# Base Change Conversions Calculator

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Convert 20 from decimal to binary (base 2) notation:

Start by raising our base of 2 to a power starting at 0 and increasing by 1 until it is >= 20
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 20

Since 32 is greater than 20, we use 1 power less as our starting point which equals 4.

Now start building our binary notation working backwards from a power of 4.

24 = 16.
The highest coefficient less than 1 we can multiply this by to stay under 20 is 1.
Multiplying this coefficient by our original value, we get: 1 * 16 = 16.
Adding our new value to our running total, we get: 0 + 16 = 16.

This is <= 20, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 16.
Our binary notation is now equal to 1

23 = 8.
The highest coefficient less than 1 we can multiply this by to stay under 20 is 1.
Multiplying this coefficient by our original value, we get: 1 * 8 = 8.
Adding our new value to our running total, we get: 16 + 8 = 24.

This is > 20, so we assign a 0 for this digit.
Our total sum remains the same at 16.
Our binary notation is now equal to 10

22 = 4.
The highest coefficient less than 1 we can multiply this by to stay under 20 is 1.
Multiplying this coefficient by our original value, we get: 1 * 4 = 4.
Adding our new value to our running total, we get: 16 + 4 = 20.

This = 20, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 20.
Our binary notation is now equal to 101

21 = 2.
The highest coefficient less than 1 we can multiply this by to stay under 20 is 1.
Multiplying this coefficient by our original value, we get: 1 * 2 = 2.
Adding our new value to our running total, we get: 20 + 2 = 22.

This is > 20, so we assign a 0 for this digit.
Our total sum remains the same at 20.
Our binary notation is now equal to 1010

20 = 1.
The highest coefficient less than 1 we can multiply this by to stay under 20 is 1.
Multiplying this coefficient by our original value, we get: 1 * 1 = 1.
Adding our new value to our running total, we get: 20 + 1 = 21.

This is > 20, so we assign a 0 for this digit.
Our total sum remains the same at 20.
Our binary notation is now equal to 10100

We are done. 20 converted from decimal to binary notation equals 101002.