A number system is a way of representing numbers using a set of digits or symbols according to certain rules. Each number system is defined by its base (or radix), which determines how many unique digits it uses.
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1. Decimal Number System (Base 10)
The most commonly used system in daily life.
Uses 10 digits: 0–9
Each position represents a power of 10.
Example:
22610=2×102+2×101+6×100
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2. Binary Number System (Base 2)
Used in computers and digital electronics.
Uses only 2 digits: 0 and 1
Each position represents a power of 2.
Example:
111000102=1×27+1×26+1×25+0×24+0×23 + 0×22+1×21+0×20=22610
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3. Octal Number System (Base 8)
Uses 8 digits: 0–7
Each position represents a power of 8.
Sometimes used in computing as a compact form of binary.
Example:
3428=3×82+4×81+2×80=22610
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4. Hexadecimal Number System (Base 16)
Uses 16 symbols: 0–9 and A–F
(A=10, B=11, C=12, D=13, E=14, F=15)
Each position represents a power of 16.
Widely used in programming and digital systems.
Example:
1A16=1×161+10×160=2610
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Summary
| Number System | Base | Digits Used |
| Decimal | 10 | 0–9 |
| Binary | 2 | 0–1 |
| Octal | 8 | 0–7 |
| Hexadecimal | 16 | 0–9, A–F |
