Answer
↓Steps Explained:↓
Convert 68 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 >= 68
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 68
Since 128 is greater than 68, we use 1 power less as our starting point which equals 6
Build binary notation
Work backwards from a power of 6
We start with a total sum of 0:
26 = 64
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 64 = 64
Add our new value to our running total, we get:
0 + 64 = 64
This is <= 68, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our binary notation is now equal to 1
25 = 32
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 32 = 32
Add our new value to our running total, we get:
64 + 32 = 96
This is > 68, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 10
24 = 16
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 16 = 16
Add our new value to our running total, we get:
64 + 16 = 80
This is > 68, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 100
23 = 8
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
64 + 8 = 72
This is > 68, so we assign a 0 for this digit.
Our total sum remains the same at 64
Our binary notation is now equal to 1000
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
64 + 4 = 68
This = 68, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 68
Our binary notation is now equal to 10001
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
68 + 2 = 70
This is > 68, so we assign a 0 for this digit.
Our total sum remains the same at 68
Our binary notation is now equal to 100010
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 68 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
68 + 1 = 69
This is > 68, so we assign a 0 for this digit.
Our total sum remains the same at 68
Our binary notation is now equal to 1000100
Final Answer
We are done. 68 converted from decimal to binary notation equals 10001002.Take the Quiz Switch to Chat Mode
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