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Convert 65 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 >= 65

16⁰ = 1

16¹ = 16

16² = 256 <--- Stop: This is greater than 65

Since 256 is greater than 65, 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 65 is 4

Multiplying this coefficient by our original value, we get: 4 * 16 = 64

Add our new value to our running total, we get:
0 + 64 = 64

This is <= 65, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 64

Our hexadecimal notation is now equal to 4

16⁰ = 1

The highest coefficient less than 15 we can multiply this by to stay under 65 is 1

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

Add our new value to our running total, we get:
64 + 1 = 65

This = 65, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 65

Our hexadecimal notation is now equal to 41

Final Answer