Answer
↓Steps Explained:↓
Convert 14 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 >= 14
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16 <--- Stop: This is greater than 14
Since 16 is greater than 14, 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 14 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 <= 14, 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 14 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 <= 14, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 12
Our binary notation is now equal to 11
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 14 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
12 + 2 = 14
This = 14, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 14
Our binary notation is now equal to 111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 14 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
14 + 1 = 15
This is > 14, so we assign a 0 for this digit.
Our total sum remains the same at 14
Our binary notation is now equal to 1110
Final Answer
We are done. 14 converted from decimal to binary notation equals 11102.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion