View source for 2.1.1 Binary Numbers (Bits, Bytes)

== How Computers Understand the World: Foundational Concepts ==
Have you ever wondered how your computer, phone, or tablet actually "sees" and "hears" all the information you give it? It's not magic! Computers have a special way of understanding everything, from the words you type to the pictures you see and the music you listen to. It all comes down to something called '''data representation'''.

=== 2.1 Data Representation: The Computer's Secret Language ===
Imagine you're trying to tell a story using only two words: "yes" and "no." It would be tough, right? But that's pretty much what computers do! They use a very simple "language" to represent ''all'' information.

==== 2.1.1 Binary Numbers (Bits & Bytes) ====
The most basic part of a computer's language is something called '''binary code'''. Binary only has two "digits": 0 and 1. Think of it like an on/off switch for electricity. A "0" might mean the switch is off, and a "1" might mean it's on.

* '''Bit:''' Each single 0 or 1 is called a '''bit''' (short for "binary digit"). It's the smallest piece of information a computer can understand.
* '''Byte:''' A single bit isn't very useful on its own. So, computers group 8 bits together to make a '''byte'''. With 8 bits in a byte, there are 256 different combinations of 0s and 1s! This is important because one byte can usually represent one character, like the letter "A" or the number "7".

When you hear about how much space a file takes up, like "5 Megabytes" or "2 Gigabytes," you're talking about huge numbers of bytes!


Let's dive deeper into '''Binary Numbers, Bits, and Bytes''' – the true ABCs of how computers understand everything!

=== 2.1.1 Binary Numbers: The Computer's Secret Code Explained ===
Imagine you're trying to communicate with someone using only a flashlight in the dark. You could agree that a quick flash means "yes" and no flash means "no." This is very similar to how computers "talk" to themselves using binary numbers.

'''Why Binary? Because Computers are Simple Machines!'''

Computers are incredibly complex machines, but at their very core, they are actually quite simple. They are made of tiny electronic switches. Each switch can only be in one of two states:

# '''On (electricity flowing)'''
# '''Off (no electricity flowing)'''

Think of a light switch in your house. It's either on or off, right? It can't be "a little bit on" or "mostly off."

This "on" or "off" state is perfectly represented by the two digits of the '''binary number system''':

* '''1''' usually means '''"on"''' (or current flowing, high voltage)
* '''0''' usually means '''"off"''' (or no current, low voltage)

So, when you type a letter, click an icon, or watch a video, the computer is rapidly turning billions of these tiny electronic switches on and off in very specific patterns. These patterns of 1s and 0s are the "code" the computer understands.

'''Bits: The Smallest Piece of Information'''

Each one of these "on" (1) or "off" (0) states is called a '''bit'''. "Bit" is short for "binary digit."

* A single bit can only tell you two things: yes/no, true/false, on/off, 1/0.
* It's like a single coin: heads or tails.

'''Bytes: Grouping Bits for More Meaning'''

A single bit isn't very useful for representing complex information, just like one coin can't tell you a whole story. But if you start grouping bits together, you can create many more combinations and represent more complicated things!

The most common and fundamental grouping of bits is a '''byte'''.

* A '''byte''' is always made up of '''8 bits'''.

Why 8 bits? Because with 8 bits, you can create <code>2 x 2 x 2 x 2 x 2 x 2 x 2 x 2</code> (or 28) different combinations of 1s and 0s. That's 256 different combinations!

Think of it like having 8 light switches in a row. You can flip them on and off in 256 different patterns. Each of those patterns can represent something specific:

* One pattern of 8 bits might represent the letter "A".
* Another pattern might represent the number 5.
* Another might represent the color red.

For example, the letter "A" in computer code is often represented by the binary pattern <code>01000001</code>. That's one byte!

'''Why are Bits and Bytes Important?'''

* '''Everything is Binary:''' Every piece of information a computer processes, from a simple text document to a high-definition movie, is broken down into millions or billions of bits and bytes.
* '''Measuring Storage:''' When you hear about storage space on your phone or computer, like "16 Gigabytes" (GB) or "1 Terabyte" (TB), you're talking about how many bytes of information it can hold.
** 1 Kilobyte (KB) = 1,024 bytes (about half a page of text)
** 1 Megabyte (MB) = 1,024 Kilobytes (about a small photo)
** 1 Gigabyte (GB) = 1,024 Megabytes (about 250 songs)
** 1 Terabyte (TB) = 1,024 Gigabytes (about 250,000 songs or thousands of movies!)
* '''Measuring Speed:''' When you talk about internet speed (like "100 Megabits per second" or Mbps), it's often measured in ''bits'' per second, not bytes. This shows how fast bits of information are traveling.

So, while we see colorful screens and hear clear sounds, deep inside the computer, it's all just a lightning-fast dance of billions of tiny electronic switches, flipping between "on" and "off" – 1s and 0s!


'''Bibliography'''

* [[wikipedia:Bit|''Bit (computing) - Wikipedia'']]
* [[wikipedia:Byte|''Byte - Wikipedia'']]
* [[wikipedia:Binary_code|''Binary code - Wikipedia'']]
* [https://web.stanford.edu/class/cs101/bits-bytes.html ''Bits and Bytes - Stanford University'']

* [[wikipedia:Data_(computer_science)|''Data (computer science) - Wikipedia'']]
* [[wikipedia:Computer_number_format|''Computer number format - Wikipedia'']]
* [https://www.lenovo.com/us/en/glossary/character/?orgRef=https%253A%252F%252Fgemini.google.com%252F ''How Characters are Stored in Computer Memory & Represented in Binary Code - Lenovo'']
* [https://www.tutorchase.com/answers/ib/computer-science/how-does-a-computer-system-represent-characters ''How does a computer system represent characters? - TutorChase'']
* [https://www.futurelearn.com/info/courses/introduction-to-digital-media/0/steps/428684 ''Representation of digital media in computers - FutureLearn'']
* [https://bitzsspace.com/articles/image-and-video-representation-in-computers/ ''Image and Video Representation in Computers - BitzsSpace'']
* [https://www.andrew.cmu.edu/user/nbier/15110/lectures/lec15a_sound_video.pdf ''Data Representation: Images and Sound - andrew.cmu.edu'']