# Number Systems: Decimal, Binary, Hexadecimal, RGB Colors

If we write a large number as a binary number, it can be quite long.
The hexadecimal, (hex) base 16, is used because every 4 binary digits can be represented by one hexadecimal digit.
In binary, base 2, there are 2 digits: 0, 1.
In decimal, base 10, there are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
In hexadecimal, base 16, there are 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.

The table below shows the corresponding values of decimal, binary, and hexadecimal:

 Decimal Binary Hexadecimal 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F

To convert a binary number to hexadecimal, first break it into groups of 4 starting on the right. You can always add 0 on the left without changing the value of a number. If the left most group does not have 4 digits, just add zeroes on the left to make a group of 4. Then replace each group of 4 with the corresponding hexadecimal digit from the table above.
Example: Convert   10110111110112 to hexadecimal (base 16)
Break into groups of 4 starting on the RIGHT: 0001,0110,1111,1011
Write the hexadecimal digit for each group of 4:
0001,0110,1111,1011
1        6         F       B
There we have it: 10110111110112 = 16FB16
The place values in hexadecimal start with the ones place on the right, then multiply by 16 for each place moving to the left:

 1,048,576 65,536 4096 256 16 1 165 164 163 162 161 160

The hexadecimal number 16FB is shown below with the place values:

 4096 256 16 1 1 6 F B

The decimal value is 1x4096 + 6x256 + 15x16 + 11x1.
Or: 4096 + 1536 + 240 +11, which is 5883.
Fortunately, we don't usually have to convert hexadecimal to decimal.