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The remainder and the quotient of the binary division $\begin{array}{ll}(101110)_{2} \div(110), \text { are respectively } & \end{array}$
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The correct answer is:
$(100)_{2}$ and $(111)_{2}$
$(101110)_{2}=1 \times 2^{5}+0 \times 2^{4}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+0 \times 2^{0}$
$=32+0+8+4+2+0$
$=(46)_{10}$
Similarly, $(110)_{2}=1 \times 2^{2}+1 \times 2^{1}+0 \times 2^{4}$
$=4+2$
$=(6)_{10}$
Quotient $=7$ Remainder $=4$ $(7)_{10}=(111)_{2}$ and $(4)_{10}=(100)_{2}$
$=32+0+8+4+2+0$
$=(46)_{10}$
Similarly, $(110)_{2}=1 \times 2^{2}+1 \times 2^{1}+0 \times 2^{4}$
$=4+2$
$=(6)_{10}$
Quotient $=7$ Remainder $=4$ $(7)_{10}=(111)_{2}$ and $(4)_{10}=(100)_{2}$
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