Base Change Conversions Calculator

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Convert 27 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 >= 27
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 27

Since 32 is greater than 27, 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.
We start with a total sum of 0:

24 = 16.
The highest coefficient less than 1 we can multiply this by to stay under 27 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 <= 27, 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 27 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 <= 27, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 24.
Our binary notation is now equal to 11

22 = 4.
The highest coefficient less than 1 we can multiply this by to stay under 27 is 1.
Multiplying this coefficient by our original value, we get: 1 * 4 = 4.
Adding our new value to our running total, we get: 24 + 4 = 28.

This is > 27, so we assign a 0 for this digit.
Our total sum remains the same at 24.
Our binary notation is now equal to 110

21 = 2.
The highest coefficient less than 1 we can multiply this by to stay under 27 is 1.
Multiplying this coefficient by our original value, we get: 1 * 2 = 2.
Adding our new value to our running total, we get: 24 + 2 = 26.

This is <= 27, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 26.
Our binary notation is now equal to 1101

20 = 1.
The highest coefficient less than 1 we can multiply this by to stay under 27 is 1.
Multiplying this coefficient by our original value, we get: 1 * 1 = 1.
Adding our new value to our running total, we get: 26 + 1 = 27.

This = 27, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 27.
Our binary notation is now equal to 11011

We are done. 27 converted from decimal to binary notation equals 110112.