Understanding Number Systems
Binary (Base 2)
Binary is the fundamental language of computers, consisting of only 0s and 1s. Each digit represents a power of 2.
Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 11₁₀
Decimal (Base 10)
Decimal is the standard numerical system used by humans, consisting of digits 0-9. It is based on powers of 10.
Example: 345₁₀ = (3×10²) + (4×10¹) + (5×10⁰)
Hexadecimal (Base 16)
Hexadecimal is widely used in computing, particularly in addressing and color codes. It uses digits 0-9 and letters A-F.
Example: 2F₁₆ = (2×16¹) + (15×16⁰) = 47₁₀
Octal (Base 8)
Octal is another base system used in computing, particularly in file permissions in UNIX-based systems.
Example: 75₈ = (7×8¹) + (5×8⁰) = 61₁₀
ASCII (Character Encoding)
ASCII (American Standard Code for Information Interchange) assigns numerical values to characters.
Example: 'A' = 65₁₀, 'B' = 66₁₀