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

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

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:

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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 * 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

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

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 * 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