
Steps:
 Get the last digit of the hex number, call this digit the currentDigit.
 Make a variable, let's call it power. Set the
value to 0.
 Multiply the current digit with (16^power),
store the result.
 Increment power by 1.
 Set the the currentDigit to the previous digit of the
hex number.
 Repeat from step 3 until all digits have been multiplied.
 Sum the result of step 3 to get the answer number.
Example 1
Convert the number 1128 HEXADECIMAL to DECIMAL
MULTIPLICATION 
RESULT 
NOTES 
8 x (16^0) 
8 
Start from the last digit of the number.
In this case, the number is 1128. The last
digit of that number is 8. Note
that any number the power of 0 is always 1
Also note the notation (16^0) means 16^{0}, and (16^1) means 16^{1},
and (16^2) means 16^{2}, and so on.

2 x (16^1) 
32 
Process the previous, which is 2. Multiply that number with an increasing power of 16. 
1 x (16^2) 
256 
Process the previous digit, which is 1, note
that 16^2 means 16^{2} or 16 x 16 
1 x (16^3) 
4096 
Process the previous digit, which is 1, note
that 16^3 means 16 x 16 x 16 


Here, we stop because there's no more digit to
process 
ANSWER 
4392 
This
number comes from the sum of the RESULTS
(8+32+256+4096)=4392 
Once discerned, notice that the above process is essentially
performing this calculation:
1x(16^3) + 1x(16^2) +
2x(16^1) + 8x(16^0)
When doing this by hand, it is easier to start backward is because:
 Counting the number of digits takes extra time, and you
might count wrongly.
 If you don't remember what a particular value of 16 to the power of n,
it's easier to calculate it from the previous power of n value. For instance, if you don't remember what the
value of 16^3 is, then just multiply the value of 16^2 (which
you'll likely already have if you started backward) with 16.
Example 2
Convert the number 589 HEXADECIMAL to DECIMAL
MULTIPLICATION 
RESULT 
9 x (16^0) 
9 
8 x (16^1) 
128 
5 x (16^2) 
1280 


ANSWER 
1417 
If you want to be a speed counter, it's beneficial to memorize
the values of the smaller power of 16s, such as in this table
POWER OF 16s 
RESULT 
16^0 
1 
16^1 = 16 
16 
16^2 = 16x16 
256 
16^3 = 16x16x16 
4096 
16^4 = 16x16x16x16 
65536 
Example 3
Convert the number 1531 HEXADECIMAL to DECIMAL
(This time, let's use the table of the powerof16s above.)
MULTIPLICATION 
RESULT 
1 x 1 
1 
3 x 16 
48 
5 x 256 
1280 
1 x 4096 
4096 


ANSWER 
5425 
Example 4
Convert the number FA8 HEXADECIMAL to HEXADECIMAL
MULTIPLICATION 
RESULT 
8 x 1 
8 
A x 16 (remember that hex A=decimal 10) 
160 
F x 256 (remember that hex F=decimal 15) 
3840 


ANSWER 
4008 
Example 5
Convert the number 8F HEXADECIMAL to DECIMAL
DIVISION 
RESULT 
F x 1 
15 
8 x 16 
128 


ANSWER 
143 
Example 6
Convert the number A0 HEXADECIMAL to DECIMAL
DIVISION 
RESULT 
0 x 1 
0 
A x 16 
160 


ANSWER 
160 
Example 7
Convert the number 12 HEXADECIMAL to DECIMAL
DIVISION 
RESULT 
2 x 1 
2 
1 x 16 
16 


ANSWER 
18 
Example 8
Convert the number 35432 HEXADECIMAL to DECIMAL
2x(16^0) + 3x(16^1) +
4x(16^2) + 5x(16^3)
+ 3x(16^4) =
2 + 3x16
+ 4*256 + 5*4096
+ 3*65536 =
2 + 48 + 1024 + 20480 + 196608 =
218162

