The remainder and the quotient of the binary division (101110)_2 (110)_2 are respectively

Correct answer: B. (100)_2 and (111)_2 aligned & (101110)_2=1 × 2^5+0 × 2^4+1 × 2^3+1 × 2^2+1 × 2^1+0 × 2^0 & =32+0+8+4+2+0 & =(46)_ 10 aligned (7)_ 10 =(111)_2 and (4)_ 10 =(100)_2 aligned & Similarly, (110)_2=1 × 2^2+1 × 2^1+0 × 2^0 & =4+2=(6)_ 10 & Quotient =7 & Remainder =4 aligned

NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Binary Numbers

NDA 2017 · Mathematics · Binary Numbers

The remainder and the quotient of the binary division (101110)_2...

The remainder and the quotient of the binary division

(101110)_2 \div(110)_2

are respectively

Options

A $(111)_2$ and $(100)_2$
B $(100)_2$ and $(111)_2$
C $(101)_2$ and $(101)_2$
D $(100)_2$ and $(100)_2$

Correct answer

B. $(100)_2$ and $(111)_2$

Step-by-step solution

\begin{aligned} & (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}\end{aligned}

(7)_{10}=(111)_2 \text{

and

}(4)_{10}=(100)_2

\begin{aligned} & \text{ Similarly, }(110)_2=1 \times 2^2+1 \times 2^1+0 \times 2^0 \\ & =4+2=(6)_{10} \\ & \text{Quotient }=7 \\ & \text{Remainder }=4\end{aligned}

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