Base Change Conversions Calculator

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Convert 107 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 >= 107

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 107

Since 512 is greater than 107, 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 107 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 <= 107, 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 107 is 5

Multiplying this coefficient by our original value, we get: 5 * 8 = 40

Add our new value to our running total, we get:
64 + 40 = 104

This is <= 107, so we assign our outside coefficient of 5 for this digit.

Our new sum becomes 104

Our octal notation is now equal to 15

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 107 is 3

Multiplying this coefficient by our original value, we get: 3 * 1 = 3

Add our new value to our running total, we get:
104 + 3 = 107

This = 107, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 107

Our octal notation is now equal to 153

Final Answer