for the result of adding the binary numbers 10102 and 11012.

Question

ScanSolve AI Tutor · Accepted Answer

The question asks for the result of adding the binary numbers $1010_2$ and $1101_2$ .

Perform binary addition column by column, starting from the rightmost digit.
$\begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline \end{array}$
Add the rightmost column ( $0 + 1$ ).
$0 + 1 = 1$ .
$\begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & & & 1 \\ \end{array}$
Add the second column from the right ( $1 + 0$ ).
$1 + 0 = 1$ .
$\begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & & 1 & 1 \\ \end{array}$
Add the third column from the right ( $0 + 1$ ).
$0 + 1 = 1$ .
$\begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & 1 & 1 & 1 \\ \end{array}$
Add the leftmost column ( $1 + 1$ ).
$1 + 1 = 10_2$ . Write down 0 and carry over 1 to the next position.
$\begin{array}{c c c c c} \text{carry} & 1 & & & \\ & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline 1 & 0 & 1 & 1 & 1_2 \\ \end{array}$
The sum is $10111_2$ .

Comparing this result with the given options:
A. $10111_2$
B. $10011_2$
C. $11111_2$
D. $11000_2$

The calculated sum matches option A.

The final answer is $\boxed{\text{A}}$ .

For the result of adding the binary numbers 10102 and 11012.