Course: From Basic Science to Web Hosting

Module 03 — Digital Information

What Is Binary?

Difficulty: Beginner → Intermediate
Prerequisites: Lesson 012 — How Does a Transistor Become a Switch?
Estimated time: 25 minutes

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1. The Big Question

We have reached an important point.

We started with:

Matter
 ↓
Atoms
 ↓
Electrons
 ↓
Electricity
 ↓
Semiconductors
 ↓
Transistors
 ↓
Switching

Now we need to answer:

How does a physical electrical switch become information?

The answer begins with:

Binary

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2. What Does Binary Mean?

Binary is a base-2 number system.

It uses only two symbols:

0
1

Compare this with decimal:

Decimal
0 1 2 3 4 5 6 7 8 9

Binary:

Binary
0 1

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3. Why Do Computers Use Binary?

Computers are built from electronic circuits.

Electronic circuits can be designed to reliably distinguish between two broad states:

LOW
HIGH

These can be interpreted as:

LOW  → 0
HIGH → 1

So:

Physical voltage
      ↓
Electrical state
      ↓
Digital interpretation
      ↓
0 or 1

This is why binary is so useful.

---

4. Binary Is an Abstraction

Remember something very important:

A computer does not contain tiny physical objects labeled “0” and “1.”

The physical system contains things such as:

Voltage
Current
Charge
Electric fields
Transistors
Capacitances

The computer’s digital circuits interpret physical states as logical values.

Therefore:

Physical world
      ↓
Electrical state
      ↓
Logical abstraction
      ↓
0 / 1

---

5. What Is a Bit?

A bit is a binary digit.

It can have two logical values:

0
1

So:

1 bit
 ↓
2 possible states

For example:

0
1

---

6. Two Bits

Now use two bits:

00
01
10
11

There are:

2² = 4

possible combinations.

---

7. Three Bits

Three bits:

000
001
010
011
100
101
110
111

There are:

2³ = 8

possible combinations.

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8. General Rule

For n bits:

Number of possible combinations = 2ⁿ

Examples:

1 bit  → 2 states
2 bits → 4 states
3 bits → 8 states
4 bits → 16 states
8 bits → 256 states

This is one of the most important formulas in digital computing.

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9. What Is a Byte?

A byte is conventionally:

8 bits

Example:

10110101

This contains:

8 binary digits

Therefore:

1 byte = 8 bits

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10. Why 8 Bits?

Eight bits provide:

2⁸ = 256

possible combinations.

These combinations can represent:

0 → 255

when interpreted as an unsigned binary integer.

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11. Binary Place Values

Decimal uses powers of 10:

1000
100
10
1

Binary uses powers of 2:

8
4
2
1

For four bits:

Binary position:

8    4    2    1
↓    ↓    ↓    ↓
0    0    0    0

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12. Example: Binary 1011

Take:

1011

Place values:

8   4   2   1
1   0   1   1

Calculate:

1×8
+
0×4
+
1×2
+
1×1

Therefore:

8 + 0 + 2 + 1 = 11

So:

1011₂ = 11₁₀

---

13. Binary 1010

8   4   2   1
1   0   1   0

Therefore:

8 + 0 + 2 + 0 = 10

So:

1010₂ = 10₁₀

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14. Decimal to Binary

Suppose we want to represent:

13

Using powers of two:

8 + 4 + 1 = 13

Therefore:

8  4  2  1
1  1  0  1

So:

13₁₀ = 1101₂

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15. Why Computers Need Binary

Consider an electronic switch:

OFF

or:

ON

We can abstract it as:

OFF → 0
ON  → 1

Now connect eight switching elements:

Switch Switch Switch Switch Switch Switch Switch Switch
   ↓      ↓      ↓      ↓      ↓      ↓      ↓      ↓
   1      0      1      1      0      0      1      0

We have:

10110010

That is a byte.

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16. From Transistor to Bit

This is the critical connection:

MOSFET
 ↓
Switching behavior
 ↓
Electrical HIGH/LOW
 ↓
Logic state
 ↓
0/1
 ↓
Bit

This is how physical electronics becomes digital information.

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17. Bits Can Represent Numbers

For example:

00000000 = 0
00000001 = 1
00000010 = 2
00000011 = 3

And:

11111111 = 255

for an unsigned 8-bit number.

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18. Bits Can Represent Text

Computers also need to represent letters.

A character encoding assigns numerical values to characters.

For example, ASCII assigns:

A = 65

65 in binary is:

01000001

So conceptually:

A
 ↓
65
 ↓
01000001
 ↓
Bits
 ↓
Electrical states

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19. Bits Can Represent Images

An image can be represented using numbers.

For a simple grayscale image:

Pixel
 ↓
Brightness value
 ↓
Number
 ↓
Binary

A color image can use multiple numerical values per pixel.

For example:

Red
Green
Blue

These values can all be represented using bits.

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20. Bits Can Represent Audio

Sound is a physical phenomenon.

A microphone converts sound pressure variations into an electrical signal.

An analog-to-digital converter then samples and quantizes the signal.

Conceptually:

Sound
 ↓
Microphone
 ↓
Electrical signal
 ↓
Sampling
 ↓
Quantization
 ↓
Binary data

That binary data can be stored or transmitted.

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21. Bits Can Represent Video

Video is essentially a sequence of images over time, usually accompanied by audio.

Conceptually:

Scene
 ↓
Camera
 ↓
Images + sound
 ↓
Digital representation
 ↓
Binary data
 ↓
File / stream

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22. Bits Can Represent Programs

This is even more important.

A program is ultimately represented in a form the computer’s processor can execute.

Simplified:

Program
 ↓
Source code
 ↓
Compiler / interpreter / runtime
 ↓
Machine instructions
 ↓
Binary representation
 ↓
CPU

At the hardware level, instructions are encoded as bit patterns.

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23. What Is Machine Code?

A CPU has an instruction set architecture (ISA).

Instructions are encoded into machine-readable bit patterns.

Conceptually:

Instruction
 ↓
Binary encoding
 ↓
CPU
 ↓
Decode
 ↓
Execute

For example, a processor might have instructions conceptually corresponding to:

LOAD
ADD
STORE
JUMP
COMPARE

The actual binary encodings depend on the processor architecture.

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24. Binary Is Not the Same as Machine Code

This distinction is important.

Binary is a number representation system.

Machine code is encoded processor instructions/data interpreted according to a specific instruction set architecture.

So:

Binary
 ↓
General representation system

while:

Machine code
 ↓
Specific encoding understood by a CPU architecture

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25. Bits in Memory

Suppose a memory system stores:

10110010

Physically, the memory cell isn’t simply a tiny box containing “10110010.”

It uses physical states.

Depending on memory technology, information may be represented through things such as:

Charge
Voltage
Transistor state
Magnetic state

Again:

Physical state
      ↓
Electrical interpretation
      ↓
Logical bit

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26. Bits Traveling Through a Network

Now we reach networking.

Suppose your browser requests:

https://templates.cresignsys.com

The information must travel through networks.

Conceptually:

Computer
 ↓
Network interface
 ↓
Electrical / optical / radio signal
 ↓
Network
 ↓
Router
 ↓
Internet
 ↓
Server

The physical signals represent digital information.

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27. The Signal Is Not Literally “1 and 0”

This is another important distinction.

An Ethernet cable doesn’t contain little physical 1s and 0s traveling through it as objects.

Instead:

Binary information
      ↓
Encoded signal
      ↓
Electrical waveform
      ↓
Cable

At the receiving end:

Electrical waveform
      ↓
Receiver
      ↓
Signal processing
      ↓
Decoded bits

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28. Optical Fiber

For fiber:

Bits
 ↓
Electrical signal
 ↓
Optical transmitter
 ↓
Light modulation
 ↓
Fiber
 ↓
Photodetector
 ↓
Electrical signal
 ↓
Bits

Therefore the Internet combines:

Digital information
+
Physical signals

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29. Wireless

Wi-Fi uses electromagnetic waves.

Conceptually:

Bits
 ↓
Digital processing
 ↓
Radio modulation
 ↓
Electromagnetic wave
 ↓
Air
 ↓
Radio receiver
 ↓
Demodulation
 ↓
Bits

So the same binary information can travel through:

Copper
Fiber
Radio

using different physical signaling technologies.

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30. From Binary to Web Hosting

Now we can connect the entire chain:

Transistor
 ↓
Switch
 ↓
0 / 1
 ↓
Bit
 ↓
Byte
 ↓
Data
 ↓
Machine instructions
 ↓
CPU
 ↓
Operating system
 ↓
Network protocols
 ↓
Internet
 ↓
HTTP/HTTPS
 ↓
Web server
 ↓
Website
 ↓
Web hosting

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31. Your WordPress Website

When WordPress serves a page, enormous amounts of digital information are being processed.

For example:

Browser request
      ↓
Network packets
      ↓
Server network interface
      ↓
Linux
      ↓
Nginx
      ↓
PHP
      ↓
WordPress
      ↓
MySQL
      ↓
HTML/CSS/JS
      ↓
Network
      ↓
Browser

At the lowest hardware level:

Software
 ↓
CPU instructions
 ↓
Transistors
 ↓
Electrical signals

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32. The Big Picture

You have now crossed another major boundary:

PHYSICAL WORLD
       ↓
Electricity
       ↓
Electronics
       ↓
Transistors
       ↓
DIGITAL WORLD
       ↓
Bits
       ↓
Data
       ↓
Programs
       ↓
Operating systems
       ↓
NETWORK WORLD
       ↓
Packets
       ↓
Internet
       ↓
WEB
       ↓
WEB HOSTING

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33. What You Should Remember

The most important chain from today’s lesson is:

Transistor
   ↓
Electrical state
   ↓
HIGH / LOW
   ↓
Logical 1 / 0
   ↓
Bit
   ↓
Byte
   ↓
Data

And:

Binary is the mathematical representation; the hardware uses physical electrical states to implement it.

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34. Quick Check

What is binary?

A base-2 number system using 0 and 1.

What is a bit?

A binary digit representing one logical binary state.

How many states can 8 bits represent?

2⁸ = 256

How many values can an unsigned 8-bit number represent?

0–255

What is a byte?

8 bits.

Can binary represent text?

Yes, through character encodings.

Can binary represent images?

Yes.

Can binary represent programs?

Yes.

Does a network cable physically contain 0s and 1s?

No. It carries physical signals that encode digital information.

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Next Lesson

Lesson 014 — What Is a Computer?

Now we assemble everything we have learned:

Transistors
      ↓
Logic gates
      ↓
Digital circuits
      ↓
ALU
      ↓
Registers
      ↓
CPU
      ↓
RAM
      ↓
Storage
      ↓
Motherboard
      ↓
Computer

Then we will continue:

Computer
 ↓
Operating System
 ↓
Linux
 ↓
Processes
 ↓
Files
 ↓
Networking
 ↓
Server
 ↓
Web Hosting

This is where the course starts moving from electronics into computer engineering and operating systems.