Convert 3 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 >= 3
20 = 1
21 = 2
22 = 4 <--- Stop: This is greater than 3
Since 4 is greater than 3, we use 1 power less as our starting point which equals 1
Build binary notation
Work backwards from a power of 1
We start with a total sum of 0:
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 3 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 is <= 3, 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 3 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 = 3, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 3
Our binary notation is now equal to 11
