Computer Science Basics for Beginners

🔢 Number Systems – Binary, Decimal, Hexadecimal

Computers understand numbers, but not the way we do. Humans commonly use the Decimal (Base-10) system. Computers use Binary (Base-2), and sometimes we also use Hexadecimal (Base-16) for programming and debugging.

🧮 1. Decimal Number System (Base-10)

This is the number system you use every day. It has 10 digits: 0 to 9.

• Each digit's place represents powers of 10
• Example: 456 = 4×10² + 5×10¹ + 6×10⁰

💡 2. Binary Number System (Base-2)

Used by all computers and digital systems. It uses only two digits: 0 and 1.

• Each position is a power of 2
• Example: 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11 in decimal
• Each bit (binary digit) is a unit of memory (0 or 1)

🎨 3. Hexadecimal Number System (Base-16)

Commonly used in programming, especially to represent colors, memory addresses, or binary shorthand.

• Uses 16 digits: 0-9 and A-F (A=10, B=11, ..., F=15)
• Example: 2F = 2×16¹ + 15×16⁰ = 47 in decimal
• 1 Hex digit = 4 Binary digits (bits)

🔁 Conversions

1. Binary to Decimal

Binary: 1101 → Decimal = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13

2. Decimal to Binary

Decimal: 13 → Binary = 1101 (by dividing by 2 and collecting remainders)

3. Binary to Hex

Binary: 11010111 → Grouped: 1101 0111 → Hex = D7

4. Hex to Binary

Hex: A3 → Binary = A=1010, 3=0011 → 10100011

🧠 Real-Life Uses

• Binary: All hardware circuits, microprocessors
• Hex: Memory dumps, color codes in HTML (e.g., #FF5733)
• Decimal: Used by humans for counting and measurement

📊 Comparison Table

📝 Practice Questions

1. Convert 1010 (binary) to decimal.
2. Convert decimal 29 to binary.
3. What is the hexadecimal value of binary 11110000?
4. Which number system uses only two digits?

✅ Coming Next

In the next chapter, you’ll learn the difference between SoftwareHardware – and how they work together to run a computer.