Convert 47 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 >= 47
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 47
Since 64 is greater than 47, we use 1 power less as our starting point which equals 5
Build binary notation
Work backwards from a power of 5
We start with a total sum of 0:
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
0 + 32 = 32
This is <= 47, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 32
Our binary notation is now equal to 1
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
32 + 16 = 48
This is > 47, so we assign a 0 for this digit.
Our total sum remains the same at 32
Our binary notation is now equal to 10
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
32 + 8 = 40
This is <= 47, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 40
Our binary notation is now equal to 101
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
40 + 4 = 44
This is <= 47, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 44
Our binary notation is now equal to 1011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
44 + 2 = 46
This is <= 47, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 46
Our binary notation is now equal to 10111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 47 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
46 + 1 = 47
This = 47, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 47
Our binary notation is now equal to 101111
