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Answer
We are done. 240 converted from decimal to binary notation equals 111100002.

↓Steps Explained:↓



Convert 240 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 >= 240

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

28 = 256 <--- Stop: This is greater than 240

Since 256 is greater than 240, 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 240 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 <= 240, 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 240 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 <= 240, 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 240 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 <= 240, 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 240 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 = 240, 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 240 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 > 240, so we assign a 0 for this digit.

Our total sum remains the same at 240

Our binary notation is now equal to 11110


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 240 is 1

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

Add our new value to our running total, we get:
240 + 4 = 244

This is > 240, so we assign a 0 for this digit.

Our total sum remains the same at 240

Our binary notation is now equal to 111100


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 240 is 1

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

Add our new value to our running total, we get:
240 + 2 = 242

This is > 240, so we assign a 0 for this digit.

Our total sum remains the same at 240

Our binary notation is now equal to 1111000


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 240 is 1

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

Add our new value to our running total, we get:
240 + 1 = 241

This is > 240, so we assign a 0 for this digit.

Our total sum remains the same at 240

Our binary notation is now equal to 11110000


Final Answer

We are done. 240 converted from decimal to binary notation equals 111100002.

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