Answer
↓Steps Explained:↓
Convert 108 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 >= 108
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 108
Since 128 is greater than 108, 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 108 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 <= 108, 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 108 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 <= 108, 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 108 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 > 108, 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 108 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 <= 108, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 104
Our binary notation is now equal to 1101
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 108 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
104 + 4 = 108
This = 108, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 108
Our binary notation is now equal to 11011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 108 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
108 + 2 = 110
This is > 108, so we assign a 0 for this digit.
Our total sum remains the same at 108
Our binary notation is now equal to 110110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 108 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
108 + 1 = 109
This is > 108, so we assign a 0 for this digit.
Our total sum remains the same at 108
Our binary notation is now equal to 1101100
Final Answer
We are done. 108 converted from decimal to binary notation equals 11011002.Take the Quiz Switch to Chat Mode
Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion