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Convert 183 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 >= 183

20 = 1

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

27 = 128

28 = 256 <--- Stop: This is greater than 183

Since 256 is greater than 183, 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 183 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 <= 183, 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 183 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 > 183, so we assign a 0 for this digit.

Our total sum remains the same at 128

Our binary notation is now equal to 10

##### 25 = 32

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
128 + 32 = 160

This is <= 183, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 160

Our binary notation is now equal to 101

##### 24 = 16

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
160 + 16 = 176

This is <= 183, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 176

Our binary notation is now equal to 1011

##### 23 = 8

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
176 + 8 = 184

This is > 183, so we assign a 0 for this digit.

Our total sum remains the same at 176

Our binary notation is now equal to 10110

##### 22 = 4

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
176 + 4 = 180

This is <= 183, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 180

Our binary notation is now equal to 101101

##### 21 = 2

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
180 + 2 = 182

This is <= 183, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 182

Our binary notation is now equal to 1011011

##### 20 = 1

The highest coefficient less than 1 we can multiply this by to stay under 183 is 1

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

Add our new value to our running total, we get:
182 + 1 = 183

This = 183, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 183

Our binary notation is now equal to 10110111

##### Final Answer

We are done. 183 converted from decimal to binary notation equals 101101112.

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