Hexadecimal to Decimal
Hexadecimal Number System
Base 16 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f}.
Decimal Number System
Base 10 number system which consists numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
Hexadecimal Number System
Decimal Number System
Hexadecimal to Decimal Conversion Procedure
1. Write down the decimal equivalent of hexadecimal.
2. Find the position of every digit. We should count the position from the right direction of the number. And the position count starts from 0.
Example
1caf - position of f = 0, a = 1, c = 2, 1 = 3.
5afb - position of b = 0, f = 1, a = 2, 5 = 3.
3. Multiply every digit with 16 to the power of their corresponding position. (16 position)
4. Finally, calculate the sum of all the multiples.
Decimal equivalent of Hexadecimal
Decimal |
Hexadecimal |
|---|---|
0 |
0 |
1 |
1 |
2 |
2 |
3 |
3 |
4 |
4 |
5 |
5 |
6 |
6 |
7 |
7 |
8 |
8 |
9 |
9 |
10 |
A or a |
11 |
B or b |
12 |
C or c |
13 |
D or d |
14 |
E or e |
15 |
F or f |
Example
(16)16 to decimal
position = {1-1, 6-0}
= 1 x 16 1 + 6 x 16 0
= 16 + 6
= (22)10
Example
ffff to decimal
position = {f-3, f-2, f-1, f-0}
f equivalent decimal = 15
= 15 x 16 3 + 15 x 16 2 + 15 x 16 1+ 15 x 16 0
= 15 x 4096 + 15 x 256 + 15 x 16 + 15 x 1
= (65535)10
Example
16ab to decimal
position = {1-3, 6-2, a-1, b-0}
a equivalent decimal = 10
b equivalent decimal = 11
= 1 x 16 3 + 6 x 16 2 + a x 16 1+ b x 16 0
= 1 x 4096 + 6 x 256 + 10 x 16 + 11 x 1
= 4096+1536+160+11
= (5803)10
Example
ab0cffcd to decimal
position = {a-7, b-6, 0-5, c-4, f-3, f-2, c-1, d-0}
a equivalent decimal = 10
b equivalent decimal = 11
c equivalent decimal = 12
d equivalent decimal = 13
f equivalent decimal = 15
= a x 16 7 + b x 16 6 + 0 x 16 5+ c x 16 4 + f x 16 3 + f x 16 2 + c x 16 1+ d x 16 0
= 10 x 268435456 + 11 x 16777216 + 0 x 1048576 + 12 x 65536 + 15 x 4096 + 15 x 256 + 12 x 16 + 13 x 1
= 2684354560+184549376+0+786432+61440+3840+192+13
= (2869755853)10