Add the following binary numbers: 1010 + 1010 =

Question

ScanSolve AI Tutor · Accepted Answer

To add binary numbers, we follow the rules of binary addition:
$0 + 0 = 0$
$0 + 1 = 1$
$1 + 0 = 1$
$1 + 1 = 0$ (with a carry of 1 to the next position)

Align the binary numbers vertically.
$\begin{array}{c} & 1 & 0 & 1 & 0 \\ + & 1 & 0 & 1 & 0 \\ \hline \end{array}$
Add the rightmost column (least significant bit).
$0 + 0 = 0$ . Write down 0.
$\begin{array}{c} & 1 & 0 & 1 & 0 \\ + & 1 & 0 & 1 & 0 \\ \hline & & & & 0 \\ \end{array}$
Add the second column from the right.
$1 + 1 = 0$ with a carry of 1. Write down 0 and carry 1 to the next column.
$\begin{array}{c c c c c} \text{carry} & & & 1 & \\ & 1 & 0 & 1 & 0 \\ + & 1 & 0 & 1 & 0 \\ \hline & & & 0 & 0 \\ \end{array}$
Add the third column from the right, including the carry.
$0 + 0 + \text{carry}(1) = 1$ . Write down 1.
$\begin{array}{c c c c c} \text{carry} & & & 1 & \\ & 1 & 0 & 1 & 0 \\ + & 1 & 0 & 1 & 0 \\ \hline & & 1 & 0 & 0 \\ \end{array}$
Add the leftmost column (most significant bit).
$1 + 1 = 0$ with a carry of 1. Write down 0 and carry 1 to the next position.
$\begin{array}{c c c c c c} \text{carry} & 1 & & & 1 & \\ & & 1 & 0 & 1 & 0 \\ + & & 1 & 0 & 1 & 0 \\ \hline & 1 & 0 & 1 & 0 & 0 \\ \end{array}$
The sum is $10100_2$ .

The correct option is $\text{10100}$ .

Add the following binary numbers: 1010 + 1010 =

Answer

Step-by-step solution

Align the binary numbers vertically.

Add the rightmost column (least significant bit).

Add the second column from the right.

Add the third column from the right, including the carry.

Add the leftmost column (most significant bit).

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