Binary System
Computers · बाइनरी सिस्टम
📋Quick Overview
Computers use the binary number system (base-2) with only two digits: 0 and 1. Each digit is called a 'bit'. Other important number systems: Decimal (base-10), Octal (base-8), and Hexadecimal (base-16). Conversion between these systems is a frequently asked topic in exams.
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Binary (base-2): uses 0,1; Octal (base-8): uses 0-7; Decimal (base-10): uses 0-9; Hex (base-16): uses 0-9, A-F
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(10)₁₀ = (1010)₂ = (12)₈ = (A)₁₆ — same number in 4 systems
📖Binary System
| Number System | Base | Digits Used | Example |
|---|---|---|---|
| Binary | 2 | 0, 1 | 1010 = 10 in decimal |
| Octal | 8 | 0–7 | 12 = 10 in decimal |
| Decimal | 10 | 0–9 | 10 (our normal system) |
| Hexadecimal | 16 | 0–9, A–F | A = 10 in decimal |
| Binary to Decimal | — | Multiply each bit by 2ⁿ | 1010 = 8+0+2+0 = 10 |
| Decimal to Binary | — | Divide by 2, note remainders | 10 ÷ 2 = 1010 |
| 1 Byte | — | 8 bits | Can store 0 to 255 (2⁸-1) |
📝Key Points
- •Binary: 1010 = 10 in decimal
- •Octal: 12 = 10 in decimal
- •Decimal: 10 (our normal system)
- •Hexadecimal: A = 10 in decimal
- •Binary to Decimal: 1010 = 8+0+2+0 = 10
- •Decimal to Binary: 10 ÷ 2 = 1010