Base Change Conversions Calculator

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Convert 212 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 >= 212

16⁰ = 1

16¹ = 16

16² = 256 <--- Stop: This is greater than 212

Since 256 is greater than 212, 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 212 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 <= 212, 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 212 is 4

Multiplying this coefficient by our original value, we get: 4 * 1 = 4

Add our new value to our running total, we get:
208 + 4 = 212

This = 212, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 212

Our hexadecimal notation is now equal to D4

Final Answer

Tags:

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