 <-- Enter Number or Notation that will be converted
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Convert 37 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 >= 37

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64 <--- Stop: This is greater than 37

Since 64 is greater than 37, we use 1 power less as our starting point which equals 5

##### Build binary notation

Work backwards from a power of 5

##### 25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

Multiplying this coefficient by our original value, we get: 1 * 32 = 32

Add our new value to our running total, we get:
0 + 32 = 32

This is <= 37, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 32

Our binary notation is now equal to 1

##### 24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

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

Add our new value to our running total, we get:
32 + 16 = 48

This is > 37, so we assign a 0 for this digit.

Our total sum remains the same at 32

Our binary notation is now equal to 10

##### 23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

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

Add our new value to our running total, we get:
32 + 8 = 40

This is > 37, so we assign a 0 for this digit.

Our total sum remains the same at 32

Our binary notation is now equal to 100

##### 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

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

Add our new value to our running total, we get:
32 + 4 = 36

This is <= 37, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 36

Our binary notation is now equal to 1001

##### 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

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

Add our new value to our running total, we get:
36 + 2 = 38

This is > 37, so we assign a 0 for this digit.

Our total sum remains the same at 36

Our binary notation is now equal to 10010

##### 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 37 is 1

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

Add our new value to our running total, we get:
36 + 1 = 37

This = 37, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 37

Our binary notation is now equal to 100101