Find \(A+B\) (in base 10), given the following addition problem:

\(4AB_6\)

\(+\) \(41_6\)

\(53A_6\)

(Should be a line horizontal line between \(41_6\) and \(53A_6\), but I don't really know how to do that in LaTeX)

BlackjackEd Sep 17, 2023

#1**0 **

To find the value of A+B in base 10, we can use the following steps:

Convert each number to base 10.

4AB_6 = 4*6^2 + 10*6^1 + 11*6^0 = 144 + 60 + 11 = 215 41_6 = 4*6^1 + 1*6^0 = 24 + 1 = 25 53A_6 = 5*6^2 + 3*6^1 + 10*6^0 = 180 + 18 + 10 = 208

Add the three numbers in base 10.

215 + 25 + 208 = 448

Convert the answer back to base 6.

448 = 6^3 + 2*6^2 + 2*6^1 + 0*6^0 = 622_6

Therefore, A + B = 2 in base 10.

The0neXWZ Sep 17, 2023