Description
1 Overview
You will write a program truthtable that reads a file containing a description of a circuit, and
prints that circuit’s truth table. The files specify (1) the number and names of each input to the
circuit, (2) the number and names of each output from the circuit, and (3) the logic gates and
components that make up the circuit. In order to indicate the connections between gates, each
connection is also given a name.
For example, this is a description for a circuit that implements a 3-argument AND gate:
INPUT 3 a b c
OUTPUT 1 d
AND a b x
AND c x d
Note that it contains three inputs (a, b, and c), a single output (d), and two AND gates, each of
which has two inputs and one output. The variable x indicates an internal connection between the
first AND gate and the second. See section 3 for details on the specification language.
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When given this file, truthtable should print:
0 0 0 | 0
0 0 1 | 0
0 1 0 | 0
0 1 1 | 0
1 0 0 | 0
1 0 1 | 0
1 1 0 | 0
1 1 1 | 1
The three columns on the left correspond to the three inputs, and the column to the right corresponds
to the output.
This assignment has two parts:
Part 1 (100 points) For this part, the circuit descriptions will be sorted so that each temporary
variable appears as an output parameter before any appearances as an input variable.
Part 2 (Extra Credit) For this part, the circuit descriptions will not be sorted, meaning that a
temporary variable may be used as an input parameter before its use as an output parameter.
2 Program
truthtable takes a single argument, which is the name of a file containing a circuit description.
The behavior of truthtable is unspecified if it receives no arguments or more than one argument,
but you should still check that the number of arguments is correct. (One possibility is to have
truthtable read from standard input if no file argument is given.)
Usage
$ ./truthtable my-cool-circuit.txt
0 0 | 0 0
0 1 | 0 1
1 0 | 0 1
1 1 | 1 0
Input The input to your program will be a single circuit description using the language described
in section 3. The first argument to truthtable will identify a file containing this circuit description.
You MAY assume that the input is correctly formatted and that no variable depends on its own
output.
Output The output of truthtable is a truth table showing each combination of inputs and the
corresponding output for the specified circuit. Each column in the table corresponds to a specific
input or output variable, which are given in the same order as their declaration in the INPUT and
OUTPUT directives. Columns are separated by a single space, and a vertical bar (|) occurs between
the input and output variables.
Note that no white space follows the final column.
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3 Specification Language
In this language, circuits are specified with a series of directives. These directives refer to various
named variables, which correspond to wires in a circuit diagram. Many of the directives describe a
logic gate or similar building block, indicating which varibles correspond to its input and output.
Each directive has the form of a name followed by one or more parameters, separated by
whitespace. The name indicates which directive and determines the number of parameters. Some
directives take a variable number of parameters; their first parameter will always be an integer which
is used to determine the number of parameters. Depending on the directive, some parameters will
be inputs and some will be outputs.
Variables in a circuit can be classified into three non-overlapping sets. Input variables must be
declared by the INPUT directive, and may only occur as input parameters. Output variables must be
declared by the OUTPUT directive and may occur exactly once in an output parameter. All other
variables are temporary variables and must occur exactly once as an output parameter and zero or
more times as an input parameter.
A variable name consists of a letter followed by zero or more letters or digits. You may assume
that variable names are no longer than 16 characters.
In addition to variables, the constant inputs 0 and 1 may be used as input parameters. These
are always false and always true, respectively.
Finally, _ may be used as the output of a gate, indicating that the output of a gate is discarded.
Use of _ is equivalent to using a temporary variable that is not used as an input to any other gate.
Gate Inputs Gate Outputs
Input variables Output variables
Temporary variables Temporary variables
0, 1 _
Note that whitespace may include one or more spaces, tabs, or newline characters. It is
recommended to use fscanf() to read the files, and to use a format code such as ” %16s” to skip
whitespace before reading the next variable or directive name.
By convention, we will use multiple spaces to separate the inputs and outputs of a gate, but this
is not required and has no special meaning. It is purely for readability. Similarly, we will often put
a blank line between OUTPUT and the first gate, but this is also done purely for readability. Your
program should treat repeated newlines the same as single newlines (or, ideally, the same as any
whitespace).
Use of fgets() is not recommended and will only make your life harder. Remember that
fscanf() is not limited to reading an entire line at once.
3.1 Directives
This section describes each of the directives used to describe a circuit. Each directive is followed by
several parameters. A parameter n is always an integer and has a special meaning. Input parameters
are indicated as i and output parameters are indicated as o. Ellipses (· · ·) are used to indicate a
variable number of parameters.
• INPUT n i1 · · ·in
Declares n input variables. This directive must always occur first in a circuit description.
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• OUTPUT n o1 · · · on
Declares n output variables. This directive must always occur second in a circuit description.
• NOT i o
Represents a not gate in logic design. Computes o = i.
• AND i1 i2 o
Represents an and gate in logic design. Computes o = i1i2.
• OR i1 i2 o
Represents an or gate in logic design. Computes o = i1 + i2.
• NAND i1 i2 o
Represents a nand gate in logic design. Computes o = i1i2
• NOR i1 i2 o
Represents a nor gate in logic design. Computes o = i1 + i2
• XOR i1 i2 o
Represents an xor gate in logic design. Computes o = i1 ⊕ i2, where ⊕ indicates exclusive or.
• DECODER n i1 · · ·in o0 · · · o2n−1
Represents an n : 2n decoder gate in logic design. The first argument gives the number of
inputs, n. The next n parameters are the inputs, followed by 2
n parameters indicating the
outputs.
The inputs are interpreted as an n-bit binary number s in the range 0, · · · , 2
n − 1, where i1
is the most significant bit and in is the least significant bit. The output os will be 1 and all
others will be 0.
• MULTIPLEXER n i0 · · ·i2n−1 i
′
1
· · ·i
′
n
o
Represents a 2
n : 1 multiplexer gate in logic design. The inputs to a multiplexer are either
regular inputs or selectors, indicated by i and i
′
, respectively. The first parameter, n, gives the
number of selectors. The next 2
n parameters give the regular inputs, followed by n selector
inputs, and finally the output.
The selector inputs are interpreted as an n-bit binary number s in the range 0, · · · , 2
n − 1.
The output is o = is.
• PASS i o
Represents the absence of a gate. Computes o = i. This may be used to convert a temporary
variable into an output variable.
3.2 Parsing
The specification language can be thought of as a sequence of tokens separated by whitespace. No
keyword or variable name in the language exceeds 16 characters, so it is safe to use fscanf() with
the format code %16s, which will read a token of up to 16 non-whitespace characters.
Each directive will be either be followed by a fixed number of parameters or by a number that
will determine the number of parameters. Thus, your parsing code will always be able to tell whether
it expects a directive name, integer, input parameter, or output parameter next.
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For safety, your program should always check that fscanf() succeeded and that it received the
expected token type. If something has gone wrong, either because of bad input or a program error,
you want to know about it!
3.3 Examples
This circuit describes a half-adder, where s is the sum and c is the carry.
INPUT 2 A B
OUTPUT 2 C S
AND A B C
XOR A B S
This circuit computes z = ab + ac:
INPUT 3 a b c
OUTPUT 1 z
AND a b x
AND a c y
OR x y z
Note that x and y are temporary variables, since they were not declared in INPUT or OUTPUT.
This circuit description is invalid, becuase it uses an output variable as an input parameter:
INPUT 3 IN1 IN2 IN3
OUTPUT 2 OUT1 OUT2
AND IN1 IN2 OUT1
OR IN3 OUT1 OUT2
This can be rewritten using PASS:
INPUT 3 IN1 IN2 IN3
OUTPUT 2 OUT1 OUT2
AND IN1 IN2 temp1
PASS temp1 OUT1
OR IN3 temp1 OUT2
This circuit demonstrates the user of MULTIPLEXER:
INPUT 3 A B C
OUTPUT 1 Z
MULTIPLEXER 3 0 0 0 1 1 0 1 1 A B C Z
As shown in class, this can be re-written to use a 4:1 multiplexer:
INPUT 3 A B C
OUTPUT 1 Z
NOT C NC
MULTIPLEXER 2 0 C NC 1 A B Z
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An equivalent circuit can be made using a 3:8 decoder:
INPUT 3 A B C
OUTPUT 1 Z
DECODER 3 A B C _ _ _ p q _ r s
OR p q t
OR r s u
OR t u Z
Note the use of _ for discarded outputs from the decoder.
4 Implementation suggestions
There are many ways to design truthtable, but the most efficient way is to create a data structure
that represents a circuit. Your program will read the circuit description file, create the corresponding
data structure, and then use that structure to determine the output values for each combination of
inputs.
Students commonly try to build the entire truth table before printing it. This is not the best
strategy, because the truth tables grow exponentially with the number of inputs. (For example, test
1.10 will produce a truth table with 2
20 = 1 048 576 rows.) A better design is to generate and print
the table one row at a time.
Use of the math library is unnecessary. Your program should not need to compute logarithms at
any point, and 2
n can be easily computed using a left shift.
A few tips for creating fast implementations of truthtable.
• When reading the circuit description file, assign a number to each new variable name and use
a linked list or other structure to maintain a table that you can use to look up the number
assigned to previously seen variables. Internally, refer to variables by number rather than name:
integer comparisons are faster than string comparisons, and you can use variable numbers as
array indices.
• Carefully consider what information you need to represent a circuit. This will likely include
the circuit’s input and outputs and the gates making up the circuit.
• Carefully consider what data is needed to represent a gate. Design a structure that is general
enough to represent any gate, and then write code that can handle any of the gates. This will
likely include a code that indicates the type of gate and the input and output variables. See
fig. 1 for one possibility.
• In order to handle DECODER and MULTIPLEXER, your gates will need to work with a
variable number of inputs and outputs. One possibility is to use an array of variable numbers
representing the inputs and outputs along with a field indicating the size of the gate. For
fixed-sized gates, such as AND, this number can simply be ignored and the array can be
assumed to contain the correct number of inputs and outputs. For MULTIPLEXER and
DECODER, one number is sufficient to determine how many inputs and outputs there are.
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typedef enum { AND, OR, NAND, NOR, XOR, NOT, PASS, DECODER, MULTIPLEXER } kind_t;
struct gate {
kind_t kind;
int size; // indicates size of DECODER and MULTIPLEXER
int *params; // length determined by kind and size;
// includes inputs and outputs, indicated by variable numbers
};
Figure 1: One possible data structure representing a logic gate
• To generate a single row of the truth table, first assign values to the circuit inputs. Then, for
each gate, determine the values for its outputs based on the values of its inputs. Once every
gate has been handled, you will know the values for the outputs and can print the table row.
If you have assigned a unique number to each variable, then you can use an array to hold the
values of all the variables.
• For each row of the truth table, note that every input value will be followed by a space, and
every output value will be preceded by a space.
• It is possible to use an integer to represent the current row of the truth table. To find bit i of
some integer n, consider n & (1 << i) != 0.
• When reading the circuit description, you may assume that the file is correctly formatted.
Thus, after reading a directive name, you may assume that it will be followed by the correct
number of parameters. Thus, it is acceptable to use the whitespace-skipping tokenizer and
ignore line breaks.
• When using a format string such as ” %16s” with fscanf(), the corresponding variable must
be the address of an array containing a sufficient number of characters (17, in this case). While
it is fine to use local variable to hold the result from fscanf(), be sure to make a copy of the
string if you intend to hold onto it.
• There are several methods for dealing with circuit descriptions where the gates are not given
in order. One way is easy to write, but slow. Another is more complicated, but fast. (Hint:
the circuit can be thought of as a directed, acyclic graph, and you have learned an algorithm
for ordering the nodes in a DAG.)
5 Submission
Your solution to the assignment will be submitted through Canvas. You will submit a Tar archive
file containing the source code and makefiles for your project. Your archive should not include any
compiled code or object files.
Your submission MUST be properly formatted. You are responsible for ensuring that
your submission can be tested with the auto-grader. You will not receive full credit for submissions
that must be modified in order to be graded. You are strongly encouraged to test your archive
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before submitting, as described in section 5.4. If you are submitting from a different computer than
you have used for testing, make sure that your archive was correctly transferred!
The remainder of this section describes the directory structure, the requirements for your
makefiles, how to create the archive, how to use the provided auto-grader, and how to create your
own test files to supplement the auto-grader.
5.1 Quick start
These steps will unpack the auto-grader archive, set up your src directory and make file, and use
the auto-grader to create the build directory. The auto-grader is flexible and many of these steps
can be customized. See the remainder of this section for more in-depth explanations.
Unpacking the auto-grader archive will create a directory pa4 containing the auto-grader and
associated test data. First, move to the directory you want to contain the pa4 directory and unpack
the archive. You can move the archive to this directory first, or simply give a path to its location.
E.g.,
$ tar -xf ~/Downloads/pa4-grader.tar
Next, move into the pa4 directory and set up your src and build directories.
$ cd pa4
pa4$ mkdir src
pa4$ cp template.make src/Makefile
pa4$ ./grader.py –init
Write your code in a file src/truthtable.c using your editor of choice.
pa4$ vim src/truthtable.c
Compile in the build directory using make.
pa4$ cd build
pa4/build$ make
gcc -g -std=c99 -Wall -Wvla -Werror -fsanitize=address,undefined
../src/truthtable.c -o truthtable
pa4/build$ ./truthtable my_circuit.txt
If you are repeatedly compiling and testing with a specific test file, you can combine both steps
into a single command using &&.
pa4/build$ make && ./truthtable test_circuit
This works well in combination with the up-arrow key (used to repeat earlier commands).
5.2 Directory structure
Your project should be stored in a directory named src, which will contain (1) a makefile, and (2)
any source files needed to compile your program. Typically, you will provide a single C file named
for the program (truthtable.c).
This diagram shows the layout of a typical project:
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src
+- Makefile
+- truthtable.c
Note that your code and makefile go directly in src, without any subdirectories.
5.3 Makefiles
We will use make to manage compilation. Your src directory will contain a file named Makefile
that describes at least two targets. The first target must compile the program. An additional
target, clean, must delete any files created when compiling the program (typically just the compiled
program).
For reference, this makefile is provided with the auto-grader in the file template.make:
TARGET = truthtable
CC = gcc
CFLAGS = -g -std=c99 -Wall -Wvla -Werror -fsanitize=address,undefined
$(TARGET): $(TARGET).c
$(CC) $(CFLAGS) $^ -o $@
clean:
rm -f $(TARGET) *.o *.a *.dylib *.dSYM
You may move this file to your source directory and rename it Makefile.
Note that the command for compiling truthtable uses warnings and includes AddressSanitizer
and UBSan. Your score may be reduced if your makefile does not include these options.
Use of -g is recommended, but not required.
If you prefer to name your source code file something other than truthtable.c, simply replace
$(TARGET).c with your preferred name. Use of multiple source files is permitted, but contact me
for tips first.
You are free to design your own makefile, but be sure to use the variables $^ or $< to refer to
your source files so that make can find your source files. Contact me if you have trouble getting
your makefile to work.
Note that the makefile format requires that lines be indented using a single tab, not
spaces. Be aware that copying and pasting text from this document will “helpfully” convert the
indentation to spaces. You will need to replace them with tabs (literal tab characters), or simply
type the makefile yourself. You are advised to use make when compiling your program, as this
will ensure (1) that your makefile works, and (2) that you are testing your program with the same
compiler options that the auto-grader will use.
5.4 Creating the archive
We will use tar to create the archive file. While in the directory containing src, execute this
command:
pa4$ tar -czvf pa4.tar src/Makefile src/truthtable.c
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tar will create a file pa4.tar that contains your makefile and source code. (If you are using multiple
source files, or have re-named your source code, you will need to adjust this command accordingly.)
This file can now be submitted through Canvas.
To verify that the archive contains the necessary files, you can print a list of the files contained
in the archive with this command:
pa4$ tar -tf pa4.tar
You should also use the auto-grader to confirm that your archive is correctly structured.
pa4$ ./grader.py -a pa4.tar
5.5 Using the auto-grader
We have provided a tool for checking the correctness of your project. The auto-grader will compile
your programs and execute them several times with different arguments, comparing the results
against the expected results.
Setup The auto-grader is distributed as an archive file pa4_grader.tar. To unpack the archive,
move the archive to a directory and use this command:
$ tar -xf pa4_grader.tar
This will create a directory pa4 containing the auto-grader itself, grader.py, a library autograde.py,
abd a directory of test cases data.
Do not modify any of the files provided by the auto-grader. Doing so may prevent the auto-grader
from correctly assessing your program.
Usage While in the same directory as grader.py and src, use this command:
pa4$ ./grader.py
The auto-grader will create a directory build, and compile your program using the make file and
source code in src, placing compiler outputs in build.
During development, you may prefer to use the –stop or -1 option, which produces more
program output but stops after the first failed test case.
pa4$ ./grader.py -1
The tests for this assignment come in two groups, for normal and extra credit. To test only a
single part, include an argument truthtable:1 or truthtable:2.
To obtain usage information, use the -h option.
Program output By default, the auto-grader will not print the output from your programs,
except for lines that are incorrect. To see all program output for all unsuccessful tests, use the
–verbose or -v option:
pa4$ ./grader.py -v
To see program output for all tests, use -vv. To see no program output, use -q.
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Checking your archive We recommend that you use the auto-grader to check an archive
before submitting. To do this, use the –archive or -a option with the archive file name. For
example,
pa4$ ./grader.py -a pa4.tar
This will unpack the archive into a temporary directory, grade the programs, and then delete the
temporary directory.
Specifying source directory If your src directory is not located in the same directory as
grader.py, you may specify it using the –src or -s option. For example,
pa4$ ./grader.py -s ../path/to/src
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