CONVERTING FROM HEXADECIMAL TO DECIMAL
Converting from Hexadecimal to Decimal
- 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
- 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.