Question

Convert 777 from base 8 to base 10.

Answer 1

To convert the number 777 from base 8 to base 10, we can expand it using the powers of 8. In base 8, the digits represent the following:

\[
777_8 = 7 \times 8^2 + 7 \times 8^1 + 7 \times 8^0
\]

Now, we calculate each term:

1. \(7 \times 8^2 = 7 \times 64 = 448\)
2. \(7 \times 8^1 = 7 \times 8 = 56\)
3. \(7 \times 8^0 = 7 \times 1 = 7\)

Now, we add these values together:

\[
448 + 56 + 7 = 511
\]

Therefore, the base 10 equivalent of \(777_8\) is:

\[
\boxed{511}
\]