Converting hexadecimal into binary is very simple. All we need is to remember that hexadecimal is a base 16 number. This means that each number column can contain 16 characters. Hexadecimal goes from 0 to F:

Decimal Number	Binary Number	Hexadecimal Number
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

Using the table – 7 in hex is 0111 in binary.

Using the table – A in hex is 1010 in binary.

Without the table for reference we can also convert the hexadecimal into decimal then convert into binary

B in hexadecimal = 11 in decimal

Create a table with the numbers 8, 4, 2, 1 in the upper columns.

8	4	2	1

Starting at the left hand side, try to subtract the number you have (11 in our case) from the number in the top column – 11 – 8 = 3. Because we can do this we put a 1 in the lower column and move our remainder to the next column.

8	4	2	1
1

In the next column we ask if we can subtract 4 from 3. We can’t because this would leave a negative number, so we put a 0 underneath the 4 and carry the 3 over to the next column.

8	4	2	1
1	0

In the next column we ask if 2 can be subtracted 3 without leaving a negative value. It can (3-2 = 1) so we put a 1 value under the 2 column and carry our remainder over to the last column.

8	4	2	1
1	0	1

In the last column we ask if 1 can be subtracted from 1 without leaving a negative value. It can (1-1=0) so we put a 1 value under the 1 column and our calculation ends because we are left at 0.

8	4	2	1
1	0	1	1

We now have our binary number written under the columns – 1011.

B in hexadecimal = 1011 in binary

2 digit Hexadecimal to Binary Conversion

What do we do when we need to convert 2 digit hexadecimal into binary? Again we need to remember that hexadecimal is a base 16 number and each number column can go from 0-9 and A-F.

Example 1

Convert hexadecimal number A2 into Binary

Split the hexadecimal number into a 2 column table.

A	2

Using the table above and our knowledge of binary, we can now convert the individual hexadecimal digits into binary.

A	2
A = 1010	2 = 0010

We now simply combine these 2 nibbles of binary into a byte:

A2 = 1010 0010 in binary

Example 2

Convert hexadecimal number 28 into binary

2	8
0010	1000

28 = 0010 1000 in binary

4 digit Hexadecimal to Binary Conversion

For the Infrastructure Technician course we need to be able to convert 4 digits of Hexadecimal into a binary so what do we do when we need to convert 4 digits of hexadecimal into binary? Again we need to remember that hexadecimal is a base 16 number and each number column can go from 0-9 and A-F.

Example 3

Convert hexadecimal number A24B into Binary

Split the hexadecimal number into a 4 column table.

A	2	4	B

Using the table above and our knowledge of binary, we can now convert the individual hexadecimal digits into binary.

A	2	4	B
A = 1100	2 = 0010	4 = 0100	1011

A24B = 1100 0010 0100 1011 in binary

Time to test yourself

Now you know how to convert hexadecimal into binary it’s time to test yourself.

4 digit hexadecimal to binary test – 10 questions

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