Add the following binary numbers and check your result by decimal addition. $\begin{array} { c}
11111\
1111 \
\hline
\end{array}$
A) 100111
B) 101001
C) 101110
D) 100101
E) 100100

Question

Add the following binary numbers and check your result by decimal addition. $\begin{array} { c} 
11111\
1111 \
\hline
\end{array}$
A) 100111
B) 101001
C) 101110
D) 100101
E) 100100

Quizplus · Accepted Answer

Adding the two binary numbers, we get:
\begin{array} { c@{}c@{}c@{}c@{}c@{}c} 
& & 1 & 1 & 1 & 1 1_2 \
+ & & 1 & 1 & 1 & 1_2 \
\cline{2-6}
& 1 & 0 & 1 & 1 & 1 0_2 \
\end{array}
To check our result, we convert both binary numbers to decimal and add them:
\begin{align*}
1 1 1 1 1_2 &= 1 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \
&= 16 + 8 + 4 + 2 + 1 \
&= 31 \
1 1 1 1_2 &= 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \
&= 8 + 4 + 2 + 1 \
&= 15 \
\end{align*}
\begin{align*}
31 + 15 &= 46 \
&= 1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 \
&= 101110_2 \
\end{align*}
So, the binary addition is correct and the best choice is (C).

Add the Following Binary Numbers and Check Your Result by Decimal