Homework answers / question archive / FIT1047 Introduction to computer systems, networks and security – S1 2023 Assignment 1 – Numbers, Encodings and Boolean Logic FACULTY OF INFORMATION TECHNOLOGY INSTRUCTIONS: 1) A document with the answers to the questions and your workings

FIT1047 Introduction to computer systems, networks and security – S1 2023 Assignment 1 – Numbers, Encodings and Boolean Logic FACULTY OF INFORMATION TECHNOLOGY INSTRUCTIONS: 1) A document with the answers to the questions and your workings

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FIT1047 Introduction to computer systems, networks and
security – S1 2023
Assignment 1 – Numbers, Encodings and Boolean Logic

FACULTY OF
INFORMATION
TECHNOLOGY
INSTRUCTIONS:
1) A document with the answers to the questions and your workings.
2) A separate .zip archive with the Logisim files for Part 2 along with your individualised
assignment specification.
Part 1: Number Systems and Character Encodings (15 marks)
In this part of the assignment, you will demonstrate your knowledge of number systems, character encodings and
conversion between different systems.
Follow the link on Moodle to access your personalised character encoding table.
Important: Your encoding table is different from the one other students are working
with. Only download the file while you are correctly logged into Moodle with your own
student account.
Task 1.1 Character encodings (6 marks)
Look up the first three letters of your last name (use upper case for the first letter followed by
lower case for the rest) in the given encoding table1. Each letter in the encoding table is
mapped to a hexadecimal number. Convert the hexadecimal numbers into 7-bit (unsigned)
binary, decimal and octal and produce a table like this:

Show your working.
Task 1.2 Upper case to lower case and lower case to upper case (9 marks)
You will now need to swap the case of two of the characters from Task 1.1. This means that
upper-case characters now become lower-case characters, and the other way around.
1.2.1: Describe the arithmetic operations that need to be performed to convert from upper
case to lower case and from lower case to upper case, based on the concrete character
encoding table that you have been given. (3 marks)
1 If your last name only has two letters, add the first letter of your first name. Use the names as
registered in the Monash system, i.e., using only English alphabet characters.
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TECHNOLOGY
1.2.2: Use 8-bit two’s complement arithmetic to perform the conversion from upper-case to
lower-case for the first character of your last name, and from lower-case to upper-case for
the second character. (3+3 marks)
Show your working.
Correct result: 3 marks. Working: 3 marks.
Part 2: Boolean Algebra (30 marks total)
Follow the link on Moodle to access your personalised truth table for this task.
Important: Your truth table is different from the one other students are working on.
Only download the file while you are correctly logged into Moodle with your own
student account.
The truth table you download describes a Boolean function with four input values
X1,X2,X3,X4 and two output values Z1,Z2.
The main result of this part will be a logical circuit correctly implementing this Boolean
function in the Logisim simulator.
Each task below needs to be documented and explained.
Task 2.1: Boolean Algebra Expressions (10 marks)
Write the Boolean function as Boolean algebra terms using the Sum of Product (SOP) form.
First, think about how to deal with the two outputs. Then, describe each single row in terms
of Boolean algebra. Finally, combine the terms for single rows into larger terms.
Briefly explain these steps for your particular truth table (e.g., explain for one particular row
how you come up with the Boolean terms for that row, and then explain how you combine all
rows). This explanation should be no more than a few sentences.
Also write the Boolean function as Boolean algebra terms using the Product of Sum (POS)
form with brief explanation of steps (e.g. how you combine all rows).
Correctness of the result: 7 marks (marks will be deducted for individual errors)
Explanation: 3 marks
Notation: Use the following symbols and notation for writing Boolean algebra expressions.
Variables are upper-case (e.g., ?1, ?2). Boolean AND is written without a symbol, e.g.?1?2.
Boolean OR is written with the + symbol, e.g. ?1 + ?2. Negation is written using an overline,
e.g. ?1. Important: when writing terms like NOT X1 AND NOT X2, there must be a clear
gap in the overlines, e.g. ?1 ?2. Tip: you can use the equation function in Word or
Google Docs to create overlines.
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Task 2.2: Logical circuit in Logisim (10 marks)
Model the resulting Boolean terms (using SOP form) from Task 2.1 in a single Logisim
circuit, using only the basic gates AND, OR, NOT. You can use gates with more than two
inputs. See the template on the next page for how to structure your circuit.
Briefly explain your construction (as for Step 1, a short explanation is enough).
Test your circuit using values from the truth table and document at least 3 test cases. You
can take screenshots or your Logisim window to document the tests.
Correctness of the circuit: 5 marks (marks will be deducted for individual errors)
Explanation: 2 marks
Test cases: 1 mark per documented test case
Task 2.3: Optimised circuit (10 marks)
The goal of this task is to find a minimal circuit using only AND, OR, and NOT gates. Based
on the truth table and Boolean algebra terms from Step 1, optimise the function using
Karnaugh maps.
You will need to create two Karnaugh maps, one for each output. Your documentation must
show
1) the maps,
2) the groups found in the maps
3) the reduced Boolean functions derived from the maps and how the maps relate to
terms in the optimised Boolean functions.
Then use Logisim to create a minimal circuit, using only AND, OR, and NOT gates.
Test your optimised circuit using values from the truth table and document your tests.
Correctness of Karnaugh maps: 4 marks (2 for each map, marks will be deducted for
individual errors)
Documentation of groups and reduced Boolean functions: 4 marks
Logisim circuit and documentation: 2 marks
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Logisim Template
Structure your circuits as shown in the Logisim diagram below.