In the previous post, we learned about the introduction to the number system and its types — Binary, Octal, Decimal, and Hexadecimal. Now, it’s time to learn some quick number system conversion tricks and shortcuts that will help you save time in exams like JEE, SSC, GATE, Banking, and Computer Science papers.
Let’s get started 🚀
🔢 1. Binary to Decimal Conversion (Shortcut Method)
Concept:
Multiply each binary digit by powers of 2 and add them all.
Example:
(1011)₂ = 1×8 + 0×4 + 1×2 + 1×1 = 11 (decimal)
Shortcut Trick:
Just remember — write powers of 2 under the binary digits:
1 0 1 1
8 4 2 1
Then add only those where binary digit = 1 → 8 + 2 + 1 = 11
✅ Tip: Practice this on 4-bit, 8-bit numbers — it’s very common in JEE & GATE exams.
🔁 2. Decimal to Binary Conversion (Quick Division Method)
Concept:
Divide the number by 2 repeatedly and note the remainders.
Steps:
- Divide by 2 → note remainder
- Continue dividing until quotient = 0
- Write remainders from bottom to top
Example:
(25)₁₀ → ? (Binary)
| Step | Division | Remainder |
|---|---|---|
| 1 | 25 ÷ 2 | 1 |
| 2 | 12 ÷ 2 | 0 |
| 3 | 6 ÷ 2 | 0 |
| 4 | 3 ÷ 2 | 1 |
| 5 | 1 ÷ 2 | 1 |
Now write remainders bottom to top → 11001₂
✅ Shortcut:
Memorize binary of 1–16 for instant recall:
1 = 1, 2 = 10, 3 = 11, 4 = 100, 5 = 101, 8 = 1000, 16 = 10000
🔄 3. Binary ↔ Octal Conversion (Grouping Trick)
Concept:
- Group 3 binary digits together (from right).
- Convert each group to its octal equivalent.
Example:
Binary: (101101)₂
Group: 101 101 → (5)(5) → (55)₈
✅ Shortcut:
Each octal digit = 3 binary bits
Binary: 000 → 0
Binary: 001 → 1
Binary: 010 → 2
Binary: 011 → 3
Binary: 100 → 4
Binary: 101 → 5
Binary: 110 → 6
Binary: 111 → 7
🧮 4. Binary ↔ Hexadecimal Conversion (4-Bit Trick)
Concept:
- Group 4 binary digits together (from right).
- Replace each with hexadecimal equivalent.
Example:
Binary: (11011001)₂
Group: 1101 1001 → D9₁₆
✅ Hexadecimal Shortcut Table:
| Binary | Hex |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | A |
| 1011 | B |
| 1100 | C |
| 1101 | D |
| 1110 | E |
| 1111 | F |
🔃 5. Decimal to Octal / Hexadecimal (Division Trick)
For Decimal → Octal:
Divide the number by 8, note remainders, reverse them.
Example:
(125)₁₀ → ? (Octal)
125 ÷ 8 = 15 remainder 5
15 ÷ 8 = 1 remainder 7
1 ÷ 8 = 0 remainder 1
→ (175)₈
For Decimal → Hexadecimal:
Same method, but divide by 16 and use letters (A–F).
Example:
(255)₁₀ → ? (Hexadecimal)
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
→ (FF)₁₆
🔁 6. Octal ↔ Binary ↔ Hexadecimal (Interconversion Shortcut)
You don’t need to convert to decimal every time!
Shortcut:
- Octal → Binary: Replace each octal digit with its 3-bit binary form.
- Hex → Binary: Replace each hex digit with its 4-bit binary form.
- Binary → Octal/Hex: Group bits in 3s or 4s respectively.
Example:
(7B)₁₆ → ? (Binary)
7 = 0111, B = 1011 → 01111011₂
🧠 7. Fast Mental Conversion Tips
| Conversion | Trick |
|---|---|
| Binary to Decimal | Use powers of 2 table: 1, 2, 4, 8, 16, 32, … |
| Decimal to Binary | Memorize powers of 2 up to 2¹⁰ = 1024 |
| Decimal to Hex | Divide by 16 → remember A=10, B=11… |
| Octal to Binary | 1 octal digit = 3 bits |
| Hex to Binary | 1 hex digit = 4 bits |
💡 Quick Reference Table
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
✅ Final Thoughts
Mastering number system conversion tricks is essential for acing exams that involve digital logic, data representation, or reasoning.
🧭 Remember:
- Grouping and remainder methods are fastest.
- Practice daily conversions to build speed.
- Binary ↔ Hex conversions are most common in Computer Science & Electronics exams.
