Computers

Computer

An electronic device that processes data by following instructions (programs)

Software

Programs and instructions that tell the hardware what to do.

Input/Output (I/O)

Input = 

Output = 

Ways a computer communicates:

data into the computer (keyboard, mouse, microphone).

results out of the computer (screen, speakers, printer).

Processor

The “brain” that executes instructions and processes data.

Microprocessor

A processor built onto a single chip (modern CPUs, GPUs, etc.).

Memory

Temporary or permanent storage that holds data and instructions.

Register

Tiny, super-fast storage locations inside the CPU for data being worked on right now.

Cache

Very fast memory near the CPU that stores recently used data/instructions to speed things up.

Booting

The process of starting up a computer, where hardware is initialized and the operating system is loaded into memory so the system becomes ready for use.

Operating System

System software that manages hardware and software resources and provides services for applications.

a) File Systems,

b) Directory Structure

a) organizes how data is stored and accessed on storage devices, often in a hierarchical b). 

a) Shell,

b) Shell Commands

a) is an interface that lets users interact with the operating system. b) allow users to control the system, automate tasks, and access powerful tools.

Character Encoding

A method of representing text as numbers so it can be stored and processed by computers. 

Shell

A command-line interface that lets the user interact with the operating system by typing commands. Examples: Bash, Zsh.

Shell script

A text file containing a sequence of shell commands that can be executed together to automate tasks.

Terminal shell

The environment you open to type and run shell commands (e.g., the Terminal app on macOS). It provides access to the shell.

vi / Vim

A powerful text editor available directly in the terminal. It’s lightweight, keyboard-based, and used for editing scripts or configuration files.

VS Code (Visual Studio Code)

A modern, graphical code editor with integrated tools like syntax highlighting, Git support, debugging, and extensions for many languages.

RStudio / Positron

Integrated development environments (IDEs) for the R programming language. They provide an interface for writing code, running scripts, visualizing data, and managing projects. (Positron is the newer version by the same company, Posit.)

Python

A high-level, general-purpose programming language known for its readability and versatility. Used in data science, web development, automation, and AI.

R

A programming language specialized for statistics, data analysis, and visualization. Commonly used in scientific and academic research.

a) Bit

b) Binary digit

A a) (b) is the smallest unit of data in computing and can have only two values: 0 or 1. It represents a single state in a digital circuit — off/on, false/true, or low/high voltage.

Byte

A group of 8 bits and can represent 256 different values (from 0 to 255). It is the basic unit for measuring digital information (e.g., 1 KB = 1000 bytes).

1000^x

This refers to units that grow by powers of 1000 — for example, 1 KB = 1000 bytes, 1 MB = 1000² bytes, 1 GB = 1000³ bytes (decimal system).

In contrast, computer memory often uses powers of 1024 (2¹⁰), so 1 KiB = 1024 bytes.

Binary representation 

Computers use the binary number system (base 2), where each digit is 0 or 1. Numbers, letters, and instructions are all stored and processed as sequences of bits in binary form.

Adding

Binary addition follows simple rules: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 10 (which means sum = 0, carry = 1). Addition is performed bit by bit, often with the help of logic circuits like adders.

Subtracting

Binary subtraction uses similar rules but often relies on 2’s complement to simplify hardware. By representing negative numbers in 2’s complement form, subtraction can be done as addition.

2’s complement

A method to represent signed integers in binary. To get the negative of a number, invert all bits and add 1. This allows hardware to handle addition and subtraction uniformly.

Floating point presentation

Used to store real (decimal) numbers, it splits the number into mantissa (significant digits) and exponent (power of 2). This format allows computers to represent very large or very small numbers efficiently but with limited precision.

Character encoding

It assigns a unique binary code to each character (letters, digits, symbols). Common systems include ASCII (1 byte per character) and Unicode/UTF-8, which supports many languages and symbols worldwide.

Logic gate symbols

They basic circuit components (AND, OR, NOT, XOR, NAND, NOR). Each gate has a symbol that visually represents its operation in circuit diagrams.

Logic table (truth table)

It lists all possible input combinations for a logic gate and their corresponding output. It shows clearly how the gate processes binary values.

Half-adder

It is a simple circuit that adds two bits, producing a sum and a carry output. It uses one XOR gate for the sum and one AND gate for the carry.

Full-adder

It three bits (two inputs plus a carry from a previous stage). It outputs a sum and a carry, and multiple full-adders can be connected to add multi-bit binary numbers.

Alphabet (Σ)

A finite set of symbols used to form words.

Example: Σ = {a, b} means all words are made from just “a” and “b”.

Word (String)

A finite sequence of symbols from an alphabet.
Example: if Σ = {a, b}, then “abba” is a word over Σ.

Language (L)

A set of words formed from an alphabet.
It can be finite or infinite, for example, L = {aⁿbⁿ | n ≥ 0} is the set of strings with equal numbers of a’s and b’s.

a) Kleene Star (∗)

The a) of  a set of strings V (written V*) is the set of all possible concatenations of zero or more elements from V, including the empty string ε. It represents “repeating something any number of times.”

Regular Expression (regex)

A regular expression is a symbolic way of describing patterns in strings. They use operators like *, |, and concatenation to define regular languages.

Regular language

A language that can be described by a regular expression or recognized by a finite automaton.

Wildcard Character

A placeholder that can match one or more unspecified characters (like or ?). They’re used in file searches and pattern matching e.g. .txt matches all text files.