Base Change Conversions Calculator

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Convert 198 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 >= 198

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 198

Since 512 is greater than 198, 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 198 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 <= 198, 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 198 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 > 198, 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 198 is 6

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

Add our new value to our running total, we get:
192 + 6 = 198

This = 198, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 198

Our octal notation is now equal to 306

Final Answer