From d070d924a378e0f19458bbda8403b504abe5fe81 Mon Sep 17 00:00:00 2001 From: TrudeEH Date: Fri, 21 Feb 2025 17:01:15 +0000 Subject: [PATCH 1/6] INC: how_to_computer --- content/.obsidian/workspace.json | 66 +- content/TODO.md | 1 + content/notes/drafts/nvim.md | 8 +- .../notes/ready/binary_operations/image68.png | Bin 22353 -> 0 bytes content/notes/ready/diodes.md | 109 --- .../AND_electronics.png} | Bin .../AND_electronics_transistors.png} | Bin .../notes/ready/how_to_computer/AND_gates.png | Bin 0 -> 21903 bytes .../ready/how_to_computer/AND_gates_big.png | Bin 0 -> 31669 bytes .../ready/how_to_computer/NAND_circuit.png | Bin 0 -> 23758 bytes .../notes/ready/how_to_computer/NOR_gates.png | Bin 0 -> 25757 bytes .../NOT_electronics.png} | Bin .../notes/ready/how_to_computer/NOT_gates.png | Bin 0 -> 20781 bytes .../OR_electronics.png} | Bin .../notes/ready/how_to_computer/OR_gates.png | Bin 0 -> 23944 bytes .../ready/how_to_computer/OR_gates_big.png | Bin 0 -> 32382 bytes 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content/notes/ready/logic_gates/index.md | 122 ---- content/notes/ready/transistors/index.md | 49 -- 41 files changed, 713 insertions(+), 308 deletions(-) delete mode 100644 content/notes/ready/binary_operations/image68.png delete mode 100644 content/notes/ready/diodes.md rename content/notes/ready/{logic_gates/image51.png => how_to_computer/AND_electronics.png} (100%) rename content/notes/ready/{logic_gates/image52.png => how_to_computer/AND_electronics_transistors.png} (100%) create mode 100644 content/notes/ready/how_to_computer/AND_gates.png create mode 100644 content/notes/ready/how_to_computer/AND_gates_big.png create mode 100644 content/notes/ready/how_to_computer/NAND_circuit.png create mode 100644 content/notes/ready/how_to_computer/NOR_gates.png rename content/notes/ready/{logic_gates/image50.png => how_to_computer/NOT_electronics.png} (100%) create mode 100644 content/notes/ready/how_to_computer/NOT_gates.png rename content/notes/ready/{logic_gates/image53.png => how_to_computer/OR_electronics.png} (100%) create mode 100644 content/notes/ready/how_to_computer/OR_gates.png create mode 100644 content/notes/ready/how_to_computer/OR_gates_big.png create mode 100644 content/notes/ready/how_to_computer/XNOR_gates.png create mode 100644 content/notes/ready/how_to_computer/XOR_gates.png create mode 100644 content/notes/ready/how_to_computer/bit_switch.png create mode 100644 content/notes/ready/how_to_computer/bus.png create mode 100644 content/notes/ready/how_to_computer/full_adder.png create mode 100644 content/notes/ready/how_to_computer/full_adder_8bit.png create mode 100644 content/notes/ready/how_to_computer/half_adder.png rename content/notes/ready/{transistors => how_to_computer}/image.png (100%) rename content/notes/ready/{transistors => how_to_computer}/image1.png (100%) rename content/notes/ready/{transistors => how_to_computer}/image2.png (100%) rename content/notes/ready/{transistors => how_to_computer}/image3.png (100%) rename content/notes/ready/{transistors => how_to_computer}/image4.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image42.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image43.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image44.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image45.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image46.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image47.png (100%) rename content/notes/ready/{logic_gates => how_to_computer}/image49.png (100%) create mode 100644 content/notes/ready/how_to_computer/index.md create mode 100644 content/notes/ready/how_to_computer/input_selector.png create mode 100644 content/notes/ready/how_to_computer/signed_negator.png delete mode 100644 content/notes/ready/logic_gates/image48.png delete mode 100644 content/notes/ready/logic_gates/index.md delete mode 100644 content/notes/ready/transistors/index.md diff --git a/content/.obsidian/workspace.json b/content/.obsidian/workspace.json index cddfa30..569265f 100644 --- a/content/.obsidian/workspace.json +++ b/content/.obsidian/workspace.json @@ -4,21 +4,33 @@ "type": "split", "children": [ { - "id": "da1c1c5ba8d6b94f", + "id": "929b0fcada89ed0e", "type": "tabs", "children": [ { - "id": "ab03f7100c1ce0fb", + "id": "28c9848f88828495", "type": "leaf", "state": { "type": "markdown", "state": { - "file": "posts/notes-update.md", + "file": "notes/ready/how_to_computer/index.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "notes-update" + "title": "index" + } + }, + { + "id": "5b5978f088ca6b22", + "type": "leaf", + "state": { + "type": "image", + "state": { + "file": "notes/ready/how_to_computer/input_selector.png" + }, + "icon": "lucide-image", + "title": "input_selector" } } ] @@ -78,7 +90,7 @@ } ], "direction": "horizontal", - "width": 200 + "width": 289.5 }, "right": { "id": "f049c1d8215eafd9", @@ -141,13 +153,13 @@ "state": { "type": "outline", "state": { - "file": "posts/notes-update.md", + "file": "notes/ready/how_to_computer/index.md", "followCursor": false, "showSearch": false, "searchQuery": "" }, "icon": "lucide-list", - "title": "Outline of notes-update" + "title": "Outline of index" } } ], @@ -155,7 +167,7 @@ } ], "direction": "horizontal", - "width": 200 + "width": 249.5 }, "left-ribbon": { "hiddenItems": { @@ -169,40 +181,42 @@ "table-editor-obsidian:Advanced Tables Toolbar": false } }, - "active": "ab03f7100c1ce0fb", + "active": "b73f137a8a755c19", "lastOpenFiles": [ - "_Templates/post.md", + "notes/ready/how_to_computer/input_selector.png", + "notes/ready/how_to_computer/index.md", + "notes/ready/how_to_computer/bit_switch.png", + "notes/ready/how_to_computer/bus.png", + "notes/ready/how_to_computer/signed_negator.png", + "notes/ready/how_to_computer/full_adder_8bit.png", + "notes/ready/how_to_computer/full_adder.png", + "notes/ready/how_to_computer/half_adder.png", + "notes/ready/binary_operations/index.md", + "notes/ready/how_to_computer/image.png", + "notes/ready/how_to_computer/OR_gates_big.png", + "notes/ready/how_to_computer/image4.png", + "TODO.md", + "notes/ready/transistors/index.md", + "notes/ready/diodes.md", + "notes/drafts/nvim.md", + "notes/drafts/linux/index.md", "posts/notes-update.md", + "_Templates/post.md", "_Templates/note.md", "posts/personal-web.md", "posts/linux-starter-guide.md", "posts/local-llm.md", "posts/nix-starter-guide.md", "posts/dotfiles.md", - "notes/drafts/linux/index.md", - "TODO.md", "notes/ready/flask.md", "notes/ready/gdb.md", "notes/ready/git.md", "notes/ready/http.md", "notes/ready/html.md", - "notes/ready/binary_operations/d1.png", - "notes/ready/binary_operations/index.md", - "notes/ready/binary_operations/d6.png", - "notes/ready/binary_operations/d5.png", - "notes/ready/binary_operations/d4.png", - "notes/ready/binary_operations/d3.png", - "notes/ready/binary_operations/d2.png", - "notes/ready/binary_operations/multiplication.png", "notes/ready/firewall.md", "drafts/nvim.md", "drafts/rust.md", "drafts/swift.md", - "drafts/TODO.md", - "drafts/Untitled.md", - "drafts/hardware-tools.md", - "drafts/macOS.md", - "ready/algorithms_and_data/index.md", - "ready/binary_operations/index.md" + "drafts/TODO.md" ] } \ No newline at end of file diff --git a/content/TODO.md b/content/TODO.md index 13f152a..8901b8f 100644 --- a/content/TODO.md +++ b/content/TODO.md @@ -19,5 +19,6 @@ In draft folder? (checkbox) - [x] Neovim, vim bindings, text editor - [x] Hardware Debug/Repair Tools (maybe integrate JCionx page?) - [ ] Android and custom ROMs +- [ ] netcat ### Enhancements diff --git a/content/notes/drafts/nvim.md b/content/notes/drafts/nvim.md index 8a966dc..bbf649a 100644 --- a/content/notes/drafts/nvim.md +++ b/content/notes/drafts/nvim.md @@ -1,14 +1,18 @@ --- -title: "nvim" +title: nvim description: draft: true -tags: +tags: + - tools + - nvim + - vim author: TrudeEH showToc: true --- ## VIM Bindings + ## Using Neovim ## Configuring Neovim diff --git a/content/notes/ready/binary_operations/image68.png b/content/notes/ready/binary_operations/image68.png deleted file mode 100644 index 48c541aaf5240217a9d94c2c91e36ca3823c1d6d..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 22353 zcmb@u^rb#RVFjv4zMdi?RH>eTnj%F1}N zM4x@9yzua4DEz$4G;u>o!H*ff0$v#W12&38k^z2>NdD(ftS?_r?+m%b3;F)CfsP zUX6@s!R0(Em(?-*zNmcX`-!`){wH=T?qb 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--git a/content/notes/ready/diodes.md b/content/notes/ready/diodes.md deleted file mode 100644 index 7354795..0000000 --- a/content/notes/ready/diodes.md +++ /dev/null @@ -1,109 +0,0 @@ ---- -title: Diodes -description: -draft: false -tags: - - electronics -author: TrudeEH -showToc: true ---- - - - -A diode allows current to only flow in one direction in a circuit. - -## Schematic - -```Plain -Anode (+) --|>|-- Cathode (-) -``` - -## Examples - -```Plain -[Conventional Current (+) -> (-)] -(+)------|>|------(-) Current can flow - The diode is now a conductor. -(+)------|<|------(-) Current can't flow - The diode is now an insulator. -``` - -## Use Cases - -- Protect a circuit (if a battery is connected incorrectly, for example) -- Convert AC to DC current -Fun fact: An LED, for example, is a Light-Emitting Diode. - -## How a Diode Works - -### Conductors and Insulators - -An atom contains the following elements: -- Nucleus (Protons - Neutrons) -- Orbital Shells (Holds the electrons, which orbit around the nucleus) -- Conduction band -The electrons closest to the nucleus hold the most energy. -The outermost shell is the valence shell. A conductor has 1-3 electrons in the valence shell. -If an electron reaches the conduction band, it can break free and move to another atom. -An insulator, however, has a conduction band that is far from the valence shell, making it difficult for an electron to escape. -For example, for copper (a great conductor), the valence shell and conduction band overlap, so it's very easy for an electron to jump between atoms. -Semiconductors have a conduction band close to the valence shell, but have one extra electron in it, making it an insulator. However, given some external energy, some electrons will gain enough energy to reach the conduction band and become free. - -### P-Type and N-Type Doping - -Silicon is a good semiconductor, having 4 electrons in its valence shell. When close to other `Si` atoms, they share 4 electrons with their neighbors, thus, having 8, each, and becoming stable. - -```Plain -Silicon: -Si Si Si Si Si Si Si Si Si Si Si -Si Si Si Si Si Si Si Si Si Si Si -Si Si Si Si Si Si Si Si Si Si Si -Si Si Si Si Si Si Si Si Si Si Si -Si Si Si Si Si Si Si Si Si Si Si -Si Si Si Si Si Si Si Si Si Si Si -``` - -#### N-Type - -Some Phosphorus is added to the Silicon. ==`p`== has one extra electron in its valence shell. -These electrons are not needed, and so, they flow freely from atom to atom. - -```Plain -Si Si p Si Si Si Si Si Si Si p -p Si Si Si Si p Si Si Si Si Si -Si Si Si p Si Si Si Si p Si Si -Si p Si Si p Si Si Si Si Si Si -Si Si Si Si Si Si p Si Si p Si -Si p Si Si Si Si Si Si p Si Si -``` - -#### P-Type - -Some Aluminum is added to the Silicon. `Al` is missing one electron, so it can't provide its 4 neighbors with an electron to share. - -```Plain -Si Si Al Si Si Si Si Si Si Si Al -Al Si Si Si Si Al Si Si Si Si Si -Si Si Si Al Si Si Si Si Al Si Si -Si Al Si Si Al Si Si Si Si Si Si -Si Si Si Si Si Si Al Si Si Al Si -Si Al Si Si Si Si Si Si Al Si Si -``` - -### Combining both Types - -When an N-Type is combined with a P-Type, some electrons from the N-Type side will move over to the P-Type side and occupy the missing electrons there. This creates a barrier between both types, creating an electric field that prevents more electrons from switching sides. - -#### Forward Bias - -If energy is provided to the Cathode, the electrons flow, as the voltage is superior to the barrier's. - -```Plain -(-)-----[P|N]-----(+) -``` - -#### Reverse Bias - -If energy is provided to the Anode, the electrons can't flow, as the barrier expands. - -```Plain -(-)--[P] [N]--(+) -``` diff --git a/content/notes/ready/logic_gates/image51.png b/content/notes/ready/how_to_computer/AND_electronics.png similarity index 100% rename from content/notes/ready/logic_gates/image51.png rename to content/notes/ready/how_to_computer/AND_electronics.png diff --git a/content/notes/ready/logic_gates/image52.png b/content/notes/ready/how_to_computer/AND_electronics_transistors.png similarity index 100% rename from content/notes/ready/logic_gates/image52.png rename to content/notes/ready/how_to_computer/AND_electronics_transistors.png diff --git 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q#<>pybAA_O9#skPsaAOBBL5E!fS*QR2@zBP0000|-- Cathode (-) +``` + +### Examples + +```Plain +[Conventional Current (+) -> (-)] +(+)------|>|------(-) Current can flow - The diode is now a conductor. +(+)------|<|------(-) Current can't flow - The diode is now an insulator. +``` + +### Use Cases + +- Protect a circuit (if a battery is connected incorrectly, for example) +- Convert AC to DC current +Fun fact: An LED, for example, is a Light-Emitting Diode. + +### How a Diode Works + +#### Conductors and Insulators + +An atom contains the following elements: +- Nucleus (Protons - Neutrons) +- Orbital Shells (Holds the electrons, which orbit around the nucleus) +- Conduction band +The electrons closest to the nucleus hold the most energy. +The outermost shell is the valence shell. A conductor has 1-3 electrons in the valence shell. +If an electron reaches the conduction band, it can break free and move to another atom. +An insulator, however, has a conduction band that is far from the valence shell, making it difficult for an electron to escape. +For example, for copper (a great conductor), the valence shell and conduction band overlap, so it's very easy for an electron to jump between atoms. +Semiconductors have a conduction band close to the valence shell, but have one extra electron in it, making it an insulator. However, given some external energy, some electrons will gain enough energy to reach the conduction band and become free. + +#### P-Type and N-Type Doping + +Silicon is a good semiconductor, having 4 electrons in its valence shell. When close to other `Si` atoms, they share 4 electrons with their neighbors, thus, having 8, each, and becoming stable. + +```Plain +Silicon: +Si Si Si Si Si Si Si Si Si Si Si +Si Si Si Si Si Si Si Si Si Si Si +Si Si Si Si Si Si Si Si Si Si Si +Si Si Si Si Si Si Si Si Si Si Si +Si Si Si Si Si Si Si Si Si Si Si +Si Si Si Si Si Si Si Si Si Si Si +``` + +##### N-Type + +Some Phosphorus is added to the Silicon. ==`p`== has one extra electron in its valence shell. +These electrons are not needed, and so, they flow freely from atom to atom. + +```Plain +Si Si p Si Si Si Si Si Si Si p +p Si Si Si Si p Si Si Si Si Si +Si Si Si p Si Si Si Si p Si Si +Si p Si Si p Si Si Si Si Si Si +Si Si Si Si Si Si p Si Si p Si +Si p Si Si Si Si Si Si p Si Si +``` + +##### P-Type + +Some Aluminum is added to the Silicon. `Al` is missing one electron, so it can't provide its 4 neighbors with an electron to share. + +```Plain +Si Si Al Si Si Si Si Si Si Si Al +Al Si Si Si Si Al Si Si Si Si Si +Si Si Si Al Si Si Si Si Al Si Si +Si Al Si Si Al Si Si Si Si Si Si +Si Si Si Si Si Si Al Si Si Al Si +Si Al Si Si Si Si Si Si Al Si Si +``` + +#### Combining both Types + +When an N-Type is combined with a P-Type, some electrons from the N-Type side will move over to the P-Type side and occupy the missing electrons there. This creates a barrier between both types, creating an electric field that prevents more electrons from switching sides. + +##### Forward Bias + +If energy is provided to the Cathode, the electrons flow, as the voltage is superior to the barrier's. + +```Plain +(-)-----[P|N]-----(+) +``` + +##### Reverse Bias + +If energy is provided to the Anode, the electrons can't flow, as the barrier expands. + +```Plain +(-)--[P] [N]--(+) +``` + +## Transistor + +Transistors are electronic components that behave like a `switch`, or `amplifier`. + +### Schematic + +```Plain + .--.,-- Collector +Base --(--|<) + `--`'-- Emitter +``` + +### Examples + +#### Switch + +If the `base` pin is provided with energy, the transistor allows current to flow in the main circuit. +![[image.png]] + +#### Amplifier + +Altering the voltage given to the `base` pin allows us to control a larger voltage in the main circuit. +![image1](image1.png) + +### Types of Transistor + +#### NPN + +An NPN transistor combines the `base` pin and `collector` pin. +![image2](image2.png) + +> Note: Even if the collector pin is disconnected from the circuit, a small amount of current still passes through. ![image3](image3.png) + +#### PNP + +A PNP transistor receives energy through the `emitter` pin, and then divides it to the remaining pins. + + +![image4](image4.png) + +## Basic Logic + +A logic gate is a device that performs one boolean operation: Two binary inputs produce a single binary output. These building blocks are the foundations of modern computing. +Each gate has its own truth table, which shows every possible input and output variations. + +### NAND + +A NAND gate, although not the simplest one, can be used to build all other basic gates. + +![image45](image45.png) + +#### Truth Table + +|A|**B**|**Output**| +|---|---|---| +|0|0|1| +|0|1|1| +|1|0|1| +|1|1|0| + +#### Implementation + +##### Electronics + +Implementation using switches and a pull-up resistor: +![[NAND_circuit.png]] + +### NOT + +Invert any given input. + +![image42](image42.png) + +#### Truth Table + +|**Input**|**Output**| +|---|---| +|0|1| +|1|0| + +#### Implementation + +##### Logic Gates + +![[NOT_gates.png]] + +##### Electronics + +![image50](NOT_electronics.png) + +### AND + +Outputs `1` only when both inputs are `1`. + +![image43](image43.png) + +#### Truth Table + +|A|**B**|**Output**| +|---|---|---| +|0|0|0| +|0|1|0| +|1|0|0| +|1|1|1| + +#### Implementation + +##### Logic Gates + +![[AND_gates.png]] + +##### Electronics + +![image51](AND_electronics.png) +![image52](AND_electronics_transistors.png) + +#### Bigger AND Gate + +AND gates can be chained to accept more inputs. + +![[AND_gates_big.png]] + +##### Truth Table + +| A | **B** | C | **Output** | +| --- | ----- | --- | ---------- | +| 0 | 0 | 0 | 0 | +| 0 | 1 | 0 | 0 | +| 1 | 0 | 0 | 0 | +| 1 | 1 | 0 | 0 | +| 0 | 0 | 1 | 0 | +| 0 | 1 | 1 | 0 | +| 1 | 0 | 1 | 0 | +| 1 | 1 | 1 | 1 | + +### OR + +Outputs `1` if at least one input is `1`. + +![image44](image44.png) + +#### Truth Table + +|A|**B**|**Output**| +|---|---|---| +|0|0|0| +|0|1|1| +|1|0|1| +|1|1|1| + +#### Implementation + +##### Logic Gates + +![[OR_gates.png]] + +##### Electronics + +![image53](OR_electronics.png) + +#### Bigger OR Gate + +![[OR_gates_big.png]] + +##### Truth Table + +| A | **B** | C | **Output** | +| --- | ----- | --- | ---------- | +| 0 | 0 | 0 | 0 | +| 0 | 1 | 0 | 1 | +| 1 | 0 | 0 | 1 | +| 1 | 1 | 0 | 1 | +| 0 | 0 | 1 | 1 | +| 0 | 1 | 1 | 1 | +| 1 | 0 | 1 | 1 | +| 1 | 1 | 1 | 1 | + +### NOR + +An OR gate followed by a NOT gate. + +A NOR gate is can also be used to build every other gate, just like NAND. However, NAND gates are preferred over NOR gates, as, in modern computers, they occupy less area and have less delay. + +![image46](image46.png) + +#### Truth Table + +|A|**B**|**Output**| +|---|---|---| +|0|0|1| +|0|1|0| +|1|0|0| +|1|1|0| + +#### Implementation + +##### Logic Gates + +![[NOR_gates.png]] + +### XOR + +Either input is `1`, exclusively. (OR, but if both inputs are on, it turns off.) + +![image47](image47.png) + +#### Truth Table + +| A | **B** | **Output** | +| --- | ----- | ---------- | +| 0 | 0 | 0 | +| 0 | 1 | 1 | +| 1 | 0 | 1 | +| 1 | 1 | 0 | + +#### Implementation + +##### Logic Gates + +![[XOR_gates.png]] + +### XNOR + +Inverted `XOR`. + +![image49](image49.png) + +#### Truth Table + +|A|**B**|**Output**| +|---|---|---| +|0|0|1| +|0|1|0| +|1|0|0| +|1|1|1| + +#### Implementation + +##### Logic Gates + +![[XNOR_gates.png]] + +## Binary + +Binary is a base-2 numeral system: A simple way to represent numbers using only two states. + +|Binary|Decimal|Hexadecimal| +|---|---|---| +|0000|00|00| +|0001|01|01| +|0010|02|02| +|0011|03|03| +|0100|04|04| +|0101|05|05| +|0110|06|06| +|0111|07|07| +|1000|08|08| +|1001|09|09| +|1010|10|0A| +|1011|11|0B| +|1100|12|0C| +|1101|13|0D| +|1110|14|0E| +|1111|15|0F| + +![Binary Calculations](binarycalc.png) + +## Arithmetic Operations + +### Addition + +Adding two numbers can be done using a simple, manual algorithm: By adding the last bit of both numbers first, carry if necessary, then move on to the next number, and so on. + +| **+** | 0 | 1 | +| ------- | --- | ---- | +| 0 | 0 | 1 | +| 1 | 1 | 10 | + +![addition](addition.png) + +#### Half Adder + +Add 2, single-digit binary numbers. + +| **A** | **B** | **Carry** | **Sum** | +| ----- | ----- | --------- | ------- | +| 0 | 0 | 0 | 0 | +| 0 | 1 | 0 | 1 | +| 1 | 0 | 0 | 1 | +| 1 | 1 | 1 | 0 | + +![[half_adder.png]] + +#### Full Adder (ADD) + +When adding 2 binary numbers, one operation might return a carry value, which the `half adder` can't accept, as it only has 2 inputs. + +![image69](image69.png) + +To solve this issue, a `full adder` accepts 3 inputs. + +![[full_adder.png]] + +#### 8-Bit Adder + +To add two bytes, chain 8 full-adders. +(The dark blue lines are buses: 8 bits in parallel, simplified for better readability) + +![[full_adder_8bit.png]] + +### Two's Complement + +The most common solution to represent negative numbers is to interpret the last bit as a negative value. For a byte, the last bit changes its value from 128 to -128. + +> A negative number is often called a *signed* number. + +The main advantage of the Two's Complement system is that the adder built previously also works with it. + +#### Invert Sign + +To switch between negative and positive numbers, flip all bits, then add 1. + +![[signed_negator.png]] + +--- + +### Subtraction + +Subtraction can result in negative numbers. Like how additions need a carry, subtraction needs a borrow. + +#### Half Subtractor + +Subtract 2, single-digit binary numbers. + +| **A** | **B** | Diff | **Borrow** | +| ----- | ----- | ---- | ---------- | +| 0 | 0 | 0 | 0 | +| 0 | 1 | 1 | 1 | +| 1 | 0 | 1 | 0 | +| 1 | 1 | 0 | 0 | + +![image72](image72.png) + +#### Full Subtractor + +A `full subtractor` accepts the borrow value, allowing us to chain results. + +| **A** | **B** | **B**in | **Diff** | **B**out | +| ----- | ----- | ------- | -------- | -------- | +| 0 | 0 | 0 | 0 | 0 | +| 0 | 0 | 1 | 1 | 1 | +| 0 | 1 | 0 | 1 | 1 | +| 0 | 1 | 1 | 0 | 1 | +| 1 | 0 | 0 | 1 | 0 | +| 1 | 0 | 1 | 0 | 0 | +| 1 | 1 | 0 | 0 | 0 | +| 1 | 1 | 1 | 1 | 1 | + +![image73](image73.png) + +#### 8-Bit Subtractor + +![image74](image74.png) + +### Multiplication + +Multiplication is also similar to its decimal counterpart, but because binary is so small compared to decimal, the steps are also much simpler. + +First, multiply the top number to every digit of the bottom one, and then add the results together. + +| X | 0 | 1 | +| --- | --- | --- | +| 0 | 0 | 0 | +| 1 | 0 | 1 | + +![multiplication](multiplication.png) + +#### 2-Bit By 2-Bit Multiplier + +![image75](image75.png) + +### Division + +1. Find the smallest part of the dividend greater than or equal to the **divisor**.![d1](d1.png) + + +2. Write the first digit of **the answer**, and **copy the original divisor down**.![d2](d2.png) + + +3. Subtract the **aligned dividend digits** by **the digits under the dividend**.![d3](d3.png) + +4. Lower **the next dividend digit**.![d4](d4.png) + +5. Is **the total** greater or equal to the **divisor**? If so, add a `1` to the answer. If not, **add a `0` to the answer and return to step 4**.![d5](d5.png) + + +6. Return to step 2, until you reach the end of the number. If you reached the end, you found **the answer**.![d6](d6.png) + +## Memory + +### Byte Switch (SWC) + +A bit switch, also known as transistor, toggles a given input, using a separate bit. + +![[bit_switch.png]] + +If 8 transistors are controlled by the same bit in parallel a Byte Switch is created. + +### Input Selector + +Using a switch, we can select which input to use. + +![[input_selector.png]] + +### Bus + +A Bus is useful to simplify wiring. One bit controls which input should be selected, and a second one, the output. This way, a single wire can transfer twice as much information. + +![[bus.png]] + +### ASCII + +Binary can also be used to represent characters. + +| Dec | Hex | Binary | HTML | Char | Description | +| --- | --- | -------- | -------- | ----------- | ------------------------- | +| 0 | 00 | 00000000 | `�` | NUL | Null | +| 1 | 01 | 00000001 | `` | SOH | Start of Heading | +| 2 | 02 | 00000010 | `` | STX | Start of Text | +| 3 | 03 | 00000011 | `` | ETX | End of Text | +| 4 | 04 | 00000100 | `` | EOT | End of Transmission | +| 5 | 05 | 00000101 | `` | ENQ | Enquiry | +| 6 | 06 | 00000110 | `` | ACK | Acknowledge | +| 7 | 07 | 00000111 | `` | BEL | Bell | +| 8 | 08 | 00001000 | `` | BS | Backspace | +| 9 | 09 | 00001001 | ` ` | HT | Horizontal Tab | +| 10 | 0A | 00001010 | ` ` | LF | Line Feed | +| 11 | 0B | 00001011 | ` ` | VT | Vertical Tab | +| 12 | 0C | 00001100 | ` ` | FF | Form Feed | +| 13 | 0D | 00001101 | ` ` | CR | Carriage Return | +| 14 | 0E | 00001110 | `` | SO | Shift Out | +| 15 | 0F | 00001111 | `` | SI | Shift In | +| 16 | 10 | 00010000 | `` | DLE | Data Link Escape | +| 17 | 11 | 00010001 | `` | DC1 | Device Control 1 | +| 18 | 12 | 00010010 | `` | DC2 | Device Control 2 | +| 19 | 13 | 00010011 | `` | DC3 | Device Control 3 | +| 20 | 14 | 00010100 | `` | DC4 | Device Control 4 | +| 21 | 15 | 00010101 | `` | NAK | Negative Acknowledge | +| 22 | 16 | 00010110 | `` | SYN | Synchronize | +| 23 | 17 | 00010111 | `` | ETB | End of Transmission Block | +| 24 | 18 | 00011000 | `` | CAN | Cancel | +| 25 | 19 | 00011001 | `` | EM | End of Medium | +| 26 | 1A | 00011010 | `` | SUB | Substitute | +| 27 | 1B | 00011011 | `` | ESC | Escape | +| 28 | 1C | 00011100 | `` | FS | File Separator | +| 29 | 1D | 00011101 | `` | GS | Group Separator | +| 30 | 1E | 00011110 | `` | RS | Record Separator | +| 31 | 1F | 00011111 | `` | US | Unit Separator | +| 32 | 20 | 00100000 | ` ` | space | Space | +| 33 | 21 | 00100001 | `!` | ! | exclamation mark | +| 34 | 22 | 00100010 | `"` | " | double quote | +| 35 | 23 | 00100011 | `#` | # | number | +| 36 | 24 | 00100100 | `$` | $ | dollar | +| 37 | 25 | 00100101 | `%` | % | percent | +| 38 | 26 | 00100110 | `&` | & | ampersand | +| 39 | 27 | 00100111 | `'` | ' | single quote | +| 40 | 28 | 00101000 | `(` | ( | left parenthesis | +| 41 | 29 | 00101001 | `)` | ) | right parenthesis | +| 42 | 2A | 00101010 | `*` | * | asterisk | +| 43 | 2B | 00101011 | `+` | + | plus | +| 44 | 2C | 00101100 | `,` | , | comma | +| 45 | 2D | 00101101 | `-` | - | minus | +| 46 | 2E | 00101110 | `.` | . | period | +| 47 | 2F | 00101111 | `/` | / | slash | +| 48 | 30 | 00110000 | `0` | 0 | zero | +| 49 | 31 | 00110001 | `1` | 1 | one | +| 50 | 32 | 00110010 | `2` | 2 | two | +| 51 | 33 | 00110011 | `3` | 3 | three | +| 52 | 34 | 00110100 | `4` | 4 | four | +| 53 | 35 | 00110101 | `5` | 5 | five | +| 54 | 36 | 00110110 | `6` | 6 | six | +| 55 | 37 | 00110111 | `7` | 7 | seven | +| 56 | 38 | 00111000 | `8` | 8 | eight | +| 57 | 39 | 00111001 | `9` | 9 | nine | +| 58 | 3A | 00111010 | `:` | : | colon | +| 59 | 3B | 00111011 | `;` | ; | semicolon | +| 60 | 3C | 00111100 | `<` | < | less than | +| 61 | 3D | 00111101 | `=` | = | equality sign | +| 62 | 3E | 00111110 | `>` | > | greater than | +| 63 | 3F | 00111111 | `?` | ? | question mark | +| 64 | 40 | 01000000 | `@` | @ | at sign | +| 65 | 41 | 01000001 | `A` | A | | +| 66 | 42 | 01000010 | `B` | B | | +| 67 | 43 | 01000011 | `C` | C | | +| 68 | 44 | 01000100 | `D` | D | | +| 69 | 45 | 01000101 | `E` | E | | +| 70 | 46 | 01000110 | `F` | F | | +| 71 | 47 | 01000111 | `G` | G | | +| 72 | 48 | 01001000 | `H` | H | | +| 73 | 49 | 01001001 | `I` | I | | +| 74 | 4A | 01001010 | `J` | J | | +| 75 | 4B | 01001011 | `K` | K | | +| 76 | 4C | 01001100 | `L` | L | | +| 77 | 4D | 01001101 | `M` | M | | +| 78 | 4E | 01001110 | `N` | N | | +| 79 | 4F | 01001111 | `O` | O | | +| 80 | 50 | 01010000 | `P` | P | | +| 81 | 51 | 01010001 | `Q` | Q | | +| 82 | 52 | 01010010 | `R` | R | | +| 83 | 53 | 01010011 | `S` | S | | +| 84 | 54 | 01010100 | `T` | T | | +| 85 | 55 | 01010101 | `U` | U | | +| 86 | 56 | 01010110 | `V` | V | | +| 87 | 57 | 01010111 | `W` | W | | +| 88 | 58 | 01011000 | `X` | X | | +| 89 | 59 | 01011001 | `Y` | Y | | +| 90 | 5A | 01011010 | `Z` | Z | | +| 91 | 5B | 01011011 | `[` | [ | left square bracket | +| 92 | 5C | 01011100 | `\` | \|backslash | | +| 93 | 5D | 01011101 | `]` | ] | right square bracket | +| 94 | 5E | 01011110 | `^` | ^ | caret / circumflex | +| 95 | 5F | 01011111 | `_` | _ | underscore | +| 96 | 60 | 01100000 | ``` | ` | grave / accent | +| 97 | 61 | 01100001 | `a` | a | | +| 98 | 62 | 01100010 | `b` | b | | +| 99 | 63 | 01100011 | `c` | c | | +| 100 | 64 | 01100100 | `d` | d | | +| 101 | 65 | 01100101 | `e` | e | | +| 102 | 66 | 01100110 | `f` | f | | +| 103 | 67 | 01100111 | `g` | g | | +| 104 | 68 | 01101000 | `h` | h | | +| 105 | 69 | 01101001 | `i` | i | | +| 106 | 6A | 01101010 | `j` | j | | +| 107 | 6B | 01101011 | `k` | k | | +| 108 | 6C | 01101100 | `l` | l | | +| 109 | 6D | 01101101 | `m` | m | | +| 110 | 6E | 01101110 | `n` | n | | +| 111 | 6F | 01101111 | `o` | o | | +| 112 | 70 | 01110000 | `p` | p | | +| 113 | 71 | 01110001 | `q` | q | | +| 114 | 72 | 01110010 | `r` | r | | +| 115 | 73 | 01110011 | `s` | s | | +| 116 | 74 | 01110100 | `t` | t | | +| 117 | 75 | 01110101 | `u` | u | | +| 118 | 76 | 01110110 | `v` | v | | +| 119 | 77 | 01110111 | `w` | w | | +| 120 | 78 | 01111000 | `x` | x | | +| 121 | 79 | 01111001 | `y` | y | | +| 122 | 7A | 01111010 | `z` | z | | +| 123 | 7B | 01111011 | `{` | { | left curly bracket | +| 124 | 7C | 01111100 | `|` | \| | vertical bar | +| 125 | 7D | 01111101 | `}` | } | right curly bracket | +| 126 | 7E | 01111110 | `~` | ~ | tilde | +| 127 | 7F | 01111111 | `` | DEL | delete | diff --git a/content/notes/ready/how_to_computer/input_selector.png b/content/notes/ready/how_to_computer/input_selector.png new file mode 100644 index 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z0jyHpho6W**wlOcou@M@)eucuSXpTY8Y0?pT(1iYS5;L0%CYDrLGqEC#uVyS10?OV rumOEd(6#0V;SX<7|Gy08FRzr=`GZaZ`ac65Trxc^W6e@^`>_83tsEt+ diff --git a/content/notes/ready/logic_gates/index.md b/content/notes/ready/logic_gates/index.md deleted file mode 100644 index 76a2131..0000000 --- a/content/notes/ready/logic_gates/index.md +++ /dev/null @@ -1,122 +0,0 @@ ---- -title: Logic Gates -description: -draft: false -tags: - - electronics - - computer-science -author: TrudeEH -showToc: true ---- - -## NOT - -Invert the input. -![image42](image42.png) - -### Truth Table - -|**Input**|**Output**| -|---|---| -|0|1| -|1|0| - -## AND - -Output `1` only when both inputs are `1`. -![image43](image43.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|0| -|0|1|0| -|1|0|0| -|1|1|1| - -## OR - -Output `1` if at least one input is `1`. -![image44](image44.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|0| -|0|1|1| -|1|0|1| -|1|1|1| - -## NAND - -An `AND` gate followed by a `NOT` gate. -![image45](image45.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|1| -|0|1|1| -|1|0|1| -|1|1|0| - -## NOR - -An `OR` gate followed by a `NOT` gate. -![image46](image46.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|1| -|0|1|0| -|1|0|0| -|1|1|0| - -## XOR - -Either input is `1`, exclusively. -![image47](image47.png) -![image48](image48.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|0| -|0|1|1| -|1|0|1| -|1|1|0| - -## XNOR - -Inverted `XOR`. -![image49](image49.png) - -### Truth Table - -|A|**B**|**Output**| -|---|---|---| -|0|0|1| -|0|1|0| -|1|0|0| -|1|1|1| - -## Implementation Examples - -### NOT - -![image50](image50.png) - -### AND - -![image51](image51.png) -![image52](image52.png) - -### OR - -![image53](image53.png) diff --git a/content/notes/ready/transistors/index.md b/content/notes/ready/transistors/index.md deleted file mode 100644 index c780791..0000000 --- a/content/notes/ready/transistors/index.md +++ /dev/null @@ -1,49 +0,0 @@ ---- -title: Transistors -description: -draft: false -tags: - - electronics -author: TrudeEH -showToc: true ---- - - - -Transistors are electronic components that behave like a `switch`, or `amplifier`. - -## Schematic - -```Plain - .--.,-- Collector -Base --(--|<) - `--`'-- Emitter -``` - -## Examples - -### Switch - -If the `base` pin is provided with energy, the transistor allows current to flow in the main circuit. -![image](image.png) - -### Amplifier - -Altering the voltage given to the `base` pin allows us to control a larger voltage in the main circuit. -![image1](image1.png) - -## Types of Transistor - -### NPN - -An NPN transistor combines the `base` pin and `collector` pin. -![image2](image2.png) - -> Note: Even if the collector pin is disconnected from the circuit, a small amount of current still passes through. ![image3](image3.png) - -### PNP - -A PNP transistor receives energy through the `emitter` pin, and then divides it to the remaining pins. - - -![image4](image4.png) From 7db2cb589bc118500a33021f88bc65a8441ce9d2 Mon Sep 17 00:00:00 2001 From: TrudeEH Date: Mon, 24 Feb 2025 16:57:22 +0000 Subject: [PATCH 2/6] UN: how to computer --- content/.obsidian/workspace.json | 55 ++++------ content/3bit_decoder.png | Bin 0 -> 147570 bytes content/8bit_register.png | Bin 0 -> 237131 bytes content/Pasted image 20250224154916.png | Bin 0 -> 24495 bytes content/Pasted image 20250224154920.png | Bin 0 -> 24495 bytes content/decoder.png | Bin 0 -> 24495 bytes .../{memory => how_to_computer}/image80.png | Bin content/notes/ready/how_to_computer/index.md | 100 +++++++++++++++++- content/notes/ready/memory/index.md | 73 ------------- content/transistor_latch.png | Bin 0 -> 86605 bytes 10 files changed, 121 insertions(+), 107 deletions(-) create mode 100644 content/3bit_decoder.png create mode 100644 content/8bit_register.png create mode 100644 content/Pasted image 20250224154916.png create mode 100644 content/Pasted image 20250224154920.png create mode 100644 content/decoder.png rename content/notes/ready/{memory => how_to_computer}/image80.png (100%) delete mode 100644 content/notes/ready/memory/index.md create mode 100644 content/transistor_latch.png diff --git a/content/.obsidian/workspace.json b/content/.obsidian/workspace.json index 569265f..b7fc3b2 100644 --- a/content/.obsidian/workspace.json +++ b/content/.obsidian/workspace.json @@ -4,11 +4,11 @@ "type": "split", "children": [ { - "id": "929b0fcada89ed0e", + "id": "da1c1c5ba8d6b94f", "type": "tabs", "children": [ { - "id": "28c9848f88828495", + "id": "ab03f7100c1ce0fb", "type": "leaf", "state": { "type": "markdown", @@ -20,18 +20,6 @@ "icon": "lucide-file", "title": "index" } - }, - { - "id": "5b5978f088ca6b22", - "type": "leaf", - "state": { - "type": "image", - "state": { - "file": "notes/ready/how_to_computer/input_selector.png" - }, - "icon": "lucide-image", - "title": "input_selector" - } } ] } @@ -167,7 +155,7 @@ } ], "direction": "horizontal", - "width": 249.5 + "width": 200 }, "left-ribbon": { "hiddenItems": { @@ -181,26 +169,22 @@ "table-editor-obsidian:Advanced Tables Toolbar": false } }, - "active": "b73f137a8a755c19", + "active": "ab03f7100c1ce0fb", "lastOpenFiles": [ - "notes/ready/how_to_computer/input_selector.png", + "3bit_decoder.png", "notes/ready/how_to_computer/index.md", - "notes/ready/how_to_computer/bit_switch.png", - "notes/ready/how_to_computer/bus.png", - "notes/ready/how_to_computer/signed_negator.png", - "notes/ready/how_to_computer/full_adder_8bit.png", - "notes/ready/how_to_computer/full_adder.png", - "notes/ready/how_to_computer/half_adder.png", - "notes/ready/binary_operations/index.md", - "notes/ready/how_to_computer/image.png", - "notes/ready/how_to_computer/OR_gates_big.png", - "notes/ready/how_to_computer/image4.png", - "TODO.md", - "notes/ready/transistors/index.md", - "notes/ready/diodes.md", - "notes/drafts/nvim.md", - "notes/drafts/linux/index.md", + "decoder.png", + "Pasted image 20250224154920.png", + "Pasted image 20250224154916.png", + "transistor_latch.png", + "8bit_register.png", + "notes/ready/memory/index.md", "posts/notes-update.md", + "notes/ready/how_to_computer/signed_negator.png", + "notes/ready/how_to_computer/input_selector.png", + "notes/ready/how_to_computer/image49.png", + "notes/ready/how_to_computer/image47.png", + "notes/ready/how_to_computer", "_Templates/post.md", "_Templates/note.md", "posts/personal-web.md", @@ -208,15 +192,20 @@ "posts/local-llm.md", "posts/nix-starter-guide.md", "posts/dotfiles.md", + "notes/drafts/linux/index.md", + "TODO.md", "notes/ready/flask.md", "notes/ready/gdb.md", "notes/ready/git.md", "notes/ready/http.md", "notes/ready/html.md", + "notes/ready/binary_operations/index.md", "notes/ready/firewall.md", "drafts/nvim.md", "drafts/rust.md", "drafts/swift.md", - "drafts/TODO.md" + "drafts/TODO.md", + "drafts/Untitled.md", + "drafts/hardware-tools.md" ] } \ No newline at end of file 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mode 100644 content/Pasted image 20250306121159.png rename content/notes/ready/{memory => how_to_computer}/image76.png (100%) rename content/notes/ready/{memory => how_to_computer}/image77.png (100%) rename content/notes/ready/{memory => how_to_computer}/image78.png (100%) rename content/notes/ready/{memory => how_to_computer}/image79.png (100%) rename content/notes/ready/{memory => how_to_computer}/image81.png (100%) rename content/notes/ready/{memory => how_to_computer}/image82.png (100%) rename content/notes/ready/{memory => how_to_computer}/image83.png (100%) rename content/notes/ready/{memory => how_to_computer}/image84.png (100%) rename content/notes/ready/{memory => how_to_computer}/image85.png (100%) rename content/notes/ready/{memory => how_to_computer}/image86.png (100%) rename content/notes/ready/{memory => how_to_computer}/image87.png (100%) rename content/notes/ready/{memory => how_to_computer}/image88.png (100%) rename content/notes/ready/{memory => how_to_computer}/image89.png (100%) rename content/notes/ready/{memory => how_to_computer}/image90.png (100%) rename content/notes/ready/{memory => how_to_computer}/image91.png (100%) rename content/notes/ready/{memory => how_to_computer}/image92.png (100%) diff --git a/content/.obsidian/workspace.json b/content/.obsidian/workspace.json index b7fc3b2..e5bcd78 100644 --- a/content/.obsidian/workspace.json +++ b/content/.obsidian/workspace.json @@ -78,7 +78,7 @@ } ], "direction": "horizontal", - "width": 289.5 + "width": 200 }, "right": { "id": "f049c1d8215eafd9", @@ -171,19 +171,21 @@ }, "active": "ab03f7100c1ce0fb", "lastOpenFiles": [ - "3bit_decoder.png", + "Pasted image 20250306121159.png", + "Pasted image 20250306120537.png", + "Pasted image 20250306113821.png", + "Pasted image 20250306113013.png", + "Pasted image 20250306105245.png", + "notes/ready/cpu_architecture/index.md", + "notes/ready/cpu_architecture/image39.png", + "notes/ready/how_to_computer/image92.png", 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a/content/notes/ready/memory/image92.png b/content/notes/ready/how_to_computer/image92.png similarity index 100% rename from content/notes/ready/memory/image92.png rename to content/notes/ready/how_to_computer/image92.png diff --git a/content/notes/ready/how_to_computer/index.md b/content/notes/ready/how_to_computer/index.md index 45e991d..27c668a 100644 --- a/content/notes/ready/how_to_computer/index.md +++ b/content/notes/ready/how_to_computer/index.md @@ -153,11 +153,11 @@ A PNP transistor receives energy through the `emitter` pin, and then divides it ## Basic Logic A logic gate is a device that performs one boolean operation: Two binary inputs produce a single binary output. These building blocks are the foundations of modern computing. -Each gate has its own truth table, which shows every possible input and output variations. +Each gate has its own truth table, which defines every possible input and output variations. ### NAND -A NAND gate, although not the simplest one, can be used to build all other basic gates. +A NAND gate can be used to build all other basic gates. It always outputs, unless both inputs are active. ![image45](image45.png) @@ -174,7 +174,7 @@ A NAND gate, although not the simplest one, can be used to build all other basic ##### Electronics -Implementation using switches and a pull-up resistor: +Implementation using switches (transistors could be used instead) and a pull-up resistor: ![[NAND_circuit.png]] ### NOT @@ -350,30 +350,37 @@ Inverted `XOR`. ##### Logic Gates -![[XNOR_gates.png]] +![[XNOR_gates.png]] + +Although this circuits works, it can be further optimized to save `1` gate. + +![[Pasted image 20250306105245.png]] + +> From this point on, circuits will become exponentially more complex. Optimizations like this one can be found almost everywhere, however, when the choice between efficiency and readability arises, I will choose to keep things simple. If you found a way to optimize any of my circuits, please let me know. I'd be happy to keep improving these notes, and credit you for your findings. ## Binary -Binary is a base-2 numeral system: A simple way to represent numbers using only two states. +Binary is a base-2 numeral system: A simple way to represent numbers using only two states. Each binary 'digit' is called a *bit*, and 8 bits together form a *byte*. +To represent large binary values, it's common to use hexadecimal as well, to shorten them into a more readable format. -|Binary|Decimal|Hexadecimal| -|---|---|---| -|0000|00|00| -|0001|01|01| -|0010|02|02| -|0011|03|03| -|0100|04|04| -|0101|05|05| -|0110|06|06| -|0111|07|07| -|1000|08|08| -|1001|09|09| -|1010|10|0A| -|1011|11|0B| -|1100|12|0C| -|1101|13|0D| -|1110|14|0E| -|1111|15|0F| +| Binary | Decimal | Hexadecimal | +| ------ | ------- | ----------- | +| 0000 | 00 | 0 | +| 0001 | 01 | 1 | +| 0010 | 02 | 2 | +| 0011 | 03 | 3 | +| 0100 | 04 | 4 | +| 0101 | 05 | 5 | +| 0110 | 06 | 6 | +| 0111 | 07 | 7 | +| 1000 | 08 | 8 | +| 1001 | 09 | 9 | +| 1010 | 10 | A | +| 1011 | 11 | B | +| 1100 | 12 | C | +| 1101 | 13 | D | +| 1110 | 14 | E | +| 1111 | 15 | F | ![Binary Calculations](binarycalc.png) @@ -381,7 +388,7 @@ Binary is a base-2 numeral system: A simple way to represent numbers using only ### Addition -Adding two numbers can be done using a simple, manual algorithm: By adding the last bit of both numbers first, carry if necessary, then move on to the next number, and so on. +Adding two numbers can be done using a simple, manual algorithm: By adding the last *bit* of both numbers first, carry if necessary, then move to the next number, and so on. | **+** | 0 | 1 | | ------- | --- | ---- | @@ -416,7 +423,7 @@ To solve this issue, a `full adder` accepts 3 inputs. #### 8-Bit Adder To add two bytes, chain 8 full-adders. -(The dark blue lines are buses: 8 bits in parallel, simplified for better readability) +(The dark blue lines are equivalent to 8 bits in parallel, simplified for better readability. The blue rectangles split the wire into 8 bits, or vice versa.) ![[full_adder_8bit.png]] @@ -434,45 +441,11 @@ To switch between negative and positive numbers, flip all bits, then add 1. ![[signed_negator.png]] ---- - ### Subtraction -Subtraction can result in negative numbers. Like how additions need a carry, subtraction needs a borrow. +Subtraction is as easy as negating (inverting the sign of) the second input. -#### Half Subtractor - -Subtract 2, single-digit binary numbers. - -| **A** | **B** | Diff | **Borrow** | -| ----- | ----- | ---- | ---------- | -| 0 | 0 | 0 | 0 | -| 0 | 1 | 1 | 1 | -| 1 | 0 | 1 | 0 | -| 1 | 1 | 0 | 0 | - -![image72](image72.png) - -#### Full Subtractor - -A `full subtractor` accepts the borrow value, allowing us to chain results. - -| **A** | **B** | **B**in | **Diff** | **B**out | -| ----- | ----- | ------- | -------- | -------- | -| 0 | 0 | 0 | 0 | 0 | -| 0 | 0 | 1 | 1 | 1 | -| 0 | 1 | 0 | 1 | 1 | -| 0 | 1 | 1 | 0 | 1 | -| 1 | 0 | 0 | 1 | 0 | -| 1 | 0 | 1 | 0 | 0 | -| 1 | 1 | 0 | 0 | 0 | -| 1 | 1 | 1 | 1 | 1 | - -![image73](image73.png) - -#### 8-Bit Subtractor - -![image74](image74.png) +![[Pasted image 20250306113013.png]] ### Multiplication @@ -491,8 +464,17 @@ First, multiply the top number to every digit of the bottom one, and then add th ![image75](image75.png) +#### 4-Bit By 4-Bit Multiplier + +![[Pasted image 20250306113821.png]] + ### Division +Division is more complex. So much so, that it is often implemented in code, instead of hardware. For example, *ARM* CPUs don't have an instruction for division. +Harder doesn't mean impossible of course, and if you are curious, there are many resources you can see. For example: [This Reddit post](https://www.reddit.com/r/TuringComplete/comments/1eqo00i/my_multiplier_and_divider_in_turing_complete/); [YouTube Video](https://www.youtube.com/watch?v=Wf_1mf6yCoc). + +The steps for binary division are as follows: + 1. Find the smallest part of the dividend greater than or equal to the **divisor**.![d1](d1.png) @@ -501,26 +483,29 @@ First, multiply the top number to every digit of the bottom one, and then add th 3. Subtract the **aligned dividend digits** by **the digits under the dividend**.![d3](d3.png) -4. Lower **the next dividend digit**.![d4](d4.png) +4. Lower **the next dividend digit**. + ![d4](d4.png) -5. Is **the total** greater or equal to the **divisor**? If so, add a `1` to the answer. If not, **add a `0` to the answer and return to step 4**.![d5](d5.png) +5. Is **the total** greater or equal to the **divisor**? If so, add a `1` to the answer. If not, **add a `0` to the answer and return to step 4**. + ![d5](d5.png) -6. Return to step 2, until you reach the end of the number. If you reached the end, you found **the answer**.![d6](d6.png) +6. Return to step 2, until you reach the end of the number. If you reached the end, you found **the answer**. + ![d6](d6.png) ## Memory ### Byte Switch (SWC) -A bit switch, also known as transistor, toggles a given input, using a separate bit. +A bit switch, also known as a transistor, toggles a given input, using a second bit. ![[bit_switch.png]] -If 8 transistors are controlled by the same bit in parallel a Byte Switch is created. +If 8 transistors are controlled by the same bit in parallel, a Byte Switch is created. ### Input Selector -Using a switch, we can select which input to use. +Using byte switches, we can select which input to use. ![[input_selector.png]] @@ -532,19 +517,23 @@ A Bus is useful to simplify wiring. One bit controls which input should be selec ### 1 Bit of Memory -There are many ways to achieve a bit of memory. +There are [many ways](https://www.geeksforgeeks.org/latches-in-digital-logic/#sr-latch) to achieve a bit of memory. #### Using Transistors and a Tick Delay -The oval component is a delay. This replaces the concept of a clock, however, in an electronic circuit, the save and load states are attached to a clock. +The oval component is a delay. This replaces the concept of a clock, however, in an electronic circuit, the save and load states are attached to a clock instead. ![[transistor_latch.png]] -#### AND-OR Latch +#### SR Latch + +A Set-Reset Latch is the simplest one. The `S` input sets the output to `1`, and the `R` input, to `0`. If both inputs are on, the latch is in an undefined state, and outputs `0`. + +![[Pasted image 20250306120537.png]] + +#### D Latch -TODO!!! -![image80](image80.png) ### 8bit Register @@ -564,30 +553,6 @@ A decoder splits two states of a bit into two separate outputs. --- -## Remembering Data - -An `OR` gate could be used to store a single bit. -![image76](image76.png) -If the input `A` is changed to `1`, the `OR` gate will output `1`, and then receive it. -![image77](image77.png) -Even after the input `A` is set to `0`, the output does not change. The `OR` gate "remembers" that, at one point in the past, the `A` input was set to `1`. -![image78](image78.png) -The inverse can be done with an `AND` gate. -![image79](image79.png) -To remember either a `1` or a `0`, we can do the following: - - -### AND-OR LATCH - -The input `A` sets the output to `1`, and the input `B` sets the output to `0`. This circuit is able to store a bit of information, while powered on, even after both inputs are set to `0`. -A slightly more advanced and intuitive version can be built as follows: -![image81](image81.png) - -### GATED LATCH - -The input `A` is the value to store, and when `B` is set to `1`, the value is stored. -This is not the only way to store data using logic gates, but it is one of the simplest. - ## Registers A single bit isn't very useful, so we can use the previous circuit to create an 8bit register. 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