257base 8 +177base 8?
We have three columns, from left to right: base squared, base, units. We add the same way we do in base 10. Start in the units column.
In base 10, 7 + 7 = 14. Convert to base 8 > 16, ie, one base (8) plus 6 units
The one base carries into the middle column, so we have 5 + 7 + 1
Adding 7 + 1 gives us a base to carry into the third column (10) + 5 left in the middle column
Adding the third column digits plus the carry, we have 2 + 1 + 1 = 4
257base 8 +177base 8 = 456base 8
If you can't follow that, convert the numbers to base 10, add, then convert back to base 8.
(2 * 64) + (5 * 8) + 7 = 128 + 40 + 7 = 175
(1 * 64) + (7 * 8) + 7 = 64 + 56 + 7 = 127
175 + 127 = 302base 10
Now, convert to base 8
302 / 64 = 4.71875 the third column holds a 4
302 - (4 * 64) = 302 - 256 = 46 left to convert
46 / 8 = 5.75 the second column holds a 5
46 - (5 * 8) = 46 - 40 = 6 left over
the first column holds a 6
456base 8