Answer
↓Steps Explained:↓
Convert 127 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 >= 127
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 127
Since 128 is greater than 127, 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 127 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 <= 127, 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 127 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 <= 127, 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 127 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 <= 127, 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 127 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 <= 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 120
Our binary notation is now equal to 1111
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 127 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
120 + 4 = 124
This is <= 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 124
Our binary notation is now equal to 11111
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 127 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
124 + 2 = 126
This is <= 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 126
Our binary notation is now equal to 111111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 127 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
126 + 1 = 127
This = 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 127
Our binary notation is now equal to 1111111
Final Answer
We are done. 127 converted from decimal to binary notation equals 11111112.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion