To convert Hexadecimal to Binary, input decimal value in the box below, and then click on the big blue button that says “CONVERT TO BINARY” and your Binary number is generated, copy it or you can download output file.
In a Hexadecimal number system there are sixteen (16) alphanumeric values from 0 to 9 and A to F. In this number system every number (value) represents with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The base of this number system is 16, because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 14, E is 15 and F is 16.
Example: What is 0xA5 in base 10?
0xA5 = A5_{16} = (10 x 16^{1}) + (5 x 16^{0}) = 165_{10}
In Binary number system there are only two digits that are 0 and 1. In this number system every number (value) represents with 0 and. The base of binary number system is 2, because it has only two digits. The binary system is mostly used in computers and electronic devices
Example: What is 0b110 in base 10?
0b110 = 110_{2} = (1 x 2^{2}) + (1 x 2^{1}) + (0 x 1^{0})
If you have a hexadecimal number in question and you're asked to convert it into its binary equivalent, then:
Step 1: At first convert each hexadecimal digit into a 4-bit-equivalent binary number.
Step 2: Now combine all those digits we get from converting each hexadecimal into binary.
Step 3: Here we have the final binary equivalent.
Here are few examples below to understand the process in brief:
Example 1.Convert 29C_{16 }into an equivalent binary number.
Solution. The hexadecimal number given is 2 9 C 4-bit binary equivalent 0010 1001 1100
Hence the equivalent binary number is (001010011100)_{2}.
Example 2.Convert 9E.AF2_{16 }into an equivalent binary number.
Solution. The hexadecimal number given is 9 E A F 2
4-bit binary equivalent 1001 1110 1010 1111 0010
Hence the equivalent binary number is (10011110.101011110010)_{2}.
Base 16 |
Base 2 |
0 |
0000 |
1 |
0001 |
2 |
0010 |
3 |
0011 |
4 |
0100 |
5 |
0101 |
6 |
0110 |
7 |
0111 |
8 |
1000 |
9 |
1001 |
A |
1010 |
B |
1011 |
C |
1100 |
D |
1101 |
E |
1110 |
F |
1111 |
Hexadecimal Numbers are commonly used in computer programming to simplify the binary numbering system. As 16 is equivalent to 2^{4}, there is a linear relation between binary and hexadecimal number system. This means four binary digits are equivalent to one hexadecimal digit. But computers understand just 0 and 1 i.e. Binary number system so computers use just binary number system while humans use hexadecimal number system to shorten binary digits to make them understandable easily. Following are the fewer applications of Hexadecimal Number system:
To define colors on web pages: To define a color on any web page we use RGB where R stand for Red, G for Green ad B for Blue in the format of #RRGGBB.
To allocate memory: We can characterize every byte just as two hexadecimal digits where as we have to use 8 digits while using binary.