Number System क्या है — Binary, Octal, Decimal, Hex हिंदी में
Number system की पूरी जानकारी हिंदी में। Binary, Octal, Decimal, Hexadecimal क्या हैं, आपस में convert कैसे करें — examples और tables के साथ।
Number System क्या होता है?
Computer science पढ़ रहे हो तो सबसे पहला chapter जो आता है वो है Number System। ये BCA, BTech, और competitive exams का most important topic है। आज हम इसे बिल्कुल आसान भाषा में समझेंगे।
🔧 अभी convert करें: Number System Converter — binary, octal, decimal, hex एक click में convert करें step-by-step working के साथ।
Number System एक mathematical system है जो numbers को represent करने का तरीका बताता है। हर number system एक base (या radix) पर काम करता है।
चार Main Number Systems
| Number System | Base | Digits Used | Use Case |
|---|---|---|---|
| Binary | 2 | 0, 1 | Computers, digital circuits |
| Octal | 8 | 0-7 | Unix permissions, old systems |
| Decimal | 10 | 0-9 | Daily life, counting |
| Hexadecimal | 16 | 0-9, A-F | Memory addresses, colors |
Decimal 0-15 in All Four Bases
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 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 |
Conversion Methods (Short Examples)
Decimal → Binary (Divide by 2)
25 को binary में convert करें:
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
नीचे से ऊपर पढ़ें: 11001
Binary → Decimal (Positional value)
1101 को decimal में: 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 8+4+0+1 = 13
Binary → Octal (Group of 3)
110111 को octal में: 110 | 111 = 6 | 7 = 67
Binary → Hex (Group of 4)
11011110 को hex में: 1101 | 1110 = D | E = DE
कहाँ Use होता है?
- Binary: Computers, RAM, processor — सब binary में काम करता है
- Octal: Linux/Unix file permissions (chmod 755)
- Decimal: Daily math, counting, money
- Hexadecimal: CSS colors (#FF5733), memory addresses, MAC addresses
BCA/BTech Exams में कैसे आता है?
- “Convert 156 decimal to binary” (2-3 marks)
- “Convert 1011101 binary to octal and hex” (3-5 marks)
- “Explain number system with base and examples” (5-10 marks)
- “Compare all four number systems” (table-based question)
Related Tools
- Number System Converter — instant multi-base conversion
- Binary to Decimal
- Hex to Decimal
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FAQ — अक्सर पूछे जाने वाले सवाल
Q: Number system में base ka matlab kya hota hai? A: Base बताता है कि उस system में कितने unique digits available हैं। Binary का base 2 (दो digits: 0,1), Decimal का base 10 (दस digits: 0-9)।
Q: Computer binary kyun use karta hai? A: क्योंकि electronic circuits sirf 2 states (ON/OFF) easily handle कर सकते हैं। 10 different voltage levels maintain करना practically mushkil है।
Q: Hexadecimal mein A-F kya represent karte hain? A: A=10, B=11, C=12, D=13, E=14, F=15 (decimal values)। ये extra digits hain kyunki base-16 mein 16 symbols chahiye।
Q: Octal system aaj bhi use hota hai? A: Haan — Linux/Unix mein file permissions octal mein likhi jaati hain (755, 644, etc.)। Lekin modern programming mein hex zyada popular hai।
Q: Exam mein sabse zyada kaunsa conversion aata hai? A: Decimal ↔ Binary sabse common hai, followed by Binary ↔ Hex। Octal conversions bhi regularly aate hain BCA/BTech papers mein।
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