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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🌟 Chapter 2: Number System - Notes 🌟
Start from the beginning
