Introduction to Numeral Systems

Numeral systems (numeral system), also called systems of numeration, are writing systems used to represent numbers, such as the Hindu–Arabic numeral system, Roman numerals, and Suzhou numerals. Numeral systems are tools that we use to encode numbers.

Generally speaking, the numbers in a numeral system are strings of symbols, together with a set of rules that establish a one-to-one correspondence between the strings and the numbers they represent. For example, the Roman numeral $\text{XLII}$, the binary number $101010_{(2)}$, and the decimal number $42$ all correspond to the same number.

In algorithm competitions, we generally focus only on conversion relationships between different numeral systems. See Positional Notation for details.

References and notes

• Numeral system - Wikipedia