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# Number Theory

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Compute 357_8 + 501_8. Give your answer as a base 8 integer.

Jun 15, 2024

#1
+1280
+1

We can convert both numbers to base 10, add them up, and convert them back.

First, let's convert the two. We have

\((357)_8 = (3 × 8^2) + (5 × 8^1) + (7 × 8^0) = (239)_{10} \)

\((501)_8 = (5 × 8^2) + (0 × 8^1) + (1 × 8^0) = (321)_{10} \)

Adding our two results up, we get the sum

\(321+239=560\)

Now, we must convert this into base 8 again.

We get \(560_{10}=1060_8\)

So our final answer is 1060.

Thanks! :)

Jun 16, 2024

#1
+1280
+1

We can convert both numbers to base 10, add them up, and convert them back.

First, let's convert the two. We have

\((357)_8 = (3 × 8^2) + (5 × 8^1) + (7 × 8^0) = (239)_{10} \)

\((501)_8 = (5 × 8^2) + (0 × 8^1) + (1 × 8^0) = (321)_{10} \)

Adding our two results up, we get the sum

\(321+239=560\)

Now, we must convert this into base 8 again.

We get \(560_{10}=1060_8\)

So our final answer is 1060.

Thanks! :)

NotThatSmart Jun 16, 2024