Answer
↓Steps Explained:↓
Convert 272 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 >= 272
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512 <--- Stop: This is greater than 272
Since 512 is greater than 272, we use 1 power less as our starting point which equals 8
Build binary notation
Work backwards from a power of 8
We start with a total sum of 0:
28 = 256
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 256 = 256
Add our new value to our running total, we get:
0 + 256 = 256
This is <= 272, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 256
Our binary notation is now equal to 1
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
256 + 128 = 384
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 10
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
256 + 64 = 320
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 100
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
256 + 32 = 288
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 1000
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
256 + 16 = 272
This = 272, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 272
Our binary notation is now equal to 10001
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
272 + 8 = 280
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 100010
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
272 + 4 = 276
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 1000100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
272 + 2 = 274
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 10001000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 272 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
272 + 1 = 273
This is > 272, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 100010000
Final Answer
We are done. 272 converted from decimal to binary notation equals 1000100002.Take the Quiz
Related Calculators: Bit Shifting | RGB and HEX conversions | Stoichiometry Conversion