When you send a message, browse the web, or save a photo to your computer, have you ever wondered: how does the computer actually "understand" these actions? In fact, no matter how complex it appears, all data that a computer processes is ultimately represented by just two simple numbers: 0 and 1.

This is the binary system – the fundamental language that all electronic devices "speak" and "understand."

In this article, we will explore:

• What is the binary system?
• Why is it so important?
• The advantages and disadvantages of the binary system.
• Applications of the binary system in real life.
• How to decode binary strings into understandable numbers and characters, with concrete examples.

Let's dive in!

1. What is the Binary System?

The binary system (Binary Number System) is a numerical system that uses only two digits: 0 and 1. Each digit in binary is called a bit (binary digit).

In computer science, binary is essential because computers operate using electrical signals that have two states: ON (1) and OFF (0).

Example of binary numbers:

1011, 110010, 00101101

2. Why is Decoding the Binary System Necessary?

• To understand how computers store and process data.
• To convert machine-readable binary data into human-readable formats (such as decimal numbers or text).
• To program and manipulate data at the bit level in fields like security, compression, and hardware design.

3. Advantages and Disadvantages of the Binary System

Advantages

• Simple and easy to design for electronic devices.
• Less prone to errors due to only two states (on/off).
• High error tolerance in communication and storage.

Disadvantages

• Representing large numbers can result in long and difficult-to-read sequences.
• Direct manipulation with binary is very inconvenient for humans.

4. Applications of the Binary System in Real Life

• Computer Processing: All CPUs, RAMs, hard drives, and communication networks are based on binary.
• Telecommunications: Data transmission via electrical signals, fiber optics.
• Encryption and Security: Data encryption, bit manipulation in blockchain, SSL/TLS protocols.
• Device Control: From LED lights to self-driving cars and drones.

5. How to Decode Binary into Decimal

To convert binary to decimal:

• Write down the binary number.
• Assign powers of 2 to each bit, starting from the right (0 power).
• Sum the values of the bits that are set to 1.

General formula:

Example: Convert 1011 to decimal

1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 8 + 0 + 2 + 1 = 11

Result: 1011 (binary) = 11 (decimal)

6. How to Decode Binary into Characters (ASCII)

In computers, characters are encoded using the ASCII (American Standard Code for Information Interchange) system. Each character corresponds to an 8-bit binary code.

Steps to decode:

1. Group binary into sets of 8 bits.
2. Convert each group from binary to decimal.
3. Look up the ASCII table to find the corresponding character.

Example:

01001000 01101001
→ 01001000 = 72 → 'H'
→ 01101001 = 105 → 'i'
Result: "Hi"

7. Practical Examples

Example 1: Convert 110010 to decimal

1 × 2⁵ + 1 × 2⁴ + 0 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰ = 50

Example 2: Decode 01000001

• 01000001 → 65 (decimal)
• 65 in ASCII → A

Result: A

8. Notes When Working with Binary

• Bit is the smallest unit.
• Byte = 8 bits.
• Other commonly used systems:
  • Decimal system (base 10)
  • Hexadecimal system (base 16)
• Tools like Windows Calculator (Programmer mode) or online converters can help with binary calculations.

9. Basic ASCII Table

👉 Note: Codes from 0-31 are control characters and are not displayed as letters.

10. Flowchart Illustration: Binary Decoding Process

Flowchart:

[Step 1] Receive binary string
        ↓
[Step 2] Group into sets of 8 bits
        ↓
[Step 3] Convert binary to decimal
        ↓
[Step 4] Lookup ASCII table
        ↓
[Step 5] Combine into readable text

Conclusion

The binary system is the "native language" of computers. Understanding how to decode binary helps you:

• Understand how computers store and process data.
• Efficiently tackle low-level programming tasks.

Wishing you clear understanding and proficiency in working with binary-related topics!