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Convert 45 from decimal to binary (base 2) notation:

Start by raising our base of 2 to a power starting at 0 and increasing by 1 until it is >= 45
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64 <--- Stop: This is greater than 45

Since 64 is greater than 45, we use 1 power less as our starting point which equals 5.

Now start building our binary notation working backwards from a power of 5.
We start with a total sum of 0:

25 = 32.
The highest coefficient less than 1 we can multiply this by to stay under 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 32 = 32.
Adding our new value to our running total, we get: 0 + 32 = 32.

This is <= 45, 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 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 16 = 16.
Adding our new value to our running total, we get: 32 + 16 = 48.

This is > 45, 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 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 8 = 8.
Adding our new value to our running total, we get: 32 + 8 = 40.

This is <= 45, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 40.
Our binary notation is now equal to 101

22 = 4.
The highest coefficient less than 1 we can multiply this by to stay under 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 4 = 4.
Adding our new value to our running total, we get: 40 + 4 = 44.

This is <= 45, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 44.
Our binary notation is now equal to 1011

21 = 2.
The highest coefficient less than 1 we can multiply this by to stay under 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 2 = 2.
Adding our new value to our running total, we get: 44 + 2 = 46.

This is > 45, so we assign a 0 for this digit.
Our total sum remains the same at 44.
Our binary notation is now equal to 10110

20 = 1.
The highest coefficient less than 1 we can multiply this by to stay under 45 is 1.
Multiplying this coefficient by our original value, we get: 1 * 1 = 1.
Adding our new value to our running total, we get: 44 + 1 = 45.

This = 45, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 45.
Our binary notation is now equal to 101101

We are done. 45 converted from decimal to binary notation equals 1011012.