🌟 Chapter 2: Number System - Notes 🌟

Start from the beginning
                                        

Bit - Binary Digit (0 or 1) 

Nibble - 4 bits

Byte - 8 bits

MSB - Most Significant Bit (leftmost)

LSB - Least Significant Bit (rightmost)

-Number System Conversions: (made long & pretty, so please follow)

💖 I. DECIMAL ➡️ BINARY

🧠 Method: Division by 2 → write remainders from bottom to top

Example 1:

Q) Convert 25 (decimal) to binary

=) 25 ÷ 2 = 12 → R1

12 ÷ 2 = 6 → R0

6 ÷ 2 = 3 → R0

3 ÷ 2 = 1 → R1

1 ÷ 2 = 0 → R1 ← STOP

Now write from bottom to top → 11001

Final Answer: 25₁₀ = 11001₂

🎀 Trick:

If you ever get confused:
Divide by 2 till you hit 0. 🕹️💖

💖 II. BINARY ➡️ DECIMAL

🧠 Method: Multiply each digit (from right) with 2ⁿ, then add all

Example 2:

Q)Convert 1011 to decimal

(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)

= 8 + 0 + 2 + 1 = 11

Final Answer: 1011₂ = 11₁₀

💖 III. DECIMAL ➡️ OCTAL

🧠 Method: Divide by 8, write remainders bottom to top

Example 3:

Q)Convert 78 to octal

78 ÷ 8 = 9 → R6

9 ÷ 8 = 1 → R1

1 ÷ 8 = 0 → R1

Read from bottom: 116

Final Answer: 78₁₀ = 116₈

💖 IV. OCTAL ➡️ DECIMAL

🧠 Method: Multiply each digit (from right) with 8ⁿ, add up

Example 4:

Q)Convert 345₈ to decimal

(3 × 8²) + (4 × 8¹) + (5 × 8⁰)

= (3 × 64) + (4 × 8) + (5 × 1)

= 192 + 32 + 5 = 229

✅ Final Answer: 345₈ = 229₁₀

💖 V. DECIMAL ➡️ HEXADECIMAL

🧠 Method: Divide by 16 → write remainders bottom to top

👉 Use letters for 10–15:


Value


Hex

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