Question

What is hexadecimal number system​

Answer 1

Our usual number system is the decimal number system. As the name suggests, it uses base 10.

Using a certain base to express numbers means to write numbers as weighted sums of powers of the base. For example, in base 10 we write

$1437 = 1\cdot 10^3 + 4\cdot 10^2 + 3\cdot 10^1 + 7\cdot 10^0$

So, the weights of the powers are what we call the digits of the number.

Note that our digits finish at 9 because it wouldn't make sense to have a digit to express 10: if we choose a weight of 10 (or more) for a certain power, we can simply scale it to the next one: for example, saying "ten hundreds" is the same as saying "one thousand":

$10\cdot 10^2 = 1\cdot 10^3$

Now, the hexadecimal number system simply uses 16 as base, instead of 10. This means that its digits are

1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

where digits from A to F represent numbers from 10 to 15.

These are some examples of hexadecimal numbers turned into our usual system:

$(47B)_{16} = 4\cdot 16^2+7\cdot 16^1+11\cdot 16^0 = 1024+112+11=(1147)_{10}$

$(CAF35)_{16} = 12\cdot 16^4+10\cdot 16^3+15\cdot 16^2+3\cdot 16^1+5\cdot 16^0 = 786432+40960+3840+48+5=(831285)_{10}$