Answer
↓Steps Explained:↓
Convert 141 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 >= 141
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 141
Since 256 is greater than 141, 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 141 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 <= 141, 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 141 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 > 141, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 10
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
128 + 32 = 160
This is > 141, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 100
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
128 + 16 = 144
This is > 141, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our binary notation is now equal to 1000
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
128 + 8 = 136
This is <= 141, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 136
Our binary notation is now equal to 10001
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
136 + 4 = 140
This is <= 141, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 140
Our binary notation is now equal to 100011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
140 + 2 = 142
This is > 141, so we assign a 0 for this digit.
Our total sum remains the same at 140
Our binary notation is now equal to 1000110
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 141 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
140 + 1 = 141
This = 141, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 141
Our binary notation is now equal to 10001101
Final Answer
We are done. 141 converted from decimal to binary notation equals 100011012.Take the Quiz
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