To convert between binary, decimal and hexadecimal simply type in the number you wish to convert from into the corresponding field. Remember that binary only allows digits of one and zero and hexadecimal 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 of these because computers only ‘think’ in binary. Being able to convert between the three will help with understanding computer and networking.
Decimal
Decimal is a system of counting using 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 have to combine two or more of our digits. For the number ten we use the digit ‘1’ and the digit ‘0’, together to write ’10’. For the number twenty-five we use the two digits ‘2’ and ‘5’. This system is also called base-10, because it uses ten digits to express the number that 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. Binary is base-2, which means there are only two symbols used to represent a number; 0 and 1. So the numbers zero and one can be represented by a single binary digit – 0 and 1, respectively. However, for any number greater than one, binary must use more than one digit to represent it. The number two is represented by two separate 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 a exponent of the number ‘two’. To really understand what is going on, get binary conversion practice and exponent practice.
Hexadecimal
Like binary, hexadecimal (or hex), is just using 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 ‘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 is going to 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’. Practicing your multiples of sixteen can help.
Translating between the three systems, the actual numerical value is always the same, it’s just that the way of representing it changes.
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