Oct 23, 2025

How Computers Represent Information

Computer Science Beginner

#computer-science #binary #encoding #fundamentals

What do emojis, music, and video games have in common? They’re all made of zeros and ones. Computer science isn’t just about how to make a program or software available on your phone. It’s about representing information. Every image, sound, and text you see on a screen consists of binary digits. Let’s explore how computers represent them behind the scenes.

What is Computer Science?

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Fun fact: In Indonesia, there are some universities that call computer science ‘information technology’. They are basically the same, but do you know why? It’s because they study information.

Basically, all fields of study are about problem solving, including computer science. It’s about problem solving involving information using computational thinking to represent and process that information.

Computer Science

Computer science is problem solving that uses computational thinking to represent and process information.

Types of Information We Encounter Daily

How do we represent this information? Before that, what forms of information do we have? Where can we find information in our daily life?

From a book, television, billboard, pamphlet, phone, internet, radio

What forms of information do they have?

Text and letters
Numbers
Images and Color
Sound and Video

How do computers process those types of information?

Numbers: From Decimal to Binary

Basically, computer hardware only knows numbers, only 0 and 1. Why does a computer only understand those two numbers? Because the transistors that make up this hardware only have two states. It’s like a switch, on and off. Modern electronic devices, such as Macs, PCs, and phones, utilize millions of microscopic light switches called transistors to store information by being turned either on (one) or off (zero).

💡 Why Binary?

Transistors are like tiny switches that can only be in two states: ON (1) or OFF (0). This physical limitation is why computers use binary—it perfectly matches how the hardware works!

Understanding the Decimal System

How do they represent numbers? Like 12345, 1 million. Numbers that we know like 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc., are called the decimal system, base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Every single number can be represented as:

a_n \cdot 10^n + a_{n-1} \cdot 10^{n-1} + \cdots + a_1 \cdot 10^1 + a_0

Decimal Example

Let’s break down the number 1234:

1234 = 1 \cdot 10^3 + 2 \cdot 10^2 + 3 \cdot 10^1 + 4 \cdot 10^0

1234 = 1000 + 200 + 30 + 4

Converting to Binary

Because computers only know $0$ and $1$ , we must represent all of those numbers in the binary system (base 2). How do we represent 11 as binary?

Converting 11 to Binary

Let’s use the division method:

11 ÷ 2 = 5 remainder 1 ← rightmost bit
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1 ← leftmost bit

Reading from bottom to top: 1011

We can verify this:

11 = 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0

11 = 8 + 0 + 2 + 1 = 11 \text{ ✓}

So $11$ in decimal = $1011$ in binary!

Level 1:

Convert 23 from decimal to binary using the division method.

Click for hint

Keep dividing by 2 and write down the remainders. The binary number is formed by reading the remainders from bottom to top!

Click for solution

Step-by-step conversion:

23 ÷ 2 = 11 remainder 1 ← rightmost bit
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1 ← leftmost bit

Answer: $23$ in decimal = $10111$ in binary

Verification:

10111_2 = 1 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0

= 16 + 0 + 4 + 2 + 1 = 23 \text{ ✓}

Text: ASCII and Unicode

Now we move on to Text and Letters. How about it? Yes, we represent it as numbers.

ASCII - The Foundation

American Standard Code for Information Interchange (ASCII)

Uses 7 bits (0-127) or extended 8 bits (0-255)
Represents about 256 characters
Sufficient for English alphabet and standard symbols
Examples:
- ‘A’ = 65
- ‘a’ = 97
- ‘0’ = 48

Unicode - Global Characters

Universal Character Encoding

Uses 16, 24, or 32 bits
Supports up to 4 billion characters
Covers all human languages and emojis
Uses “code points” (e.g., U+0041)
Superset of ASCII

Unicode Code Points

Here are some examples of Unicode code points:

‘A’ = U+0041 (Latin capital letter A)
‘你’ = U+4F60 (Chinese character meaning “you”)
’😀’ = U+1F600 (Grinning face emoji)

Notice how each character, regardless of language or type, gets a unique code point!

Images: Pixels and Colors

How do computers display an emoji and images?

Emojis and images consist of several colors that represent them. Did you ever see people make an image from Lego bricks? The idea to represent those images is similar to how we represent images on the screen. We can represent the images using pixels, which are single dots on the screen. Those pixels are represented by our primary colors.

Pixel

A pixel (picture element) is a single dot on the screen. It’s the smallest unit of a digital image. Each pixel has a color defined by combining Red, Green, and Blue (RGB) values.

Understanding Color Mixing

Physical Paint (Subtractive)

Mixing Pigments

Uses Cyan, Magenta, Yellow (CMY)
Subtracts light wavelengths
Mixing all colors → Black
Used in printing

Think: Paint absorbs light!

Computer Light (Additive)

Mixing Light

Uses Red, Green, Blue (RGB)
Adds light wavelengths
Mixing all colors → White
Used in screens

Think: Light adds up!

RGB Color System

In computers, the color is defined by Red, Green, and Blue. Each color has an intensity that we can define from 0 to 255. If we increase the number, the color will be brighter.

RGB Color Values

Each color channel ranges from 0 to 255 (that’s $2^8 = 256$ values):

$(255, 0, 0)$ = Pure red (max red, no green, no blue)
$(0, 255, 0)$ = Pure green (no red, max green, no blue)
$(0, 0, 255)$ = Pure blue (no red, no green, max blue)
$(255, 255, 0)$ = Yellow (red + green)
$(255, 255, 255)$ = White (all lights on)
$(0, 0, 0)$ = Black (all lights off)
$(128, 128, 128)$ = Gray (medium intensity all)

With 3 channels × 256 values each = 16,777,216 possible colors!

💡 File Size

Large photographs require millions of bytes because of the high number of pixels. A 1920×1080 image has over 2 million pixels, and each pixel needs 3 bytes (RGB) = over 6 MB for a single uncompressed image!

Video and Sound

How about Video and Sound?

Video: Sequences of Images

Videos can be represented as a sequence of images that play at a fast speed. Did you ever see a cartoonist draw images in the corner of books, and then open the book quickly? It makes the images move like a video.

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Flipbook Animation: This is exactly how video works! Modern videos typically show 24, 30, or 60 frames (images) per second. Our eyes perceive this rapid sequence as smooth motion.

Sound: Digital Sampling

Sound is different—it’s a continuous wave signal. To digitize it:

A microphone samples the wave thousands of times per second
Each sample measures the wave’s amplitude (loudness) at that instant
These measurements become bytes stored in audio files

Sampling Rate

The sampling rate is how many times per second we measure the sound wave. CD-quality audio uses 44,100 samples per second (44.1 kHz).

Higher sample rates = better quality but larger files.

Context: How Computers Know What’s What

It depends on the context, similar to words. In Software Engineering, “staging” means a deployment phase. In Data Engineering, it’s about a layering phase. Computers can differentiate how to transform data depending on the context we provide.

File Formats as Context

What is the representation of context in computers? It lies in the file format. We have .JPEG for images, .txt for text. This format represents context as special bytes called a header. This header tells the computer that the next million bytes are image data so the computer can decode them as pixels, or that the next bytes are ASCII text.

File Headers

Every file starts with special bytes called a header that tells the computer what type of data follows:

JPEG images: Start with bytes FF D8 FF
PNG images: Start with bytes 89 50 4E 47
MP3 audio: Start with bytes FF FB or ID3
PDF documents: Start with %PDF

Without these headers, the computer wouldn’t know if those bytes represent an image, sound, or text!

💡 The Power of Programming

The power of the programmer lies in writing code that tells the computer how to treat these patterns—whether to store a number, a letter, a color, or something else. Same bytes, different meaning!

Conclusion

Finally, we understand that every app, website, film, and game is built on binary data that is converted by computer hardware to represent real-world information.

Key Takeaways

Computers use binary (0 and 1) because transistors have two states
Numbers are converted from decimal to binary using division
Text is encoded using ASCII (English) or Unicode (global languages)
Images are made of pixels, each with RGB color values (0-255)
Video is a sequence of images played rapidly
Sound is digitized by sampling continuous wave signals
File formats provide context through headers

Understanding how computers represent information is fundamental to computer science. This knowledge helps you appreciate the digital world around you and forms the foundation for deeper programming and system design concepts.

Next in this series: Introduction to Algorithms and Problem Solving