**Number systems are essential for quantifying values using distinct digits, with each system defined by its base or radix.**The decimal system (base 10) is the most common, while binary (base 2), octal (base 8), duodecimal (base 12), and hexadecimal (base 16) offer alternatives for digital representation.

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**The decimal system has ten digits**: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. - 🔢
**Binary uses just two digits**: 0 and 1, known as bits. - ⚖️
**Weighted systems have positional value**: In decimal, 7392 = 7×10³ + 3×10² + 9×10¹ + 2×10⁰. - ⚙️
**Unweighted systems do not assign positional weight**: Examples include Gray code and excess-3 code.

**Decimal (Base 10)**: Digits 0-9, most commonly used in daily life.**Binary (Base 2)**: Digits 0-1 (bits), essential for computing.**Octal (Base 8)**: Digits 0-7, provides a more compact representation than binary.**Duodecimal (Base 12)**: Digits 0-9, A, B (10, 11), useful in some theoretical contexts.**Hexadecimal (Base 16)**: Digits 0-9, A-F (10-15), widely used in programming and digital electronics.**Base 4 Example**: Digits 0-3, illustrating how number systems scale with base.

- For the number 7392:
**Decimal**: 4 digits (7392)**Binary**: 13 bits (11100111000)**Octal**: 5 digits (16340)**Hexadecimal**: 4 digits (1CE0)

**Observation**: As the base increases, the number of digits required decreases; base 2 has the highest digit count.

**Weighted Codes**:- Decimal, Binary, Octal, BCD (Binary-Coded Decimal).

**Unweighted Codes**:- Gray Code, Excess-3.

- "The base of a number system is also called as radix."
- "In binary, we do not call them digits but we call them bits."
- "When base increases, the digits required to represent the quantity decreases."
- "Weighted systems take into account the positional value of their coefficients."
- "In unweighted systems, there is no weight on the position."

This summary contains AI-generated information and may have important inaccuracies or omissions.