Convert 9 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 >= 9
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16 <--- Stop: This is greater than 9
Since 16 is greater than 9, we use 1 power less as our starting point which equals 3
Build binary notation
Work backwards from a power of 3
We start with a total sum of 0:
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 9 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
0 + 8 = 8
This is <= 9, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8
Our binary notation is now equal to 1
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 9 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
8 + 4 = 12
This is > 9, so we assign a 0 for this digit.
Our total sum remains the same at 8
Our binary notation is now equal to 10
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 9 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
8 + 2 = 10
This is > 9, so we assign a 0 for this digit.
Our total sum remains the same at 8
Our binary notation is now equal to 100
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 9 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
8 + 1 = 9
This = 9, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 9
Our binary notation is now equal to 1001
