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 the power of 0 of any number is always 1
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 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 a
power-of-16 is, it's easier to calculate it from the previous
power 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 power-of-16s 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
