trude/web
1
0
Fork 0
mirror of https://github.com/TrudeEH/web.git synced 2025-12-06 08:23:37 +00:00
Code Issues Packages Projects Releases Wiki Activity

INC: Continued work on the computer post

Browse Source
This commit is contained in:
TrudeEH
2025-03-06 16:14:48 +00:00
parent 7db2cb589b
commit a885e1a9c0
23 changed files with 72 additions and 106 deletions
Download Patch File Download Diff File Expand all files Collapse all files

157
content/notes/ready/how_to_computer/index.md
View File

@@ -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.