ACI2605
Assignment 3 2025
Detailed Solutions, References & Explanations
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
Terms of use
the pattern of summing powers of two (1×8 + 0×4 + 1×2 + 1×1). This repetitive, logical
By making use of this document you agree to:
structure reflects Steen’s view Useofthis
mathematics
document as a as
guide for search
the learning, comparison and reference purpose,
for, and exploitation of,
Terms of use
Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
By making use of this document you agree to:
document
Use this Fully accept the consequences
solely as a guide forshould you plagiarise
learning, or and
reference, misuse this document.
comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
Assignment 3 2025
Detailed Solutions, References & Explanations
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
Terms of use
the pattern of summing powers of two (1×8 + 0×4 + 1×2 + 1×1). This repetitive, logical
By making use of this document you agree to:
structure reflects Steen’s view Useofthis
mathematics
document as a as
guide for search
the learning, comparison and reference purpose,
for, and exploitation of,
Terms of use
Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
By making use of this document you agree to:
document
Use this Fully accept the consequences
solely as a guide forshould you plagiarise
learning, or and
reference, misuse this document.
comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
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
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
