Answer
↓Steps Explained:↓
Convert 237 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 >= 237
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 237
Since 256 is greater than 237, we use 1 power less as our starting point which equals 7
Build binary notation
Work backwards from a power of 7
We start with a total sum of 0:
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 128
Our binary notation is now equal to 1
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
128 + 64 = 192
This is <= 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 192
Our binary notation is now equal to 11
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
192 + 32 = 224
This is <= 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 224
Our binary notation is now equal to 111
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
224 + 16 = 240
This is > 237, so we assign a 0 for this digit.
Our total sum remains the same at 224
Our binary notation is now equal to 1110
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
224 + 8 = 232
This is <= 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 232
Our binary notation is now equal to 11101
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
232 + 4 = 236
This is <= 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 236
Our binary notation is now equal to 111011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
236 + 2 = 238
This is > 237, so we assign a 0 for this digit.
Our total sum remains the same at 236
Our binary notation is now equal to 1110110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 237 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
236 + 1 = 237
This = 237, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 237
Our binary notation is now equal to 11101101
Final Answer
We are done. 237 converted from decimal to binary notation equals 111011012.Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion