Number Systems and Conversions
⏱ Estimated reading time: 2 min
Number Systems and Conversions
A number system is a way to represent numbers using digits or symbols. Computers primarily use binary systems, but humans commonly use decimal numbers.
1. Common Number Systems
| Number System | Base | Digits Used | Example |
|---|---|---|---|
| Decimal (Base-10) | 10 | 0–9 | 237, 405 |
| Binary (Base-2) | 2 | 0, 1 | 1011, 1100 |
| Octal (Base-8) | 8 | 0–7 | 57, 145 |
| Hexadecimal (Base-16) | 16 | 0–9, A–F | 1A, 3F |
2. Conversions Between Number Systems
a) Decimal to Binary
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Divide the decimal number by 2 repeatedly.
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Record remainders in reverse order.
b) Binary to Decimal
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Multiply each binary digit by 2^position (position counted from right, starting at 0).
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Sum the results.
c) Decimal to Octal
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Divide decimal by 8 repeatedly.
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Write remainders in reverse order.
d) Octal to Decimal
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Multiply each digit by 8^position (position from right starting at 0) and sum.
e) Decimal to Hexadecimal
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Divide decimal by 16 repeatedly.
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Map remainders 0–9 stay same, 10–15 → A–F.
f) Hexadecimal to Decimal
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Multiply each hex digit by 16^position (position from right starting at 0) and sum.
g) Binary ↔ Octal Conversion
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Group binary digits in sets of 3 (from right to left) for octal conversion.
h) Binary ↔ Hexadecimal Conversion
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Group binary digits in sets of 4 (from right to left) for hexadecimal conversion.
Key Points
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Decimal system (base 10) is human-friendly; binary (base 2) is computer-friendly.
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Octal (base 8) and hexadecimal (base 16) are shorthand for binary numbers.
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Conversion involves division-remainder method (decimal → other) or positional method (other → decimal).
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Understanding number systems is essential for computer programming, digital electronics, and networking.
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