Answer
↓Steps Explained:↓
Convert 291 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 >= 291
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 291
Since 512 is greater than 291, 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 291 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 <= 291, 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 291 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 > 291, 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 291 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 > 291, 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 291 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 <= 291, 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 291 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 > 291, 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 291 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 > 291, 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 291 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 > 291, 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 291 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 <= 291, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 290
Our binary notation is now equal to 10010001
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 291 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
290 + 1 = 291
This = 291, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 291
Our binary notation is now equal to 100100011
Final Answer
We are done. 291 converted from decimal to binary notation equals 1001000112.Take the Quiz
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