<-- Enter Number or Notation that will be converted
Conversion TypeBinaryOctalHexadecimalBase
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Convert 255 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 >= 255

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

28 = 256 <--- Stop: This is greater than 255

Since 256 is greater than 255, 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 255 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 <= 255, 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 255 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 <= 255, 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 255 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 <= 255, 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 255 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 <= 255, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 240

Our binary notation is now equal to 1111

##### 23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 255 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
240 + 8 = 248

This is <= 255, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 248

Our binary notation is now equal to 11111

##### 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 255 is 1

Multiplying this coefficient by our original value, we get: 1 * 4 = 4

Add our new value to our running total, we get:
248 + 4 = 252

This is <= 255, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 252

Our binary notation is now equal to 111111

##### 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 255 is 1

Multiplying this coefficient by our original value, we get: 1 * 2 = 2

Add our new value to our running total, we get:
252 + 2 = 254

This is <= 255, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 254

Our binary notation is now equal to 1111111

##### 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 255 is 1

Multiplying this coefficient by our original value, we get: 1 * 1 = 1

Add our new value to our running total, we get:
254 + 1 = 255

This = 255, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 255

Our binary notation is now equal to 11111111

##### Final Answer

We are done. 255 converted from decimal to binary notation equals 111111112.

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