Convert values between the binary, decimal, and hexadecimal number systems.

To convert between binary, decimal, and hexadecimal, type in the number you wish to convert into the corresponding field. Remember that binary only allows digits of one and zero, and the hexadecimal number system allows digits from zero to the letter F.

Remember, IPv6 is written in hexadecimal and IPv4 in decimal. However, computers use the binary version of both hexadecimal and decimal numbers because computers only ‘think’ in binary. Converting between the three will help with understanding computers and networking.

The converter can also be used as a binary-to-hex and decimal converter, decimal-to-hex and binary converter, or a hex-to-decimal and binary converter.

## Decimal

The decimal number system uses ten different symbols to represent numbers. These ten symbols or ‘digits’ are** 0, 1, 2, 3, 4, 5, 6, 7, 8, 9**. Using these digits, we can represent every number from zero to nine using a single one of these symbols. However, when we need to represent a larger number, like ten or eleven, we must combine two or more of our digits. For the number ten, we use the digit ‘1’ and the digit ‘0’ together to write ’10’. We use the two digits ‘2’ and ‘5’ for the number twenty-five. This system is called base-10 because it uses ten digits to express the number we mean. Each time we add another digit to the left, its value goes up by a factor of ten. For example, 752 is seven 100s, five 10s and two 1s.

## Binary

Other number systems use a different amount of symbols or digits to represent a number. The binary is base-2, which means there are only two symbols used to represent a number; 0 and 1. So zero and one can be represented by a single binary digit – **0** and **1**, respectively. However, for any number greater than one, the binary must use more than one digit to represent it. The number two is represented by two separate binary digits, ’10’. The number three is also represented by two digits, ’11’. The number four, however, cannot be represented by two digits, so now binary has to use three digits. The number four is ‘100’. Five is ‘101’, and so on.

When translating from binary, the right-most digit is always going to represent a value of ‘one’ or ‘zero’, the second right-most is always going to be ‘two’ or ‘zero’, the third will be ‘four’ or ‘zero’, the fifth will be ‘eight’ or zero, and so on. Each digit’s place is always an exponent of the number ‘two’. To really understand what is going on, get binary conversion practice and exponent practice.

## Hexadecimal

Like binary, the hexadecimal system (or hex) uses a different set of symbols to represent the same numbers. Hexadecimal is base-16, which means it uses sixteen different digits to represent numbers. They are **0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F**. The letters represent numbers, so the hex value ‘A’ is actually the number ten, and ‘B’ is eleven. Because hexadecimal uses more than ten digits to represent numbers, it can represent any value between zero and fifteen using only a single digit. And as with other systems, any number above fifteen will need more than one digit. For example, sixteen is written as ’10’, seventeen is ’11’, eighteen is ’12’, twenty-six ‘1A’, and twenty-seven is ‘1B’. Practising your multiples of sixteen can help.

The actual numerical value is always the same when translating between the three systems. It’s just that the way of representing it changes.

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