Computer Science Basics for Beginners

🔢 Number Systems – Binary, Decimal, Hexadecimal

Computers don’t understand human language. At their core, they only understand numbers — more specifically, the Binary Number System. But humans use Decimal, and programmers also use Hexadecimal and Octal. Understanding these systems is fundamental to computer science, programming, and working with hardware.

🔟 1. Decimal Number System (Base-10)

This is the number system you’ve used since childhood. It has 10 digits: 0 to 9.

• Each digit's position corresponds to a power of 10
• Example: 325 = 3×10² + 2×10¹ + 5×10⁰
• This system is intuitive for humans but inefficient for computers

⚙️ 2. Binary Number System (Base-2)

Used by all digital electronics including computers. Consists of only two digits: 0 and 1. Each digit is called a bit (binary digit).

• Each place value is a power of 2
• Example: 1101 = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13
• Everything in computing (text, images, music) is encoded in binary
• 8 bits = 1 byte
• 1024 bytes = 1 KB, 1024 KB = 1 MB, etc.

🔶 3. Hexadecimal Number System (Base-16)

Programmers often use Hexadecimal because it's shorter and easier to read than binary.

• Digits used: 0-9 and A-F (A=10, B=11, ..., F=15)
• Base = 16 → each digit represents 4 binary bits
• Used in memory addresses, MAC addresses, color codes (e.g., #FF5733)
• Example: 2F = 2×16¹ + 15×16⁰ = 47 (decimal)

🧾 4. Octal Number System (Base-8)

Less common, but used in some programming scenarios like Unix file permissions.

• Uses digits 0 to 7
• 1 Octal digit = 3 Binary bits
• Example: 345 (octal) = 3×8² + 4×8¹ + 5×8⁰ = 229 (decimal)

🔁 Conversions Between Number Systems

🔹 Decimal → Binary

Divide the number by 2 repeatedly and record the remainders.

Decimal 25 → Binary:
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary = 11001

🔹 Binary → Decimal

Binary 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10

🔹 Binary → Hexadecimal

Binary: 11011111 → Group: 1101 1111 → Hex = DF

🔹 Hexadecimal → Binary

Hex: 3C → 0011 1100 (Binary)

📊 Comparison Table

🧠 Real-Life Applications

• Binary: Internal CPU processing, boolean logic, memory storage
• Hexadecimal: Memory addresses, low-level programming, HTML colors
• Octal: Unix file permissions (e.g., chmod 755)
• Decimal: Day-to-day calculations, UI-level representation

📝 Practice Questions

1. Convert decimal 29 to binary.
2. Convert binary 1111 to hexadecimal.
3. Convert hexadecimal A7 to decimal.
4. Why is binary preferred in computers over decimal?
5. How many bits are there in 4 bytes?

✅ Coming Next

In the next chapter, we’ll explore Software vs Hardware — understanding the difference between physical components and digital instructions.