 # Base Change Conversions Calculator

<-- Enter Number or Notation that will be converted
Convert Decimal to:
Base:
Convert to Decimal from:

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

## Power Test

Raise our base of 2 to a power
Start at 0 and increasing by 1 until it is >= 2
20 = 1
21 = 2 <--- Stop: This is equal to 2

Since 2 is equal to 2, we use our current power as our starting point which equals 1

## Build binary notation

Work backwards from a power of 1

## 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 2 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
0 + 2 = 2

This = 2, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 2
Our binary notation is now equal to 1

## 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 2 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
2 + 1 = 3

This is > 2, so we assign a 0 for this digit.
Our total sum remains the same at 2
Our binary notation is now equal to 10  