Answer
↓Steps Explained:↓
Convert 81 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 >= 81
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 81
Since 128 is greater than 81, 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 81 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 <= 81, 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 81 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 > 81, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 81 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This is <= 81, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 80
Our binary notation is now equal to 101
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 81 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
80 + 8 = 88
This is > 81, so we assign a 0 for this digit.
Our total sum remains the same at 80
Our binary notation is now equal to 1010
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 81 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
80 + 4 = 84
This is > 81, so we assign a 0 for this digit.
Our total sum remains the same at 80
Our binary notation is now equal to 10100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 81 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
80 + 2 = 82
This is > 81, so we assign a 0 for this digit.
Our total sum remains the same at 80
Our binary notation is now equal to 101000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 81 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
80 + 1 = 81
This = 81, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 81
Our binary notation is now equal to 1010001
Final Answer
We are done. 81 converted from decimal to binary notation equals 10100012.Take the Quiz
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