Convert 23 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 >= 23
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 23
Since 32 is greater than 23, we use 1 power less as our starting point which equals 4
Build binary notation
Work 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 23 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
0 + 16 = 16
This is <= 23, 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 23 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
16 + 8 = 24
This is > 23, 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 23 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
16 + 4 = 20
This is <= 23, 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 23 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
20 + 2 = 22
This is <= 23, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 22
Our binary notation is now equal to 1011
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 23 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
22 + 1 = 23
This = 23, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 23
Our binary notation is now equal to 10111
