Answer
↓Steps Explained:↓
Convert 15 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 >= 15
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16 <--- Stop: This is greater than 15
Since 16 is greater than 15, 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 15 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 <= 15, 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 15 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 <= 15, 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 15 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 is <= 15, 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 15 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 = 15, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 15
Our binary notation is now equal to 1111
Final Answer
We are done. 15 converted from decimal to binary notation equals 11112.Take the Quiz
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