit, in an adder, is the carry that comes up from the previous
column. Normally (that is, when we’re adding), the first column has a carry-in
which is zero. But, in this case (when we’re doing subtraction), we will set it to
1 – meaning that (in essence) we are performing an extra +1 to our numbers.
In execute add(), you must:
• Read the isSubtraction field out of the struct.
• If isSubtraction is set to 1, then do a carry-in to the very first column
of your adder.
• If isSubtraction is set to 1, then negate each bit of the second input,
as you perform the addition.
Pay attention to the following rules:
• You must NOT use the – operator (arithmetic negation) to simply negate
the input. Instead, you must use bitwise logic!
• You must NOT split the ADD and SUB features into two different pieces
of code. You must have one loop, which does all of the work of the adder
(for both addition and subtraction).
Don’t worry, this isn’t crazy-hard. In fact, turning an adder into a subtractor will only require you to change a few lines.
5.4.3 2’s Complement, Special Cases
When we perform 2’s complement, there are two special values: 0 and the
most-negative number (0x0000 0000, 0x8000 0000). In both cases, the 2’s
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complement has the same sign as the original number! This means that it can
be a little confusing to decide whether or not overflow has occured.
For that reason, we’ll promise to never set b to either of these numbers while
performing subtraction.
6 Bit Shifting and Extraction
I know that some of you aren’t terribly familiar with bit shifting and masking.
So here’s a quick summary of the important operators. (All of these operators
exist in both C and Java.):
• val >> n
Shifts the bit pattern val to the right (that is, toward the less-significant
bits) by n bits. Any bits which “fall off the bottom” are simply lost. 3
EXAMPLE:
Suppose that
val == 0101 10112
Now shift it right by 2 bits.
val>>2 == 0001 01102
• val << n
Shifts the bit pattern val to the left. Any bits which fall off the top are
lost; zeroes are added at the bottom.
• val & mask
Bitwise AND. Usually used for “masking” – that is, for zeroing out all
bits in a number except the ones of interest. For instance, the following
operation will zero out every bit in val, except for bits 2-4 (the 4’s through
16’s columns):
val & 0x1c
When used in conjuction with right shift, it allows you to read any individual bit:
(val >> n) & 0x1
• val | bitsToSet
Bitwise OR. Usually used for setting bits in a number. For instance, the
following operation will set bits 2-4 to 1 (no matter what they used to be):
val | 0x1c
3What happens at the top? Do we sign extend the value, or just add zeroes? Java has two
shift operators, >> and >>> to solve that problem. In C, there is only one shift operator, and
different machines work in different ways. But in our problem, we’ll be using & to get a single
bit after the shift, so it doesn’t matter!
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When used in conjuction with left shift, it allows you to set any individual
bit:
val | (0x1 << n)
7 A Note About Grading
Your code will be tested automatically. Therefore, your code must:
• Use exactly the filenames that we specify (remember that names are case
sensitive).
• Not use any other files (unless allowed by the project spec) – since our
grading script won’t know to use them.
• Follow the spec precisely (don’t change any names, or edit the files I give
you, unless the spec says to do so).
• (In projects that require output) match the required output exactly! Any
extra spaces, blank lines, misspelled words, etc. will cause the testcase to
fail.
To make it easy to check, I have provided the grading script. I strongly recommend that you download the grading script and all of the testcases, and use
them to test your code from the beginning. You want to detect any problems
early on!
7.1 Testcases
The testcases will be in the zip file you downloaded from Piazza.
In this project, we have C testcases (named test *.c) and Java testcases
(named Test *.java). Use all of them, since the grading script will use both
sets.
For each of these testcases, we have also provided a .out file, which gives
exactly what your code must print (to stdout) when this testcase runs4
.
For many projects, we will have “secret testcases,” which are additional
testcases that we do not publish. These may cover corner cases not covered
by the basic testcases, or may simply provide additional testing. You are
encouraged to write testcases of your own, in order to better test
your code. You are also encouraged to share your testcases on Piazza!
7.2 Automatic Testing
We have provided a testing script (in the same directory), named grade sim1.
Place this script, all of the testcase files, and your program files in the same
4NOTE: Do not simply cut-n-paste the file, since that will mess up the whitespace in the
file! Instead, make sure to download the file, so that you get an exact copy.
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directory. (I recommend that you do this on Lectura, or a similar department
machine. It might also work on your Mac, but no promises!)
Below, I’ve provided some example output from the script:
7.2.1 Example: Passed Testcase
When a testcase passes, it looks something like this:
******************************
* Testcase ’Test_05_2sComplement.java’ passed
******************************
7.2.2 Example: Failed Testcase
When a testcase fails, it looks something like this:
******************************
* TESTCASE ’Test_03_ADD.java’ FAILED
******************************
—– diff OUTPUT —-
4c4
< 00100000100100110010111001111011

> 00000000000000010000010101010001
6c6
< carryOut = 1

> carryOut = 0
—– END diff —-
7.2.3 Example: If You Use Addition
If the script finds that you used addition:
ERROR: The grading script found that you used + or += in your C or Java code –
your grade will be cut in half.
7.2.4 Example: Summary
Look at the end of the output for your score:
*******************************************
* OVERALL REPORT
* attempts: 10
* passed: 10
*
* score: 70
*******************************************
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Note that this score does not indicate the grade you will receive on the assignment. It only indicates which of the testcases inside your directory that you
passed.
7.3 Writing Your Own Testcases
The grading script will grade your code based on the testcases it finds in the
current directory. Start with the testcases I provide – however, I encourage you
to write your own as well. If you write your own, simply name your testcases
using the same pattern as mine, and the grading script will pick them up.
While you normally cannot share code with friends and classmates, testcases are the exception. We encourage you to share you testcases – ideally
by posting them on Piazza. Sometimes, I may even pick your testcase up to be
part of the official set when I do the grading!
8 Turning in Your Solution
You must turn in your code using Gradescope. Turn in only your program; do
not turn in any testcases or other files.
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