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:
Binary
Hexadecimal
0
0000
1
0001
2
0010
3
0011
4
0100
5
0101
6
0110
7
0111
8
1000
9
1001
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:
65,536
4096
256
16
165
164
163
162
161
160
The hexadecimal number 16FB is shown below with the place values:
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.
Hexadecimal Numbers: Base 16