ACI2605
Assignment 3 2025
Unique Number:
Due date: 3 July 2025
QUESTION 1
1.1.1 The Binary Number System: Critical Analysis of Steen’s Definition
Steen (1988) describes mathematics as the science of patterns, focusing on the
identification, explanation, and application of patterns in numbers and structures. This
definition is highly relevant to the binary number system, which is built on one of the simplest
and most fundamental patterns in mathematics—using only two digits: 0 and 1. The binary
system is foundational in computer science and digital technology, demonstrating how
simple numeric patterns can be harnessed to create complex systems.
In binary, each place value represents a power of two, unlike the decimal system’s power of
ten. This pattern allows for clear and consistent conversions between binary and decimal,
and it underpins how computers process and store information. For example, the binary
sequence 1011 represents the decimal number eleven by following the pattern of summing
powers of two (1×8 + 0×4 + 1×2 + 1×1). This repetitive, logical structure reflects Steen’s
view of mathematics as the search for, and exploitation of, underlying patterns.
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
1.1.1 The Binary Number System: Critical Analysis of Steen’s Definition
Steen (1988) describes mathematics as the science of patterns, focusing on the
identification, explanation, and application of patterns in numbers and structures.
This definition is highly relevant to the binary number system, which is built on one of
the simplest and most fundamental patterns in mathematics—using only two digits: 0
and 1. The binary system is foundational in computer science and digital technology,
demonstrating how simple numeric patterns can be harnessed to create complex
systems.
In binary, each place value represents a power of two, unlike the decimal system’s
power of ten. This pattern allows for clear and consistent conversions between
binary and decimal, and it underpins how computers process and store information.
For example, the binary sequence 1011 represents the decimal number eleven by
following the pattern of summing powers of two (1×8 + 0×4 + 1×2 + 1×1). This
repetitive, logical structure reflects Steen’s view of mathematics as the search for,
and exploitation of, underlying patterns.
Moreover, mathematical operations in binary, such as addition and multiplication, are
based on rules and patterns that are consistent and predictable. These patterns
make binary not just useful for computers but also a clear example of how
mathematics can represent and manipulate information efficiently. Functions and
operators in binary—such as AND, OR, and NOT—also show how patterns are
transformed and related, supporting Steen’s emphasis on functions and maps that
connect different types of patterns.
Thus, Steen’s definition is well suited to the binary system, as the entire system is a
manifestation of a simple pattern applied recursively. This pattern-based approach
allows binary to serve as the foundation for modern computing, demonstrating how
abstract mathematical patterns can lead to practical, real-world applications (Steen,
1988).
1.1.2 The Decimal Number System: Critical Analysis of Steen’s Definition
Assignment 3 2025
Unique Number:
Due date: 3 July 2025
QUESTION 1
1.1.1 The Binary Number System: Critical Analysis of Steen’s Definition
Steen (1988) describes mathematics as the science of patterns, focusing on the
identification, explanation, and application of patterns in numbers and structures. This
definition is highly relevant to the binary number system, which is built on one of the simplest
and most fundamental patterns in mathematics—using only two digits: 0 and 1. The binary
system is foundational in computer science and digital technology, demonstrating how
simple numeric patterns can be harnessed to create complex systems.
In binary, each place value represents a power of two, unlike the decimal system’s power of
ten. This pattern allows for clear and consistent conversions between binary and decimal,
and it underpins how computers process and store information. For example, the binary
sequence 1011 represents the decimal number eleven by following the pattern of summing
powers of two (1×8 + 0×4 + 1×2 + 1×1). This repetitive, logical structure reflects Steen’s
view of mathematics as the search for, and exploitation of, underlying patterns.
DISCLAIMER & TERMS OF USE
Educational Aid: These study notes are intended to be used as educational resources and should not be seen as a
replacement for individual research, critical analysis, or professional consultation. Students are encouraged to perform
their own research and seek advice from their instructors or academic advisors for specific assignment guidelines.
Personal Responsibility: While every effort has been made to ensure the accuracy and reliability of the information in
these study notes, the seller does not guarantee the completeness or correctness of all content. The buyer is
responsible for verifying the accuracy of the information and exercising their own judgment when applying it to their
assignments.
Academic Integrity: It is essential for students to maintain academic integrity and follow their institution's policies
regarding plagiarism, citation, and referencing. These study notes should be used as learning tools and sources of
inspiration. Any direct reproduction of the content without proper citation and acknowledgment may be considered
academic misconduct.
Limited Liability: The seller shall not be liable for any direct or indirect damages, losses, or consequences arising from
the use of these notes. This includes, but is not limited to, poor academic performance, penalties, or any other negative
consequences resulting from the application or misuse of the information provided.
, For additional support +27 81 278 3372
QUESTION 1
1.1.1 The Binary Number System: Critical Analysis of Steen’s Definition
Steen (1988) describes mathematics as the science of patterns, focusing on the
identification, explanation, and application of patterns in numbers and structures.
This definition is highly relevant to the binary number system, which is built on one of
the simplest and most fundamental patterns in mathematics—using only two digits: 0
and 1. The binary system is foundational in computer science and digital technology,
demonstrating how simple numeric patterns can be harnessed to create complex
systems.
In binary, each place value represents a power of two, unlike the decimal system’s
power of ten. This pattern allows for clear and consistent conversions between
binary and decimal, and it underpins how computers process and store information.
For example, the binary sequence 1011 represents the decimal number eleven by
following the pattern of summing powers of two (1×8 + 0×4 + 1×2 + 1×1). This
repetitive, logical structure reflects Steen’s view of mathematics as the search for,
and exploitation of, underlying patterns.
Moreover, mathematical operations in binary, such as addition and multiplication, are
based on rules and patterns that are consistent and predictable. These patterns
make binary not just useful for computers but also a clear example of how
mathematics can represent and manipulate information efficiently. Functions and
operators in binary—such as AND, OR, and NOT—also show how patterns are
transformed and related, supporting Steen’s emphasis on functions and maps that
connect different types of patterns.
Thus, Steen’s definition is well suited to the binary system, as the entire system is a
manifestation of a simple pattern applied recursively. This pattern-based approach
allows binary to serve as the foundation for modern computing, demonstrating how
abstract mathematical patterns can lead to practical, real-world applications (Steen,
1988).
1.1.2 The Decimal Number System: Critical Analysis of Steen’s Definition
