Base Change Conversions Calculator

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Convert 257 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 >= 257

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 257

Since 512 is greater than 257, 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 257 is 4

Multiplying this coefficient by our original value, we get: 4 * 64 = 256

Add our new value to our running total, we get:
0 + 256 = 256

This is <= 257, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 256

Our octal notation is now equal to 4

8¹ = 8

The highest coefficient less than 7 we can multiply this by to stay under 257 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
256 + 8 = 264

This is > 257, so we assign a 0 for this digit.

Our total sum remains the same at 256

Our octal notation is now equal to 40

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 257 is 1

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

Add our new value to our running total, we get:
256 + 1 = 257

This = 257, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 257

Our octal notation is now equal to 401

Final Answer