Answer
↓Steps Explained:↓
Convert 269 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 >= 269
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 269
Since 512 is greater than 269, 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 269 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 <= 269, 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 269 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 > 269, 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 269 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 > 269, 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 269 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 > 269, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 1000
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 269 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 > 269, so we assign a 0 for this digit.
Our total sum remains the same at 256
Our binary notation is now equal to 10000
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 269 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
256 + 8 = 264
This is <= 269, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 264
Our binary notation is now equal to 100001
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 269 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
264 + 4 = 268
This is <= 269, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 268
Our binary notation is now equal to 1000011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 269 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
268 + 2 = 270
This is > 269, so we assign a 0 for this digit.
Our total sum remains the same at 268
Our binary notation is now equal to 10000110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 269 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
268 + 1 = 269
This = 269, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 269
Our binary notation is now equal to 100001101
Final Answer
We are done. 269 converted from decimal to binary notation equals 1000011012.Take the Quiz
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