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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