Answer
↓Steps Explained:↓
Convert 177 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 >= 177
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 177
Since 256 is greater than 177, 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 177 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 <= 177, 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 177 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 > 177, 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 177 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 <= 177, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 160
Our binary notation is now equal to 101
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 177 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
160 + 16 = 176
This is <= 177, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 176
Our binary notation is now equal to 1011
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 177 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
176 + 8 = 184
This is > 177, so we assign a 0 for this digit.
Our total sum remains the same at 176
Our binary notation is now equal to 10110
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 177 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
176 + 4 = 180
This is > 177, so we assign a 0 for this digit.
Our total sum remains the same at 176
Our binary notation is now equal to 101100
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 177 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
176 + 2 = 178
This is > 177, so we assign a 0 for this digit.
Our total sum remains the same at 176
Our binary notation is now equal to 1011000
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 177 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
176 + 1 = 177
This = 177, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 177
Our binary notation is now equal to 10110001
Final Answer
We are done. 177 converted from decimal to binary notation equals 101100012.Take the Quiz
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