# Code-Breaking: Number systems

## Binary

Binary numbers is the basis for modern computing. It uses only the digits 0 and 1 to describe numbers.

## Hex

Hexadecimal numbers is a numeral system with a base of 16. It uses sixteen symbols, 0-9 and A-F to represent the values of 0-15. Hexadecimal numbers are widely used by computer programmers and applications, because they are much easier to convert to bytes of data than decimal numbers and more compact than binary numbers.

## Babylonian numerals

Babylonian numerals uses a sexagesimal (base 60) number system. It was written in cuneiform, on soft clay tablets which later were exposed to the sun to harden. The legacy of the Babylonian numerals still survives today through the clock (60 minutes and seconds) and in trigonometry.

## Mayan numerals

Maya numerals was the number system of the Mayan civilization. It was a vigesimal (base 20) number system. The numerals are made up of three symbols, of which one denotes zero.

## Roman numerals

Roman numerals originated in ancient Rome and remained in use in Europe well into the late middle ages. Roman numbers are represented by a combination of letters from the latin alphabet.

## Prime numbers

A prime number is a natural number that cannot be formed by multiplying two smaller natural numbers. The number 1 is a special case, which is not considered a prime number. Prime numbers play a very important role in mathematics and therefore a of interest to puzzle makers.

## Number sequences

A number sequence is a sequence of numbers that follows a specific pattern. For instande the Fibonacci sequence, 0, 1, 1, 2, 3, 5, 8, etc is calculated by adding the two last numbers to generate the next number. Solving certain logical puzzles can require you to identify the number sequence being used.

## Pi (π)

π, or 3.14..., is a mathematical constant. It describes the ratio of a circle's circumference to its diameter. Being an irrational number, it has infinite number of decimals. In the 5th century AD Chinese mathematics approximated π to seven digits. Modern supercomputers can calculate π with billions of decimals.

## Euler number (e)

The number e, or 2.718..., is a mathematical constant. It is the base of the natural logarithm and named after the Swiss mathematician Leonhard Euler. Being an irrational number, it has infinite number of decimals. The number e is of eminent importance in mathematics alongside with π.

## Golden ratio (φ)

The golden ratio is also called the divine proportion, divine section and golden number. It is the ratio of two quantities, a and b, where (a+b)/a = a/b and a is greater than b. The solution is an irrational number, 1.618..., with infinite number of decimals. It appears commonly in art, architecture and nature.