Answer
Steps Explained:
Convert 21 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 >= 21
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32 <--- Stop: This is greater than 21
Since 32 is greater than 21, 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 21 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 <= 21, 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 21 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 > 21, 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 21 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 <= 21, 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 21 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 > 21, so we assign a 0 for this digit.
Our total sum remains the same at 20
Our binary notation is now equal to 1010
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 21 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
20 + 1 = 21
This = 21, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 21
Our binary notation is now equal to 10101
Final Answer
We are done. 21 converted from decimal to binary notation equals 101012.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion