Convert 57 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 >= 57
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 57
Since 64 is greater than 57, 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 57 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 <= 57, 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 57 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 <= 57, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 48
Our binary notation is now equal to 11
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 57 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
48 + 8 = 56
This is <= 57, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 56
Our binary notation is now equal to 111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 57 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
56 + 4 = 60
This is > 57, so we assign a 0 for this digit.
Our total sum remains the same at 56
Our binary notation is now equal to 1110
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 57 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
56 + 2 = 58
This is > 57, so we assign a 0 for this digit.
Our total sum remains the same at 56
Our binary notation is now equal to 11100
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 57 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
56 + 1 = 57
This = 57, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 57
Our binary notation is now equal to 111001
