Answer
↓Steps Explained:↓
Convert 204 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 >= 204
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 204
Since 256 is greater than 204, we use 1 power less as our starting point which equals 7
Build binary notation
Work backwards from a power of 7
We start with a total sum of 0:
27 = 128
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 128 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This is <= 204, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 128
Our binary notation is now equal to 1
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
128 + 64 = 192
This is <= 204, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 192
Our binary notation is now equal to 11
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
192 + 32 = 224
This is > 204, so we assign a 0 for this digit.
Our total sum remains the same at 192
Our binary notation is now equal to 110
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
192 + 16 = 208
This is > 204, so we assign a 0 for this digit.
Our total sum remains the same at 192
Our binary notation is now equal to 1100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
192 + 8 = 200
This is <= 204, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 200
Our binary notation is now equal to 11001
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
200 + 4 = 204
This = 204, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 204
Our binary notation is now equal to 110011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
204 + 2 = 206
This is > 204, so we assign a 0 for this digit.
Our total sum remains the same at 204
Our binary notation is now equal to 1100110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 204 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
204 + 1 = 205
This is > 204, so we assign a 0 for this digit.
Our total sum remains the same at 204
Our binary notation is now equal to 11001100
Final Answer
We are done. 204 converted from decimal to binary notation equals 110011002.Take the Quiz Switch to Chat Mode
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