Answer
↓Steps Explained:↓
Convert 193 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 >= 193
80 = 1
81 = 8
82 = 64
83 = 512 <--- Stop: This is greater than 193
Since 512 is greater than 193, 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 193 is 3
Multiplying this coefficient by our original value, we get: 3 * 64 = 192
Add our new value to our running total, we get:
0 + 192 = 192
This is <= 193, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 192
Our octal notation is now equal to 3
81 = 8
The highest coefficient less than 7 we can multiply this by to stay under 193 is 1
Multiplying this coefficient by our original value, we get: 1 * 8 = 8
Add our new value to our running total, we get:
192 + 8 = 200
This is > 193, so we assign a 0 for this digit.
Our total sum remains the same at 192
Our octal notation is now equal to 30
80 = 1
The highest coefficient less than 7 we can multiply this by to stay under 193 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
192 + 1 = 193
This = 193, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 193
Our octal notation is now equal to 301
Final Answer
We are done. 193 converted from decimal to octal notation equals 3018.Take the Quiz Switch to Chat Mode
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