Answer
↓Steps Explained:↓
Convert 115 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 >= 115
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 115
Since 128 is greater than 115, 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 115 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 <= 115, 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 115 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 <= 115, 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 115 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 <= 115, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 112
Our binary notation is now equal to 111
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 115 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
112 + 8 = 120
This is > 115, so we assign a 0 for this digit.
Our total sum remains the same at 112
Our binary notation is now equal to 1110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 115 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
112 + 4 = 116
This is > 115, so we assign a 0 for this digit.
Our total sum remains the same at 112
Our binary notation is now equal to 11100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 115 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
112 + 2 = 114
This is <= 115, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 114
Our binary notation is now equal to 111001
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 115 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
114 + 1 = 115
This = 115, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 115
Our binary notation is now equal to 1110011
Final Answer
We are done. 115 converted from decimal to binary notation equals 11100112.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion