Hexadecimal Numbers: Base 16

4 binary digits can be represented by 1 hex digit.

Hexadecimal
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.

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