Convert 71 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 >= 71
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 71
Since 128 is greater than 71, we use 1 power less as our starting point which equals 6
Build binary notation
Work backwards from a power of 6
We start with a total sum of 0:
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 71, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our binary notation is now equal to 1
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
64 + 32 = 96
This is > 71, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This is > 71, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
64 + 8 = 72
This is > 71, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 1000
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
64 + 4 = 68
This is <= 71, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 68
Our binary notation is now equal to 10001
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
68 + 2 = 70
This is <= 71, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 70
Our binary notation is now equal to 100011
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 71 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
70 + 1 = 71
This = 71, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 71
Our binary notation is now equal to 1000111
