Answer
↓Steps Explained:↓
Convert 128 from decimal to octal
(base 8) notation:
Power Test
Raise our base of 8 to a power
Start at 0 and increasing by 1 until it is >= 128
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 128
Since 512 is greater than 128, we use 1 power less as our starting point which equals 2
Build octal notation
Work backwards from a power of 2
We start with a total sum of 0:
82 = 64
The highest coefficient less than 7 we can multiply this by to stay under 128 is 2
Multiplying this coefficient by our original value, we get: 2 * 64 = 128
Add our new value to our running total, we get:
0 + 128 = 128
This = 128, so we assign our outside coefficient of 2 for this digit.
Our new sum becomes 128
Our octal notation is now equal to 2
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 128 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 > 128, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our octal notation is now equal to 20
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 128 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
128 + 1 = 129
This is > 128, so we assign a 0 for this digit.
Our total sum remains the same at 128
Our octal notation is now equal to 200
Final Answer
We are done. 128 converted from decimal to octal notation equals 2008.Take the Quiz
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