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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 160, and (16^1) means 161,
and (16^2) means 162, 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 162 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 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
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
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