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Hexadecimal to Binary Conversion
Hexadecimal to Binary Conversion
We can convert a hexadecimal number into its equivalent binary by using the mapping method. In this method, we replace each digit of the given hexadecimal number by its equivalent 4-bit binary group.
The following table shows the equivalent 4-bit binary group of each hexadecimal digit −
| Hexadecimal | Binary | |||
|---|---|---|---|---|
| (2)3 = 8 | (2)2 = 4 | (2)1 = 2 | (2)0 = 1 | |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 2 | 0 | 0 | 1 | 0 |
| 3 | 0 | 0 | 1 | 1 |
| 4 | 0 | 1 | 0 | 0 |
| 5 | 0 | 1 | 0 | 1 |
| 6 | 0 | 1 | 1 | 0 |
| 7 | 0 | 1 | 1 | 1 |
| 8 | 1 | 0 | 0 | 0 |
| 9 | 1 | 0 | 0 | 1 |
| A (10) | 1 | 0 | 1 | 0 |
| B (11) | 1 | 0 | 1 | 1 |
| C (12) | 1 | 1 | 0 | 0 |
| D (13) | 1 | 1 | 0 | 1 |
| E (14) | 1 | 1 | 1 | 0 |
| F (15) | 1 | 1 | 1 | 1 |
Let us understand the conversion of a hexadecimal number to binary number with the help of examples.
Example 1
Convert (3A94.C5D)16 to binary equivalent.
Solution
The given hexadecimal number can be converted into equivalent binary number as follows −
| Hexadecimal Number | 3 | A | 9 | 4 | . | C | 5 | D |
| 3 | 10 | 9 | 4 | . | 12 | 5 | 13 | |
| 4-bit Binary Equivalent | 0011 | 1010 | 1001 | 0100 | . | 1100 | 0101 | 1101 |
Thus, the binary equivalent of the given hexadecimal number is (0011101010010100.110001011101)2.
Example 2
Convert (ABD.2E)16 to binary equivalent.
Solution
The conversion of given hexadecimal number to its binary is done as follows −
| Hexadecimal Number | A | B | D | . | 2 | E |
| 10 | 11 | 13 | . | 2 | 14 | |
| 4-bit Binary Equivalent | 1010 | 1011 | 1101 | . | 0010 | 1110 |
Hence, the equivalent binary of (ABD.2E)16 is (101010111101.00101110)2.
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