Number Theory

Let's first convert both numbers into base 10 before adding them together. We have

\((A710)_{16} = (10 × 16^3) + (7 × 16^2) + (1 × 16^1) + (0 × 16^0) = (42768)_{10}\)

\((51)_{16} = (5 × 16^1) + (1 × 16^0) = (81)_{10}\)

 

Now we have to add up 81 and 42768. We get \(42768+81=42849\)

 

Now we want to convert 42849 into base 16. 

 

We go in order, so we have

\(42849/16 = 2678 R1\)

\(2678/16 =167 R6\)

\(167/16 =10R 7 \)

\(10/16 =0R 10 \)

 

So our final answer is \(A761\)

 

Thanks! :)