Answer
↓Steps Explained:↓
Convert 91 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 >= 91
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 91
Since 128 is greater than 91, 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 91 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 <= 91, 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 91 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 > 91, 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 91 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 <= 91, 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 91 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 <= 91, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 88
Our binary notation is now equal to 1011
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 91 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
88 + 4 = 92
This is > 91, so we assign a 0 for this digit.
Our total sum remains the same at 88
Our binary notation is now equal to 10110
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 91 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
88 + 2 = 90
This is <= 91, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 90
Our binary notation is now equal to 101101
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 91 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
90 + 1 = 91
This = 91, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 91
Our binary notation is now equal to 1011011
Final Answer
We are done. 91 converted from decimal to binary notation equals 10110112.Take the Quiz
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