Convert 289 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 >= 289
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256
29 = 512 <--- Stop: This is greater than 289
Since 512 is greater than 289, we use 1 power less as our starting point which equals 8
Build binary notation
Work backwards from a power of 8
We start with a total sum of 0:
28 = 256
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 256 = 256
Add our new value to our running total, we get:
0 + 256 = 256
This is <= 289, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 256
Our binary notation is now equal to 1
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
256 + 128 = 384
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 10
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
256 + 64 = 320
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 100
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
256 + 32 = 288
This is <= 289, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 288
Our binary notation is now equal to 1001
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
288 + 16 = 304
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 288
Our binary notation is now equal to 10010
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
288 + 8 = 296
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 288
Our binary notation is now equal to 100100
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
288 + 4 = 292
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 288
Our binary notation is now equal to 1001000
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
288 + 2 = 290
This is > 289, so we assign a 0 for this digit.
Our total sum remains the same at 288
Our binary notation is now equal to 10010000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 289 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
288 + 1 = 289
This = 289, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 289
Our binary notation is now equal to 100100001
