The hexadecimal system of numbering is used in computing systems and other fields like mathematics and language coding. For simplification, these numbers are converted into decimal digits, and the opposite process is also possible. Read this Techspirited article to know more about such conversion methodologies in more detail.
In the hexadecimal numbering system, the numbers consist of a base of 16, and each character can be correlated with sixteen different symbols. These are the numbers ‘0’ to ‘9’ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and the letters ‘A’ to ‘F’ (A, B, C, D, E, F). When used in computer systems and for programming, the numbers are represented with the help of a prefix or suffix. For example, a hexadecimal number can be written as 0x 2DC7 or 2DC716, wherein ‘0x’ and ’16’ are a prefix and suffix, respectively.
Four binary digits (called bits) together make up one hexadecimal digit, and one of these is called a nibble (meaning half of an octet or byte, as 8 bits make one byte). This analogy is used to write memory addresses in computing systems, and it is always better to represent coded language in the form of such numbers, instead of the decimal type. This is more convenient when any computing and programming process and tasks are undertaken.
The converter given below will enable you to convert hexadecimal to decimal digits, and vice versa.
In order to convert hexadecimal numbers into decimal ones, and vice versa, it is crucial to understand a few basics regarding the methodology. Thus, in the following sections, the methods, basics, formula, etc., have been explained with the help of examples. Have a look at the reference conversion chart given below before proceeding.
Each individual number in a hexadecimal form corresponds to its specific symbol. Thus, write the number in the form of its representative symbol, and put additional signs in between.
Each number is then multiplied by the nth power of 16, which depends on the position of the number in the expanded form.
The nth power depends upon the positional variation of the particular number. If it is in the hundred’s position, the exponential will be 2, in case of ten’s position it will be 1, and in unit’s position, it will be 0.
After multiplying all the values with the respective numbers, add them to get the final answer, which is the decimal form of the original hex number.
Take a look at the following examples to understand the method in more detail.
First, find out the highest value of base 16 that is less than the given decimal number.
If the number is divided by this power, then the highest value of the hex digit is equal to an integer.
The difference between the number and the multiplied value of the hex digit and the exponential power of base 16 is to be calculated.
Continue to calculate the individual digits till you get zero value. Note down the individual numbers, and by correlating them with the chart, you will get the hexadecimal representations.
The above methods deal with simplicity regarding the conversion between hexadecimal and decimal units and numbers. Ensure that you always refer to the conversion chart, as even a small error or a mistake in the calculations will give out completely different results. This aspect needs to be strictly followed, especially by those who are into programming and coding. A small deviation might cause the entire code to go wrong.