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The multiplication of the number $(10101)_{2}$ by $(1101)_{2}$ yields which one of the following ?
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Verified Answer
The correct answer is:
$(100010001)_{2}$
$\begin{aligned} \because(10101)_{2} &=2^{4} \times 1+0 \times 2^{3}+1 \times 2^{2}+0 \times 2+1 \times 2^{0} \\ &=16+4+1=21 \end{aligned}$
and $\begin{aligned}(1101)_{2} &=1 \times 2^{3}+1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0} \\ &=8+4+1=13 \end{aligned}$
$\therefore(10101)_{2} \times(1101)_{2}=21 \times 13$
$=273=256+16+1=2^{8}+2^{4}+2^{0}$
So, there will be 1 at $9^{\text {th }}, 5^{\text {th }}$ and first place from right and zero at other places So, $(273)_{10}=(100010001)_{2}$
and $\begin{aligned}(1101)_{2} &=1 \times 2^{3}+1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0} \\ &=8+4+1=13 \end{aligned}$
$\therefore(10101)_{2} \times(1101)_{2}=21 \times 13$
$=273=256+16+1=2^{8}+2^{4}+2^{0}$
So, there will be 1 at $9^{\text {th }}, 5^{\text {th }}$ and first place from right and zero at other places So, $(273)_{10}=(100010001)_{2}$
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