From e80b332060017afa4c5215be204e5fef8330964a Mon Sep 17 00:00:00 2001 From: thomasabishop Date: Fri, 18 Oct 2024 20:00:02 +0100 Subject: [PATCH] Autosave: 2024-10-18 20:00:02 --- zk/Additive_inverse_property.md | 2 + zk/Algebra_key_terms.md | 2 + zk/Axioms_of_set_theory.md | 2 + zk/Basic_properties_of_sets.md | 2 + zk/Conjunction_Introduction.md | 2 + zk/Creating_a_Linux_partition_table.md | 3 +- zk/DRAM_and_SRAM_memory.md | 2 +- zk/Docker_CLI.md | 2 +- zk/Environmental_and_shell_variables.md | 5 +- zk/Equivalent_equations.md | 38 ++++++++---- zk/Equivalent_fractions.md | 2 + zk/Expressing_whole_numbers_as_fractions.md | 2 + zk/Factors_and_divisors.md | 2 +- zk/Formal_conventions.md | 8 ++- zk/Fundamental_Theorem_of_Arithmetic.md | 2 + zk/HTTP_request_types.md | 2 + ...easing_fractions_to_their_highest_terms.md | 2 + zk/Intro_to_the_Unix_shell.md | 2 + zk/Inversion_of_operators.md | 13 ++++- zk/Invoking_the_shell_in_Python.md | 2 +- zk/Killing_processes.md | 2 + ...and_navigating_directories_in_the_Shell.md | 2 + zk/Magnetic_core_memory.md | 2 +- zk/Mainframe_computers.md | 2 +- zk/Memory_versus_processor.md | 2 +- zk/Module_wrapping_at_runtime.md | 2 + zk/Natural_numbers.md | 2 + zk/Negative_exponents.md | 2 + zk/Network_card.md | 2 +- zk/Network_hosts.md | 2 +- zk/NodeJS_scripts.md | 3 +- zk/Order_of_operations.md | 2 + zk/Prime_factorization.md | 6 +- zk/Primes_and_composites.md | 2 +- zk/ROM versus disk loading.md | 58 ------------------- zk/ROM_versus_disk_loading.md | 56 +++++++++++++----- zk/Reducing_fractions.md | 2 +- 37 files changed, 139 insertions(+), 107 deletions(-) delete mode 100644 zk/ROM versus disk loading.md diff --git a/zk/Additive_inverse_property.md b/zk/Additive_inverse_property.md index 01c0b18..9811df0 100644 --- a/zk/Additive_inverse_property.md +++ b/zk/Additive_inverse_property.md @@ -3,6 +3,8 @@ tags: - theorems --- +# Additive inverse property + **Let $a$ represent any member of $\mathbb{Z}$. Then there is a unique member of $\mathbb{Z}$ $-a$ such that:** diff --git a/zk/Algebra_key_terms.md b/zk/Algebra_key_terms.md index 15dacd9..3ab742d 100644 --- a/zk/Algebra_key_terms.md +++ b/zk/Algebra_key_terms.md @@ -2,6 +2,8 @@ tags: [algebra] --- +# Algebra key terms + - **Variable** - A symbol that stands for a value which may vary - **Equation** diff --git a/zk/Axioms_of_set_theory.md b/zk/Axioms_of_set_theory.md index f0795d2..091d6d5 100644 --- a/zk/Axioms_of_set_theory.md +++ b/zk/Axioms_of_set_theory.md @@ -4,6 +4,8 @@ tags: - theorems --- +# Axioms of set theory + The basic notions of set theory are defined in [Basic properties of sets](Basic%20properties%20of%20sets.md). There we introduced a formal syntax that will be utilised to define the axioms. For easy diff --git a/zk/Basic_properties_of_sets.md b/zk/Basic_properties_of_sets.md index 82d8fc0..d87ac82 100644 --- a/zk/Basic_properties_of_sets.md +++ b/zk/Basic_properties_of_sets.md @@ -3,6 +3,8 @@ tags: - set-theory --- +# Basic properties of sets + ## Set theory Set theory is a sub-discipline of both mathematics and formal logic. In diff --git a/zk/Conjunction_Introduction.md b/zk/Conjunction_Introduction.md index be90243..59aa5f0 100644 --- a/zk/Conjunction_Introduction.md +++ b/zk/Conjunction_Introduction.md @@ -4,6 +4,8 @@ tags: - logic --- +# Conjunction Introduction + If two conjuncts have each been independently derived then they can be conjoined. Also known more simply as _Conjunction_ diff --git a/zk/Creating_a_Linux_partition_table.md b/zk/Creating_a_Linux_partition_table.md index b5571d6..0d18e08 100644 --- a/zk/Creating_a_Linux_partition_table.md +++ b/zk/Creating_a_Linux_partition_table.md @@ -1,11 +1,12 @@ --- -id: h7f8 tags: - disks - Linux created: Monday, May 06, 2024 --- +# Creating a Linux partition table + ## Creating a partition table To demonstrate the process of partitioning a harddrive I am going to repartition diff --git a/zk/DRAM_and_SRAM_memory.md b/zk/DRAM_and_SRAM_memory.md index 5e0a786..255c59f 100644 --- a/zk/DRAM_and_SRAM_memory.md +++ b/zk/DRAM_and_SRAM_memory.md @@ -3,7 +3,7 @@ tags: [memory, hardware] created: Friday, July 12, 2024 --- -# DRAM_and_SRAM_memory +# DRAM and SRAM memory There are two types of RAM memory: [SRAM and DRAM](./DRAM_and_SRAM_memory.md). diff --git a/zk/Docker_CLI.md b/zk/Docker_CLI.md index 26b5282..19588cb 100644 --- a/zk/Docker_CLI.md +++ b/zk/Docker_CLI.md @@ -6,7 +6,7 @@ tags: created: Saturday, March 30, 2024 --- -# Docker_CLI +# Docker CLI ```sh # List images diff --git a/zk/Environmental_and_shell_variables.md b/zk/Environmental_and_shell_variables.md index 131b733..4b54c63 100644 --- a/zk/Environmental_and_shell_variables.md +++ b/zk/Environmental_and_shell_variables.md @@ -3,6 +3,8 @@ tags: - shell --- +# Environmental and shell variables + ## Important! To understand the difference between environmental and shell variables know @@ -43,8 +45,7 @@ spawned instances? Is this even possible or do they die on `exit` . - The environment is an area that the shell builds every time that it starts a session. It contains variables that define system properties. -- Every time a - [shell session](Shell-sessions-e6dd743dec1d4fe3b1ee672c8f9731f6) +- Every time a [shell session](Shell-sessions-e6dd743dec1d4fe3b1ee672c8f9731f6) spawns, a process takes place to gather and compile information that should be available to the shell process and its child processes. It obtains the data for these settings from a variety of different files and settings on the diff --git a/zk/Equivalent_equations.md b/zk/Equivalent_equations.md index 7c83b55..be0da1a 100644 --- a/zk/Equivalent_equations.md +++ b/zk/Equivalent_equations.md @@ -2,7 +2,7 @@ tags: [algebra] --- -## Equivalent equations +# Equivalent equations > Two equations are equivalent if they have the same > [solution](Algebra%20key%20terms.md#678811) set. @@ -30,11 +30,16 @@ of the $=$ symbol). Adding or subtracting the same quantity from both sides ### Demonstration with addition -$$ x - 4 = 3 $$ +x - 4 = 3 +$$ + The [solution](Algebra%20key%20terms.md#678811) to this equation is $7$ -$$ x - -4 (+4) = 3 (+ 4) $$ + +$$ +x - +4 (+4) = 3 (+ 4) +$$ Here we have added $4$ to each side of the equation. If $x = 7$ then: @@ -46,11 +51,16 @@ $$ 3 + 4 = 7 $$ ### Demonstration with subtraction -$$ x + 4 = 9 $$ +x + 4 = 9 +$$ + The [solution](Algebra%20key%20terms.md#678811) to this equation is $5$. -$$ x + -4 (-4) = 9(-4) $$ + +$$ +x + +4 (-4) = 9(-4) +$$ Here we have subtracted $4$ from each side of the equation. If $x = 5$ then: @@ -62,8 +72,9 @@ $$ 9 - 4 = 5 $$ ### Demonstration with multiplication -$$x \cdot 2 = 10 $$ -The [solution](Algebra%20key%20terms.md#678811) to this equation is $5$. +$$x \cdot 2 = 10 $$ The [solution](Algebra%20key%20terms.md#678811) to this +equation is $5$. + $$ (x \cdot 2) \cdot 3 = 10 \cdot 3 $$ Here we have multiplied each side of the equation by $3$. If $x =5$ then @@ -78,7 +89,12 @@ The [solution](Algebra%20key%20terms.md#678811) to this equation is $6$. $$\frac{x \cdot 3}{3} = \frac{18}{3} $$ + Here we have divided each side of the equation by $3$. If $x$ is 6, then -$$\frac{6 -\cdot 3}{3} = 6$$ + +$$ +\frac{6 +\cdot 3}{3} = 6 +$$ + $$\frac{18}{3} = 6 $$ diff --git a/zk/Equivalent_fractions.md b/zk/Equivalent_fractions.md index 365a19c..a2bf728 100644 --- a/zk/Equivalent_fractions.md +++ b/zk/Equivalent_fractions.md @@ -4,6 +4,8 @@ tags: - fractions --- +# Equivalent fractions + Two fractions are equivalent if they represent the same value. To begin with we can represent this visually: diff --git a/zk/Expressing_whole_numbers_as_fractions.md b/zk/Expressing_whole_numbers_as_fractions.md index 8183aab..44a14fe 100644 --- a/zk/Expressing_whole_numbers_as_fractions.md +++ b/zk/Expressing_whole_numbers_as_fractions.md @@ -4,6 +4,8 @@ tags: - fractions --- +# Expressing whole numbers as fractions + Being asked to express a natural number as a fraction seems confusing at first but you need to just know that for any whole number $n$, you express it as a fraction with $\frac{n}{1}$. diff --git a/zk/Factors_and_divisors.md b/zk/Factors_and_divisors.md index 52aee66..1f0a76f 100644 --- a/zk/Factors_and_divisors.md +++ b/zk/Factors_and_divisors.md @@ -3,7 +3,7 @@ tags: - prealgebra --- -## Factors and divisors +# Factors and divisors The terms **factor** and **divisor** are used interchangeably. They are different ways of expressing the same mathematical truth and this is because of diff --git a/zk/Formal_conventions.md b/zk/Formal_conventions.md index 713e4a1..c3d7d11 100644 --- a/zk/Formal_conventions.md +++ b/zk/Formal_conventions.md @@ -3,6 +3,8 @@ tags: - prealgebra --- +# Formal conventions + ## Grouping symbols We use parentheses to delimit the part of an expression we want evaluated first. @@ -14,8 +16,10 @@ grouping symbols first, We only write one equals sign per line. For example, if we are resolving parentheses: -$$ \begin{equation} \begin{split} 2 + \[3 + (4+5)\] = 2 + \[3 +9\] \\ = 2 + 12 -\\ = 14 \end{split} \end{equation} $$ +$$ +\begin{equation} \begin{split} 2 + \[3 + (4+5)\] = 2 + \[3 +9\] \\ = 2 + 12 +\\ = 14 \end{split} \end{equation} +$$ We call parentheses (`()`), brackets (`[]`) and braces `{}`) grouping symbols. When groupings (say parentheses) are used, the expression inside any pair of diff --git a/zk/Fundamental_Theorem_of_Arithmetic.md b/zk/Fundamental_Theorem_of_Arithmetic.md index e1b8b0e..7749287 100644 --- a/zk/Fundamental_Theorem_of_Arithmetic.md +++ b/zk/Fundamental_Theorem_of_Arithmetic.md @@ -4,6 +4,8 @@ tags: - theorems --- +# Fundamental Theorem of Arithmetic + > Every integer greater than one is either a prime number itself or is product > of a unique combination of primes. diff --git a/zk/HTTP_request_types.md b/zk/HTTP_request_types.md index b43d114..b38f1ca 100644 --- a/zk/HTTP_request_types.md +++ b/zk/HTTP_request_types.md @@ -3,6 +3,8 @@ tags: - REST --- +# HTTP request types + ## GET - Get data diff --git a/zk/Increasing_fractions_to_their_highest_terms.md b/zk/Increasing_fractions_to_their_highest_terms.md index 496b194..f88b42c 100644 --- a/zk/Increasing_fractions_to_their_highest_terms.md +++ b/zk/Increasing_fractions_to_their_highest_terms.md @@ -4,6 +4,8 @@ tags: - fractions --- +# Increasing fractions to their highest terms + Given the equivalence between factors and divisors we can increase fractions to higher terms in a very similar way to when we reduce fractions. In the latter case we are dividing by divisors to reduce. In the former, we are multiplying by diff --git a/zk/Intro_to_the_Unix_shell.md b/zk/Intro_to_the_Unix_shell.md index c14e32a..6bddd6f 100644 --- a/zk/Intro_to_the_Unix_shell.md +++ b/zk/Intro_to_the_Unix_shell.md @@ -3,6 +3,8 @@ tags: - shell --- +# Introduction to the Unix shell + ## Unix based systems Many operating systems are based on the UNIX software architecture. macOS/OSX diff --git a/zk/Inversion_of_operators.md b/zk/Inversion_of_operators.md index 548b1e6..84cc71f 100644 --- a/zk/Inversion_of_operators.md +++ b/zk/Inversion_of_operators.md @@ -3,17 +3,24 @@ tags: - prealgebra --- +# Inversion of operators + ## Addition, subtraction Addition is the inverse of subtraction: $$(x - a) + a = x$$ $$ (6 - 2) + 2 = 6 + $$ Subtraction is the inverse of addition: $$(x + a) - a = x$$ $$ (3 + 2) - 2 = 3$$ Division is the inverse of multiplication $$ \frac{a \cdot x}{a} = x$$ $$ \frac{6 -\cdot 3}{6} = 3$$ +\cdot 3}{6} = 3 +$$ Multiplication is the inverse of division $$ a \cdot \frac{x}{a} = x$$ -$$ 2 \cdot -\frac{8}{2} = 8$$ + +$$ +2 \cdot +\frac{8}{2} = 8 +$$ diff --git a/zk/Invoking_the_shell_in_Python.md b/zk/Invoking_the_shell_in_Python.md index 7e0a57e..8fe0faa 100644 --- a/zk/Invoking_the_shell_in_Python.md +++ b/zk/Invoking_the_shell_in_Python.md @@ -4,7 +4,7 @@ tags: [python, shell] created: Monday, April 29, 2024 --- -# Invoking the shell_in_Python +# Invoking the shell in Python ```py import subprocess diff --git a/zk/Killing_processes.md b/zk/Killing_processes.md index cb88ff8..c33200d 100644 --- a/zk/Killing_processes.md +++ b/zk/Killing_processes.md @@ -4,6 +4,8 @@ tags: - procedural --- +# Killing processes + ## Kill a process running on a port For example a local server. diff --git a/zk/Listing_and_navigating_directories_in_the_Shell.md b/zk/Listing_and_navigating_directories_in_the_Shell.md index 0de3415..d1546dc 100644 --- a/zk/Listing_and_navigating_directories_in_the_Shell.md +++ b/zk/Listing_and_navigating_directories_in_the_Shell.md @@ -3,6 +3,8 @@ tags: - shell --- +# Listing and navigating directories in the shell + ## Listing options Obviously we know that in order to list the files and sub-directories in our diff --git a/zk/Magnetic_core_memory.md b/zk/Magnetic_core_memory.md index fc46976..d97e706 100644 --- a/zk/Magnetic_core_memory.md +++ b/zk/Magnetic_core_memory.md @@ -3,7 +3,7 @@ tags: [computer-history, memory] created: Friday, September 27, 2024 --- -# Magnetic_core_memory +# Magnetic core memory ![](../img/magnetic-core-memory.jpg) diff --git a/zk/Mainframe_computers.md b/zk/Mainframe_computers.md index e09ee43..8ac888e 100644 --- a/zk/Mainframe_computers.md +++ b/zk/Mainframe_computers.md @@ -3,7 +3,7 @@ tags: [computer-history] created: Friday, September 27, 2024 --- -# Mainframe_computers +# Mainframe computers A mainframe computer, also known as a "big iron" is a high performance computer used for resource-intensive tasks that require greater security and availability diff --git a/zk/Memory_versus_processor.md b/zk/Memory_versus_processor.md index e9fa3bb..41313fd 100644 --- a/zk/Memory_versus_processor.md +++ b/zk/Memory_versus_processor.md @@ -3,7 +3,7 @@ tags: ["question"] created: Thursday, August 01, 2024 --- -# Memory_versus_processor +# Memory versus processor > Would a more powerful processor with average or reduced memory capacity > perform better than, equal to, or less than a less powerful processor with diff --git a/zk/Module_wrapping_at_runtime.md b/zk/Module_wrapping_at_runtime.md index 4c51776..8907a92 100644 --- a/zk/Module_wrapping_at_runtime.md +++ b/zk/Module_wrapping_at_runtime.md @@ -3,6 +3,8 @@ tags: - node-js --- +# Module wrapping at runtime in NodeJS + ## The Module Wrapper Function When Node runs each of our module files are wrapped within an diff --git a/zk/Natural_numbers.md b/zk/Natural_numbers.md index e66d070..f6d6602 100644 --- a/zk/Natural_numbers.md +++ b/zk/Natural_numbers.md @@ -3,6 +3,8 @@ tags: - prealgebra --- +# Natural numbers + ## The set of natural numbers $$ \mathbb{N} = {1, 2, 3, ...} $$ diff --git a/zk/Negative_exponents.md b/zk/Negative_exponents.md index 025fb51..29c13b2 100644 --- a/zk/Negative_exponents.md +++ b/zk/Negative_exponents.md @@ -2,6 +2,8 @@ tags: [algebra, exponents] --- +# Negative exponents + When calculating the exponents of a negative number the answer will always will be positive: diff --git a/zk/Network_card.md b/zk/Network_card.md index ce5e0aa..f27e47e 100644 --- a/zk/Network_card.md +++ b/zk/Network_card.md @@ -3,7 +3,7 @@ tags: [networks, hardware] created: Tuesday, August 06, 2024 --- -# Network_card +# Network card The network card (technically know as the Network Interface Card (NIC)) or _network adapter_ is the hardware device that allows a computer to connect to a diff --git a/zk/Network_hosts.md b/zk/Network_hosts.md index f23363f..7606771 100644 --- a/zk/Network_hosts.md +++ b/zk/Network_hosts.md @@ -3,7 +3,7 @@ tags: [networks] created: Saturday, August 03, 2024 --- -# Network_hosts +# Network hosts A network **host** or **node** is a single computing device attached to a ![network](Network_fundamentals.md) diff --git a/zk/NodeJS_scripts.md b/zk/NodeJS_scripts.md index 9743dfa..19fedd5 100644 --- a/zk/NodeJS_scripts.md +++ b/zk/NodeJS_scripts.md @@ -1,10 +1,9 @@ --- -id: 5043 tags: [node-js] created: Friday, April 26, 2024 --- -# NodeJS_scripts +# NodeJS scripts If we want to use NodeJS as a scripting language without going to the trouble of setting up an NPM-based development environment, we can use the following diff --git a/zk/Order_of_operations.md b/zk/Order_of_operations.md index a483c08..99eb5ce 100644 --- a/zk/Order_of_operations.md +++ b/zk/Order_of_operations.md @@ -3,6 +3,8 @@ tags: - prealgebra --- +# Order of operations + 1. Evaluate expressions in **parentheses** 1. Evaluate **exponents** 1. Evaluate **multiplications and divisions** from left to right in the order diff --git a/zk/Prime_factorization.md b/zk/Prime_factorization.md index d63d9a5..0786091 100644 --- a/zk/Prime_factorization.md +++ b/zk/Prime_factorization.md @@ -4,7 +4,7 @@ tags: - number-theory --- -### Prime factorisation +# Prime factorisation Prime factorisation is the activity of expressing a composite number as the unique product of [prime numbers](Primes%20and%20composites.md). There are two @@ -17,8 +17,8 @@ main approaches to this: > $n$. We then repeat this process with the resulting factors working > recursively until the numbers we are left with are primes. -![Untitled Diagram-Page-1.drawio.png](Untitled%20Diagram-Page-1.drawio.png) -_The prime factors of 27 are 2, 3, 3_ +![Untitled Diagram-Page-1.drawio.png](Untitled%20Diagram-Page-1.drawio.png) _The +prime factors of 27 are 2, 3, 3_ it doesn't matter which products we choose as the interim factors, we should always reach the same outcome: diff --git a/zk/Primes_and_composites.md b/zk/Primes_and_composites.md index c687833..b93dcbf 100644 --- a/zk/Primes_and_composites.md +++ b/zk/Primes_and_composites.md @@ -4,7 +4,7 @@ tags: - number-theory --- -## Prime and composite numbers +# Prime and composite numbers Definition of a **prime number**: diff --git a/zk/ROM versus disk loading.md b/zk/ROM versus disk loading.md deleted file mode 100644 index 978ef28..0000000 --- a/zk/ROM versus disk loading.md +++ /dev/null @@ -1,58 +0,0 @@ ---- -id: rmvm -tags: [computer-architecture, memory] -created: Monday, June 24, 2024 ---- - -# ROM versus disk loading - -I will explore the concept via the practical examples of cartridge-based and -disk-based video games console. - -When you insert a disk into an Xbox, the game data is typically read from the -disk and transferred into the console's memory by the OS. If the game is -installed to the hard drive, this initially involves transferring substantial -amounts of data to speed up future access. When you insert a cartridge into a -console like the SNES, the data is not transferred in the same way. Instead, the -cartridge contains a ROM chip that, when inserted, integrates directly with the -motherboard. From the operating system’s point of view, this ROM chip behaves as -an extension of the system’s memory architecture. - -The primary advantage of a ROM-based game is significantly reduced latency. The -game data can be accessed as rapidly as any other data moving along the buses of -the motherboard. With a disk, the data must first be read into a buffer and then -transferred to a memory address where it can be accessed by the CPU. - -With a ROM, while the console CPU still uses its own RAM to run the game -(similar to disk-based systems), the game data on the ROM can be loaded into -this RAM more quickly because it is directly attached to the motherboard. This -makes the ROM cartridge effectively a fast, directly connected storage device. - -However, despite its speed, the limitation of a ROM cartridge is its storage -capacity—it can hold only as much data as the chip can accommodate. In contrast, -a disk can store much more data. This larger storage capacity allows not just -for bigger and more complex games but also for the possibility of expanding the -game through additional data downloaded to the console's hard drive. Such -expansions or patches represent additional data from the console’s storage that, -combined with the original disk data, are synthesized in memory at runtime for -enhanced or updated gameplay experiences. - -(Note however that modern cartridge-based consoles like the Nintendo Switch can -also combine ROM-data with expanded data from the console HDD, sourced from the -internet.) - -Both disks and ROMs are forms of static storage in the context of a game -console. While disks can technically be overwritten with new data, in practice, -manufacturers implement various locks and protections to prevent this. Any -changes or additions to the game, such as patches or expansions, are not written -back to the original disk. Instead, these updates are stored on the console's -hard drive. - -Therefore, if you download an expansion for a game on your Xbox, the original -disk remains unchanged as when you first purchased it. Consequently, if you were -to take that disk and load it on another Xbox, it would not include any of the -expansions or updates. The game would function in its original form, as the -additional content and updates reside solely on the hard drive of the first -console where they were downloaded. - -## Related notes diff --git a/zk/ROM_versus_disk_loading.md b/zk/ROM_versus_disk_loading.md index 35cfd7e..978ef28 100644 --- a/zk/ROM_versus_disk_loading.md +++ b/zk/ROM_versus_disk_loading.md @@ -9,22 +9,50 @@ created: Monday, June 24, 2024 I will explore the concept via the practical examples of cartridge-based and disk-based video games console. -When you insert a disk into an XBox, the game data is transferred from the disk -into the console's memory by the OS. When you insert a cartridge into a SNES, -there is no transferral of data. The game data is stored on a chip and this chip -is attached to the motherboard. From the point of view of the OS, it is just -another chip along with the others that comprise the motherboard. +When you insert a disk into an Xbox, the game data is typically read from the +disk and transferred into the console's memory by the OS. If the game is +installed to the hard drive, this initially involves transferring substantial +amounts of data to speed up future access. When you insert a cartridge into a +console like the SNES, the data is not transferred in the same way. Instead, the +cartridge contains a ROM chip that, when inserted, integrates directly with the +motherboard. From the operating system’s point of view, this ROM chip behaves as +an extension of the system’s memory architecture. -The chief advantage with a ROM game is that the latency is greatly reduced. The -game data can be accessed as rapidly as any other data travelling along the -busses of the motherboard. With a disk, the bytes have to be transferred in a -buffer from the disk into a memory address and from there, accessed by the CPU. +The primary advantage of a ROM-based game is significantly reduced latency. The +game data can be accessed as rapidly as any other data moving along the buses of +the motherboard. With a disk, the data must first be read into a buffer and then +transferred to a memory address where it can be accessed by the CPU. -With a ROM, the console CPU still uses its own memory to run the game (as with -disk-based consoles), it is just that the game data on the ROM can be loaded -into memory quicker because it is attached to the motherboard. +With a ROM, while the console CPU still uses its own RAM to run the game +(similar to disk-based systems), the game data on the ROM can be loaded into +this RAM more quickly because it is directly attached to the motherboard. This +makes the ROM cartridge effectively a fast, directly connected storage device. -becomes part of the motherboard just like the other chips that comprise the -motherboard. +However, despite its speed, the limitation of a ROM cartridge is its storage +capacity—it can hold only as much data as the chip can accommodate. In contrast, +a disk can store much more data. This larger storage capacity allows not just +for bigger and more complex games but also for the possibility of expanding the +game through additional data downloaded to the console's hard drive. Such +expansions or patches represent additional data from the console’s storage that, +combined with the original disk data, are synthesized in memory at runtime for +enhanced or updated gameplay experiences. + +(Note however that modern cartridge-based consoles like the Nintendo Switch can +also combine ROM-data with expanded data from the console HDD, sourced from the +internet.) + +Both disks and ROMs are forms of static storage in the context of a game +console. While disks can technically be overwritten with new data, in practice, +manufacturers implement various locks and protections to prevent this. Any +changes or additions to the game, such as patches or expansions, are not written +back to the original disk. Instead, these updates are stored on the console's +hard drive. + +Therefore, if you download an expansion for a game on your Xbox, the original +disk remains unchanged as when you first purchased it. Consequently, if you were +to take that disk and load it on another Xbox, it would not include any of the +expansions or updates. The game would function in its original form, as the +additional content and updates reside solely on the hard drive of the first +console where they were downloaded. ## Related notes diff --git a/zk/Reducing_fractions.md b/zk/Reducing_fractions.md index 427253c..46b2a9c 100644 --- a/zk/Reducing_fractions.md +++ b/zk/Reducing_fractions.md @@ -4,7 +4,7 @@ tags: - fractions --- -## Reducing fractions to their lowest terms +# Reducing fractions to their lowest terms > A fraction is said to be _reduced to its lowest terms_ if the > [greatest common divisor](Factors%20and%20divisors.md#greatest-common-divisor)