Answer
↓Steps Explained:↓
Convert 99 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 >= 99
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 99
Since 128 is greater than 99, 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 99 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 <= 99, 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 99 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 <= 99, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 96
Our binary notation is now equal to 11
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 99 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
96 + 16 = 112
This is > 99, so we assign a 0 for this digit.
Our total sum remains the same at 96
Our binary notation is now equal to 110
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 99 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
96 + 8 = 104
This is > 99, so we assign a 0 for this digit.
Our total sum remains the same at 96
Our binary notation is now equal to 1100
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 99 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
96 + 4 = 100
This is > 99, so we assign a 0 for this digit.
Our total sum remains the same at 96
Our binary notation is now equal to 11000
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 99 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
96 + 2 = 98
This is <= 99, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 98
Our binary notation is now equal to 110001
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 99 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
98 + 1 = 99
This = 99, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 99
Our binary notation is now equal to 1100011
Final Answer
We are done. 99 converted from decimal to binary notation equals 11000112.Take the Quiz
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