Question

What is the result of the binary addition: 1101 + 1010?

• A. 10111
• B. 10011
• C. 11110
• D. 11000

Hint:

When performing binary addition, a good way to check your work is to convert the operands and the result to their decimal equivalents and see if the addition holds true.

Answer 1

The Correct Option is A

We perform binary addition column by column from right to left, following these rules:
$0 + 0 = 0$ $0 + 1 = 1$ $1 + 0 = 1$ $1 + 1 = 0$, carry 1 $1 + 1 + 1 = 1$, carry 1
Let's add the numbers:
tabular@c@ c@c@c@c@c & & 1 & 1 & 0 & (carry)
& 1 & 1 & 0 & 1 &
+ & 1 & 0 & 1 & 0 &
tabular
Column 1 (rightmost): $1 + 0 = 1$.
Column 2: $0 + 1 = 1$.
Column 3: $1 + 0 = 1$.
Column 4: $1 + 1 = 0$, carry over 1.
Column 5: The carry-over 1 comes down.
The result is:
tabular@c@c@c@c@c@c & 1 & 1 & 0 & 0 & (carry)
& & 1 & 1 & 0 & 1
+ & & 1 & 0 & 1 & 0
& 1 & 0 & 1 & 1 & 1
tabular
So, the result is 10111.
Alternatively, convert to decimal: $1101_2 = 13_{10}$, $1010_2 = 10_{10}$. $13+10 = 23$.
Convert result to decimal: $10111_2 = 16+0+4+2+1 = 23_{10}$. This confirms the answer.