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
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
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
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.
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.
9. What Is a Byte?
A byte is conventionally:
8 bits
Example:
10110101
This contains:
8 binary digits
Therefore:
1 byte = 8 bits
10. Why 8 Bits?
Eight bits provide:
2⁸ = 256
possible combinations.
These combinations can represent:
0 → 255
when interpreted as an unsigned binary integer.
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
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
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
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.
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.
17. Bits Can Represent Numbers
For example:
00000000 = 0
00000001 = 1
00000010 = 2
00000011 = 3
And:
11111111 = 255
for an unsigned 8-bit number.
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
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.
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.
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
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.
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.
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
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
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.
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
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
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.
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
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
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
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.
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.
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.