Answer
↓Steps Explained:↓
Convert 11 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 >= 11
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16 <--- Stop: This is greater than 11
Since 16 is greater than 11, 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 11 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 <= 11, 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 11 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 > 11, 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 11 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 <= 11, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 10
Our binary notation is now equal to 101
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 11 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
10 + 1 = 11
This = 11, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 11
Our binary notation is now equal to 1011
Final Answer
We are done. 11 converted from decimal to binary notation equals 10112.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion