Convert 8633 from decimal to binary
(base 2) notation:
Raise our base of 2 to a power
Start 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
Work backwards from a power of 13
We start with a total sum of 0:
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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
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
Add 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 100001101110
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
Add 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 1000011011100
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
Add 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 10000110111001