As we are going through the basics of the digital electronics the first and very important part is understanding the different types of number system. As we have already discussed about the properties of various number system and interrelation among some of them, now this is the time to interrelate binary and hexadecimal number system. The conversion from one number system is quite easy and we will discuss both the cases in the following articles i.e. from binary to hexadecimal and from hexadecimal to binary conversion.
Binary to Hexadecimal Conversion
Just as you can convert any binary numbers to decimal, or convert binary numbers to octal, any number in the binary number system can be converted into the hexadecimal number system.
To convert a binary number to hexadecimal number first we have to divide the digits of the binary number into groups of four taking from the right most side of the number and in the last group the number of digits is made four by putting zeroes in the left most side.
After that the groups are converted into decimal numbers individually and written side by side in the same order as they were previously, now we have got the desired equivalent hexadecimal number of the binary number, an example will make it all clear for us.
We take any binary number suppose 1000101001012.
Breaking it into groups of 4 we get
Now converting all the groups into decimal numbers individually we get
8 | 10 | 5
So the desired hexadecimal equivalent of the binary number 1000101001012 is 8A516
Hexadecimal to Binary Conversion
Similarly the vice versa operation is also possible, i.e. we can convert any hexadecimal number into its equivalent binary number directly without any intermediate steps. The method is pretty easy, first of all we have to convert every digit of the hexadecimal number into its equivalent binary numbers (making every group a group of four by adding 0s to the left of the number).
After all the digits are converted into binary numbers they are merged according to their positions to make the final binary number which is equivalent to the hexadecimal number is obtained. Now we will try to understand the method with the help of an example.
3DC16 is the hexadecimal number which we want to convert into binary. We know D and C are equivalent to 13 and 12 respectively in decimal number system.
Now converting each digit into its binary equivalent number we get
Now merging all these groups binary numbers to make the final binary number we get 11110111002 which is the binary equivalence of the hexadecimal number 3DC16