Converting Decimal to Hexadecimal

Converting Decimal to Hexadecimal: The Decimal Numbering System

Decimal is a base 10 numbering system that is made up of 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.  It is the most commonly used numbering system.  The reason behind that is convenience.  We have 10 fingers that we use for counting, so it is easier to count with a base 10 numbering system, thus decimal is widely used.

Hexadecimal Numbering System

Hexadecimal is a base 16 numbering system that is made up of 16 digits: 0 – 9 and six more, which is A through F.

Conversion from Decimal to Hexadecimal

Conversion can be done by dividing the decimal number by 16 repeatedly until the final result is 0.
For example, the decimal number 357 is converted to a hexadecimal number as follows:

Division	Result	Remainder
357 / 16	22	5
22 / 16	1	6
1 / 16	0	1

Hexadecimal number is taken from the remainder starting from the last to the first, or in the illustration above, from bottom to top, which is 165.

Note: For the remainder between 0 to 9, the hexadecimal equivalent is the same, see table below.

Hexadecimal	Decimal
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9

So decimal number 357 is 165 in hexadecimal number.
357₁₀ = 165₁₆

Another example, with a remainder greater than 9, in order to have an alphabet result.

Decimal number 2856 is converted to a hexadecimal number as follows:

Division	Result	Remainder
2856 / 16	178	8
178 / 16	11	2
11 / 16	0	11

Hexadecimal number is taken from the remainder starting from the last to the first, or in the illustration above, from bottom to top, which is 1128.  Looking at the table below, 11 is B in hexadecimal.

Hexadecimal	Decimal
A	10
B	11
C	12
D	13
E	14
F	15

So decimal number 2856 is B28 in a hexadecimal number.
2856₁₀ = B28₁₆

Conversion from Hexadecimal to Decimal

Conversion can be done by multiplying the hexadecimal number by 16.  Each digit will be multiplied by the corresponding power of 16 values.  It would be easier to convert by putting the hexadecimal on the power of 16 columns as follows:

Exponent	162	161	160
Value	256	16	1
Hexadecimal	1	6	5

Multiply each value by the hexadecimal digit as follows:
(1 x 256) = 256
(6 x 16) = 96
(5 x 1) = 5
Total value = (256 + 96 + 5) = 357

So, the hexadecimal number 165 is 357 in decimal number.
165₁₆ = 357₁₀

Another example, with alphabet hexadecimal digits.

Conversion can be done by multiplying the hexadecimal number by 16.  Each digit will be multiplied by the corresponding power of 16 values.  It would be easier to convert by putting the hexadecimal on the power of 16 columns as follows:

Exponent	162	161	160
Value	256	16	1
Hexadecimal	B	2	8

Multiply each value by the hexadecimal digit as follows:

(B x 256) = (11 x 256) = 2,816
(2 x 16) = 32
(8 x 1) = 8
Total value = (2,816 + 32 + 8) = 2,856

So, the hexadecimal number B28 is 2,856 in decimal number.
B28₁₆ = 2,856₁₀

Conversion may seem difficult at first, but with just a little practice and understanding the principles behind the conversion, it would be easier over time.  Of course, there are online conversion tools and calculators, but it would be handy to know how it is done manually and understand the concept behind the different numbering systems.

Further Readings:

• Hexadecimal