Introduction to Number Systems

The Nugget

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.

Make it stick

📊 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:
1. Decimal: 4 digits (7392)
2. Binary: 13 bits (11100111000)
3. Octal: 5 digits (16340)
4. Hexadecimal: 4 digits (1CE0)
Observation: As the base increases, the number of digits required decreases; base 2 has the highest digit count.

"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.