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Convert 105 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 >= 105

16⁰ = 1

16¹ = 16

16² = 256 <--- Stop: This is greater than 105

Since 256 is greater than 105, 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 105 is 6

Multiplying this coefficient by our original value, we get: 6 * 16 = 96

Add our new value to our running total, we get:
0 + 96 = 96

This is <= 105, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 96

Our hexadecimal notation is now equal to 6

16⁰ = 1

The highest coefficient less than 15 we can multiply this by to stay under 105 is 9

Multiplying this coefficient by our original value, we get: 9 * 1 = 9

Add our new value to our running total, we get:
96 + 9 = 105

This = 105, so we assign our outside coefficient of 9 for this digit.

Our new sum becomes 105

Our hexadecimal notation is now equal to 69

Final Answer

Tags:

• base change conversions
• base
• binary
• conversion
• hexadecimal
• octal