HowTo: Convert Hexadecimal numbers to other systems

 

The Hexadecimal number system is a number system which has base/radix as 15, meaning there are 16 digits in this system, namely 0-9 and A-F representing the values 10-15. In this post we will see as how we can convert Hexadecimal numbers into decimal, binary and octal number systems.

Hexadecimal To Decimal

To convert Hexadecimal numbers into the Decimal System, we simply multiply each digit in the Hexadecimal number with its place value, that is 16ⁿ or 16^-n. Eg:-

To convert 2B(16) into decimal, we do:

2 * 16¹ + B * 16⁰, which is equal to 32 + 11 (B represents the value 11 in the hexadecimal system), which is 43. Therefore, 2B(16) = 43(10).

Hexadecimal To Binary

To convert a Hexadecimal Number to its binary equivalent, we convert each digit of the Hexadecimal number into its corresponding 4 bit binary value, and then write all of the binary equivalents as one. Eg:-

To convert 2B(16), to binary, we do:

2(16) = 0010(2)

B(16) = 1011(2)

Thus, 2B(16) = 00101011(2) or simply 101011(2).

Hexadecimal To Octal

To convert a Hexadecimal number to its Octal equivalent, we first convert the Hexadecimal number to its Binary equivalent as shown above, and then convert that into an Octal number. To learn how to convert Binary to Octal, click here.