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Convert 21 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 >= 21

16⁰ = 1

16¹ = 16

16² = 256 <--- Stop: This is greater than 21

Since 256 is greater than 21, 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 21 is 1

Multiplying this coefficient by our original value, we get: 1 * 16 = 16

Add our new value to our running total, we get:
0 + 16 = 16

This is <= 21, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 16

Our hexadecimal notation is now equal to 1

16⁰ = 1

The highest coefficient less than 15 we can multiply this by to stay under 21 is 5

Multiplying this coefficient by our original value, we get: 5 * 1 = 5

Add our new value to our running total, we get:
16 + 5 = 21

This = 21, so we assign our outside coefficient of 5 for this digit.

Our new sum becomes 21

Our hexadecimal notation is now equal to 15

Final Answer