Convert 274 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 >= 274
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 274
Since 512 is greater than 274, we use 1 power less as our starting point which equals 8
Work backwards from a power of 8
We start with a total sum of 0:
The highest coefficient less than 1 we can multiply this by to stay under 274 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 <= 274, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 256
Our binary notation is now equal to 1
The highest coefficient less than 1 we can multiply this by to stay under 274 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 > 274, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 10
The highest coefficient less than 1 we can multiply this by to stay under 274 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 > 274, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 100
The highest coefficient less than 1 we can multiply this by to stay under 274 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 > 274, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 1000
The highest coefficient less than 1 we can multiply this by to stay under 274 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
256 + 16 = 272
This is <= 274, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 272
Our binary notation is now equal to 10001
The highest coefficient less than 1 we can multiply this by to stay under 274 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
272 + 8 = 280
This is > 274, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 100010
The highest coefficient less than 1 we can multiply this by to stay under 274 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
272 + 4 = 276
This is > 274, so we assign a 0 for this digit.
Our total sum remains the same at 272
Our binary notation is now equal to 1000100
The highest coefficient less than 1 we can multiply this by to stay under 274 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
272 + 2 = 274
This = 274, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 274
Our binary notation is now equal to 10001001
The highest coefficient less than 1 we can multiply this by to stay under 274 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
274 + 1 = 275
This is > 274, so we assign a 0 for this digit.
Our total sum remains the same at 274
Our binary notation is now equal to 100010010