Base Change Conversions Calculator

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Convert 102 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 >= 102

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 102

Since 512 is greater than 102, 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 102 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 <= 102, 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 102 is 4

Multiplying this coefficient by our original value, we get: 4 * 8 = 32

Add our new value to our running total, we get:
64 + 32 = 96

This is <= 102, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 96

Our octal notation is now equal to 14

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 102 is 6

Multiplying this coefficient by our original value, we get: 6 * 1 = 6

Add our new value to our running total, we get:
96 + 6 = 102

This = 102, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 102

Our octal notation is now equal to 146

Final Answer