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Convert 288 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 >= 288

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 288

Since 512 is greater than 288, 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 288 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 <= 288, 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 288 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 > 288, 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 288 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 > 288, 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 288 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 = 288, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 288

Our binary notation is now equal to 1001


24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 288 is 1

Multiplying this coefficient by our original value, we get: 1 * 16 = 16

Add our new value to our running total, we get:
288 + 16 = 304

This is > 288, so we assign a 0 for this digit.

Our total sum remains the same at 288

Our binary notation is now equal to 10010


23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 288 is 1

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

Add our new value to our running total, we get:
288 + 8 = 296

This is > 288, so we assign a 0 for this digit.

Our total sum remains the same at 288

Our binary notation is now equal to 100100


22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 288 is 1

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

Add our new value to our running total, we get:
288 + 4 = 292

This is > 288, so we assign a 0 for this digit.

Our total sum remains the same at 288

Our binary notation is now equal to 1001000


21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 288 is 1

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

Add our new value to our running total, we get:
288 + 2 = 290

This is > 288, so we assign a 0 for this digit.

Our total sum remains the same at 288

Our binary notation is now equal to 10010000


20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 288 is 1

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

Add our new value to our running total, we get:
288 + 1 = 289

This is > 288, so we assign a 0 for this digit.

Our total sum remains the same at 288

Our binary notation is now equal to 100100000


Final Answer


We are done. 288 converted from decimal to binary notation equals 1001000002.