## What is the decimal number system?

The decimal number system is the most used system for denoting integer and non-integer numbers. It is a system that has a base of 10. The way of representing numbers is often referred to as decimal notation.

Decimal numeral or less correct number generally refers to the notation of a number in that numerical system. The decimal separator is often used for the identification of it (in particular with “.” Or “;”). For example, 27.47 or 59,145.

## Origin

Many numerical systems of ancient civilizations used a base of 10 to represent numbers. Most likely because of our ten fingers on both hands. Examples are Greek numerals, Roman numerals, Chinese numerals. Large numbers were difficult to calculate and represent; the Hindu-Arabic numeral system for representing integers has solved this problem.

## Notation

For writing decimal numbers we use decimal digits, and the minus sign “-” is used for marking negative numbers. The characters are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; and those numbers are separated by a point “.”, and in some countries with a comma “,”.

## Counting

The decimal counting system uses ten symbols from 0 to 9. Counting begins with the incremental substitution of the last digit (right digit), otherwise called the first digit. After we use all positions with all ten symbols we need to reset the right digit do 0 and left increase by one (overflow).

Counting example: 001, 002, 003, 004, …, 009 (then you reset right digit to 0 and left increase by 1) and will be: 010, 011, 012, 013, 014.

## What is the hexadecimal counting system?

In mathematics and computing, a Hexadecimal or simply “Hex” numeric system represents numbers using a base of 16 symbols. They are a popular choice for representing long binary values because their format is much easier to understand compared to the long binary strings of 1’s and 0’s. The most commonly used symbols are from 0 to 9, which represent values from 0 to 9, the other five characters are from A – F, representing values from 10 to 15.

## Example of converting

16295957_{10} = F8A815_{16}

111110001010100000010101 | Binary |

16295957 | _{Decimal} |

F8A815 | _{Hexadecimal} |

Conversion steps:

- Divide the number by 16.
- Get the integer quotient for the next iteration.
- Get the remainder for the hex digit.
- Repeat all steps until the quotient is equal to 0.

If you want to know more about Binary to Hex. conversion check out our Binary to Hexadecimal converter!