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jmc

number theory intermediate

Problem

Add Express your answer in base 2.
Solution
We can line up the numbers and add just as we do in base 10. For example, when we sum the digits in the rightmost column, we get a sum of 4. Since 4 divided by 2 gives a quotient of 2 and a remainder of 0, we leave 0 as the rightmost digit of the sum and carry 2 to the next column. Continuing in this way, we find \begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & 1 & 1 & 1 & 1_2 \\ & & & 1 & 1 & 1_2 \\ & & & & 1 & 1_2 \\ & + & & & & 1_2 \\ \cline{2-6} & 1 & 1 & 0 & 1 & 0_2, \\ \end{array}so the sum is .
Final answer
11010_2