Answer
↓Steps Explained:↓
Convert 168 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 >= 168
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
28 = 256 <--- Stop: This is greater than 168
Since 256 is greater than 168, 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 168 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 <= 168, 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 168 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 > 168, 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 168 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 <= 168, 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 168 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 > 168, so we assign a 0 for this digit.
Our total sum remains the same at 160
Our binary notation is now equal to 1010
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 168 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
160 + 8 = 168
This = 168, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 168
Our binary notation is now equal to 10101
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 168 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
168 + 4 = 172
This is > 168, so we assign a 0 for this digit.
Our total sum remains the same at 168
Our binary notation is now equal to 101010
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 168 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
168 + 2 = 170
This is > 168, so we assign a 0 for this digit.
Our total sum remains the same at 168
Our binary notation is now equal to 1010100
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 168 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
168 + 1 = 169
This is > 168, so we assign a 0 for this digit.
Our total sum remains the same at 168
Our binary notation is now equal to 10101000
Final Answer
We are done. 168 converted from decimal to binary notation equals 101010002.Take the Quiz
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