Answer
↓Steps Explained:↓
Convert 240 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 >= 240
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 240
Since 256 is greater than 240, 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 240 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 <= 240, 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 240 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 <= 240, 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 240 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 <= 240, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 224
Our binary notation is now equal to 111
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 240 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
224 + 16 = 240
This = 240, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 240
Our binary notation is now equal to 1111
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 240 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
240 + 8 = 248
This is > 240, so we assign a 0 for this digit.
Our total sum remains the same at 240
Our binary notation is now equal to 11110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 240 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
240 + 4 = 244
This is > 240, so we assign a 0 for this digit.
Our total sum remains the same at 240
Our binary notation is now equal to 111100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 240 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
240 + 2 = 242
This is > 240, so we assign a 0 for this digit.
Our total sum remains the same at 240
Our binary notation is now equal to 1111000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 240 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
240 + 1 = 241
This is > 240, so we assign a 0 for this digit.
Our total sum remains the same at 240
Our binary notation is now equal to 11110000
Final Answer
We are done. 240 converted from decimal to binary notation equals 111100002.Take the Quiz
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