Positional Notation Calculator (Base Converter)

How to use the tool

Type the number you want to convert in the value field, it will be displayed below:

Value:

From: Positional notation Binary System (Base 2) Ternary System (Base 3) Quaternary System (Base 4) Quinario System (Base 5) Senary System (Base 6) Septenary System (Base 7) Octal System (Base 8) Nonary System (Base 9) Decimal System (Base 10) Duodecimal System (Base 12) Hexadecimal System (Base 16) Vigesimal System (Base 20) Duotrigesimal System (Base 32)

To: Positional notation Binary system Base 3 Base 4 Base 5 Base 6 Base 7 Octal system Base 9 Decimal system Hexadecimal system Vigesimal system

Decimal places: 0 decimal places 1 decimal place 2 decimal places 3 decimal places 4 decimal places 5 decimal places 6 decimal places 7 decimal places 8 decimal places 9 decimal places 10 decimal places

Conversion tables

What is positional notation?

Converting numbers between bases is the procedure where a certain numerical representation (decimal base) is modified proportionally to suit a new representation (binary base). For example, the number '11' in the decimal base can be written as 'B' in the hexadecimal base or '1011' in the binary base.

Today's society is familiar with the decimal base or base 10 (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9), current computers and electronic devices work exclusively with calculations based on the base binary (0 and 1), so that humans and machines can communicate (insert data, processing, data outputs) and understanding, it is necessary to convert the machine language (binary - 0 and 1) to "human language" ( decimal), and vice versa.

You may be wondering "if computers work with 0 and 1, how can humans (who speak the English language and do calculations with numerals from 0 to 9) manage to create programs and understand this equipment?", it turns out that among these there are chips capable of "translating" what humans say to what machines need to hear, that is, human beings can speak normally in their language (decimal base) that the computer can understand in their own language (binary base) . This is done automatically, without the lay user knowing or needing to interact.

Links to other base conversions