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Convert 8633 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 >= 8633
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512
210 = 1024
211 = 2048
212 = 4096
213 = 8192
214 = 16384 <--- Stop: This is greater than 8633

Since 16384 is greater than 8633, we use 1 power less as our starting point which equals 13.

Now start building our binary notation working backwards from a power of 13.
We start with a total sum of 0:

213 = 8192.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 8192 = 8192.
Adding our new value to our running total, we get: 0 + 8192 = 8192.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8192.
Our binary notation is now equal to 1

212 = 4096.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 4096 = 4096.
Adding our new value to our running total, we get: 8192 + 4096 = 12288.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8192.
Our binary notation is now equal to 10

211 = 2048.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 2048 = 2048.
Adding our new value to our running total, we get: 8192 + 2048 = 10240.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8192.
Our binary notation is now equal to 100

210 = 1024.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 1024 = 1024.
Adding our new value to our running total, we get: 8192 + 1024 = 9216.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8192.
Our binary notation is now equal to 1000

29 = 512.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 512 = 512.
Adding our new value to our running total, we get: 8192 + 512 = 8704.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8192.
Our binary notation is now equal to 10000

28 = 256.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 256 = 256.
Adding our new value to our running total, we get: 8192 + 256 = 8448.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8448.
Our binary notation is now equal to 100001

27 = 128.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 128 = 128.
Adding our new value to our running total, we get: 8448 + 128 = 8576.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8576.
Our binary notation is now equal to 1000011

26 = 64.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 64 = 64.
Adding our new value to our running total, we get: 8576 + 64 = 8640.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8576.
Our binary notation is now equal to 10000110

25 = 32.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 32 = 32.
Adding our new value to our running total, we get: 8576 + 32 = 8608.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8608.
Our binary notation is now equal to 100001101

24 = 16.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 16 = 16.
Adding our new value to our running total, we get: 8608 + 16 = 8624.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8624.
Our binary notation is now equal to 1000011011

23 = 8.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 8 = 8.
Adding our new value to our running total, we get: 8624 + 8 = 8632.

This is <= 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8632.
Our binary notation is now equal to 10000110111

22 = 4.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 4 = 4.
Adding our new value to our running total, we get: 8632 + 4 = 8636.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8632.
Our binary notation is now equal to

21 = 2.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 2 = 2.
Adding our new value to our running total, we get: 8632 + 2 = 8634.

This is > 8633, so we assign a 0 for this digit.
Our total sum remains the same at 8632.
Our binary notation is now equal to 0

20 = 1.
The highest coefficient less than 1 we can multiply this by to stay under 8633 is 1.
Multiplying this coefficient by our original value, we get: 1 * 1 = 1.
Adding our new value to our running total, we get: 8632 + 1 = 8633.

This = 8633, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 8633.
Our binary notation is now equal to

We are done. 8633 converted from decimal to binary notation equals 2.