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Number Systems

Computers compute internally with binary numbers (base 2), but hexadecimal numbers (base 16) are often used as a compact shorthand for binary, since two hex digits always make exactly one byte. A digit at position $k$ has weight $b^k$ , where $b$ is the base.

\text{value}=\sum_k d_k\cdot b^k

positional system: each digit d_k is weighted by b^k

Symbols

$b$	base (2, 16 or 10)
$d_k$	digit at position k

Example

$\texttt{0x1F}$ in decimal:

$1\cdot16+15\cdot1=31$ .

Two hex digits are always exactly one byte – handy for reading memory addresses and color codes.

Practise number systems and digital logic for free →

Two's Complement →

Part of Embedded Systems and Instrumentation: Number systems and digital logic.