Convert 217 from decimal to hexadecimal
(base 16) notation:
Power Test
Raise our base of 16 to a power
Start at 0 and increasing by 1 until it is >= 217
160 = 1
161 = 16
162 = 256 <--- Stop: This is greater than 217
Since 256 is greater than 217, we use 1 power less as our starting point which equals 1
Build hexadecimal notation
Work backwards from a power of 1
We start with a total sum of 0:
161 = 16
The highest coefficient less than 15 we can multiply this by to stay under 217 is 13
Multiplying this coefficient by our original value, we get: 13 * 16 = 208
Add our new value to our running total, we get:
0 + 208 = 208
Hexadecimal (10 - 15) are represented by an (A-F) where 13 translates to the letter D
This is <= 217, so we assign our outside coefficient of D for this digit.
Our new sum becomes 208
Our hexadecimal notation is now equal to D
160 = 1
The highest coefficient less than 15 we can multiply this by to stay under 217 is 9
Multiplying this coefficient by our original value, we get: 9 * 1 = 9
Add our new value to our running total, we get:
208 + 9 = 217
This = 217, so we assign our outside coefficient of 9 for this digit.
Our new sum becomes 217
Our hexadecimal notation is now equal to D9
