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for example 0101011(base 16) + 0111011 (base 16) =? another ex: 7FE + 3AB = ?

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2 Answers 2

For your first example, all you need is $0+1=1+0=1, 1+1=2, 0+0=0$ as there are no carries. For the second, you can make an addition table base 16 like below and add just like in base 10. Anything with a 1 in the left place is a carry.

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$0101011+0111011 = 101011+111011 = 212022$ in every number system of base $>2$ (where the digit $2$ is allowed). Similarly, $11^3=12321$ in every number system of base $>3$, etc.

If you intended these as in binary format, then: $$\begin{align} & 0101011 \\ +&0111011 \\ \hline \\ &1100110 \end{align}$$ As Ross wrote, start from behind, you find $1+1$ that is $10$ in binary, so write down the zero and carry the $+1$ as remainder and add to the next digit, just as in decimal...

$\mathtt{7FE+3AB =(800-2)+3AB=BAB-2=BA9 }\ $ in hexadecimal.

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