Answer
↓Steps Explained:↓
Convert 78 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 >= 78
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128 <--- Stop: This is greater than 78
Since 128 is greater than 78, 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 78 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 <= 78, 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 78 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 > 78, 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 78 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 > 78, 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 78 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 <= 78, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 72
Our binary notation is now equal to 1001
22 = 4
The highest coefficient less than 1 we can multiply this by to stay under 78 is 1
Multiplying this coefficient by our original value, we get: 1 * 4 = 4
Add our new value to our running total, we get:
72 + 4 = 76
This is <= 78, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 76
Our binary notation is now equal to 10011
21 = 2
The highest coefficient less than 1 we can multiply this by to stay under 78 is 1
Multiplying this coefficient by our original value, we get: 1 * 2 = 2
Add our new value to our running total, we get:
76 + 2 = 78
This = 78, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 78
Our binary notation is now equal to 100111
20 = 1
The highest coefficient less than 1 we can multiply this by to stay under 78 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
78 + 1 = 79
This is > 78, so we assign a 0 for this digit.
Our total sum remains the same at 78
Our binary notation is now equal to 1001110
Final Answer
We are done. 78 converted from decimal to binary notation equals 10011102.Take the Quiz Switch to Chat Mode
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