We can convert hexadecimal to decimal by simply representing the given each digit of the given Hexadecimal number as sum of powers of 16, since for hexadecimal number system 16 is the base or radix. Here we first convert each individual hexadecimal digit separately and then add it together to get the final decimal equivalent. Detailed steps explaining the process of converting Hexadecimal to decimal, with illustrated examples of hexadecimal to decimal conversions.
Hex to Decimal Converter
How to Convert Hex to Decimal
Step 1: First we write down the given hexadecimal number separately and identify the LSD and MSD for hexadecimal numbers with only integer part and no fractional part.
Step 2: We then represent each digit of the given hexadecimal number as powers of 16, starting from 160 from right to left.
Step 3: We then evaluate the power of 16 values such as 160 is 1 and 161 is 16. And from the number system conversion table we can identify the decimal equivalent of individual hexadecimal digits such as for example the decimal equivalent of hexadecimal digit A is 10.
Step 4: We then multiply the decimal equivalent obtained from the number system table with the evaluated power of 16 values, and write it down as sum of products.
Step 5: We then add all the individual products and this sum total gives the final decimal equivalent of the given hexadecimal number.
Hexadecimal to Decimal Examples
Example 1: Convert ( 2 5 A )16 Hexadecimal to Decimal ( ? )10
= 2 5 A
↑ ↑
MSD LSD= 2 x 162 + 5 x 161 + A x 160= 2 x 256 + 5 x 16 + 10 x 1= 512 + 80 + 10= 602Therefore ( 2 5 A )16 = ( 6 0 2 )10Example 2: Convert ( 2 0 D 0 )16 Hex to decimal ( ? )10
= 2 0 D 0
↑ ↑
MSD LSD= 2 x 163 + 0 x 162 + D x 161+ 0 x 160= 8192 + 0 + 208 + 0= 8400Therefore ( 2 0 D 0 )16 = ( 8 4 0 0 )10Example 3 : Convert ( F F F F )16= ( ? )10
= F F F F
↑ ↑
MSD LSD= F x 163 + F x 162 + F x 161+ F x 160= 15 x 4096 + 15 x 256 + 15 x 16 + 15 x 1= 61440 + 3840 + 240 + 15= 65535Therefore ( F F F F )16 = ( 6 5 5 3 5 )10
Example 4 : Convert ( A B C 0 )16= ( ? )10
= A B C 0= A x 163+ B x 162+ C x 161+ 0 x 160= 10 x 4096 + 11 x 256+ 12 x 16 + 0 x 1= 40960 + 2816 + 192 + 0 = 43968Therefore ( A B C 0 )16 = ( 4 3 9 6 8 )10
Convert Hexadecimal Fraction to Decimal
Solved examples of Hexadecimal to decimal with the given hexadecimal number containing fractional part.
Example 1: Convert ( E F . B 1 )16= ( ? )10
= E F . B 1
↑ ↑
MSD LSD= E x 161 + F x 160 . B x 16-1 + 1 x 16-2 = 14 x 16 + 15 x 1 . 11 x ( 1 / 16 ) + 1 x ( 1 / 256 )
= 224 + 15 . ( 0. 6 8 7 5 ) + ( 0 . 0 0 3 9 0 6 2 5 )
= 239 + 0. 6914= 239 . 691406Therefore ( E F . B 1 )16 = ( 2 3 9 . 6 9 1 4 0 6 )10Example 2 : Convert ( 0.9D9 )16= ( ? )10
= 0 . 9 D 9
↑ ↑
MSD LSD= 0 x 160 . 9 x 16-1 + D x 16-2 + 9 x 16-3= 0 x 1 . 9 x ( 1 / 16 ) + 13 x ( 1 / 256 ) + 9 x ( 1 / 4096 ) = 0 . (0. 5625) + (0 . 050781 ) + ( 0. 0021972 ) = 0 . ( 0 . 6154782 )= 0 . 6154782Therefore ( 0 . 9 D 9 )16 = ( 0 . 6 1 5 4 7 8 2 )10Example 3: Convert ( BCC.1 0 )16= ( ? )10
= B C C . 1 0
↑ ↑
MSD LSD= B x 162 + C x 161 + C x 160 . 1 x 16-1 + 0 x 16-2
= 11 x 256+ 12 x 16+ 12 x 1 . 1 x ( 1 / 16 ) + 1 x ( 1 / 256 )= 2816 + 192 + 12 . ( 0 . 0625 ) + ( 0 ) = 3020 . ( 0. 0625 )= 3020 . 0625Therefore ( B C C . 1 0 )16 = ( 3 0 2 0 . 0 6 2 5 )10Hex to Decimal Chart
| Hexadecimal | Decimal |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| A | 10 |
| B | 11 |
| C | 12 |
| D | 13 |
| E | 14 |
| F | 15 |
Hex to Decimal FAQs
What is 20 hex to decimal?
The Decimal equivalent of hexadecimal number 20 is 32.
What is 3f hex to decimal?
63 is the decimal equivalent of hexadecimal 3F.
What is abc hexadecimal to decimal?
abc in hexadecimal is equal to 2748 in decimal number system.