Answer
↓Steps Explained:↓
Convert 127 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 >= 127
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 127
Since 512 is greater than 127, 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 127 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 <= 127, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 64
Our octal notation is now equal to 1
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 127 is 7
Multiplying this coefficient by our original value, we get: 7 * 8 = 56
Add our new value to our running total, we get:
64 + 56 = 120
This is <= 127, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 120
Our octal notation is now equal to 17
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 127 is 7
Multiplying this coefficient by our original value, we get: 7 * 1 = 7
Add our new value to our running total, we get:
120 + 7 = 127
This = 127, so we assign our outside coefficient of 7 for this digit.
Our new sum becomes 127
Our octal notation is now equal to 177
Final Answer
We are done. 127 converted from decimal to octal notation equals 1778.Take the Quiz Switch to Chat Mode
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