Question

Q1.Convert the decimal number 222 into binary number.

A) 11011101

B) 11011110

C) 10111110

D) 11010110

Q2.Convert the binary number 10101010 into decimal number.

A) 140

B) 150

C) 160

D) 170

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Answer 1

Answer:

$1.(b) 11011110 \\ 2. \: \: \: \: \: 170 \: \: \: \: thanks$

Answer 2

$\large{\bold{\underline{Question - \: }}}$

Q1.Convert the decimal number 222 into binary number.

$\large{\bold{\underline{Solution - \: }}}$

Divide 222 successively by 2 we get the quotient as 0

$\tt \: \dfrac{22}{2} = 111 ,\: remainder \: = 0$

$\\ \tt \: \dfrac{111}{2} = 55 ,\: remainder \: = 1$

$\\ \tt \: \dfrac{55}{2} = 27 ,\: remainder \: = 1$

$\\ \tt \: \dfrac{27}{2} = 13 ,\: remainder \: = 1$

$\\ \tt \: \dfrac{13}{2} = 6 ,\: remainder \: = 1$

$\\ \tt \: \dfrac{6}{2} = 3 ,\: remainder \: = 0$

$\\ \tt \: \dfrac{3}{2} = 1 ,\: remainder \: = 1$

$\\ \tt \: \dfrac{1}{2} = 0 ,\: remainder \: = 1$

Write the remainder from bottom to top as 11011110.

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\tt{\odot\;hence\;Answer\;=\;\bf{\blue{B) 11011110}}}}}\end{gathered} \end{gathered}\end{gathered}$

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$\large{\bold{\underline{Question - \: }}}$

Q2.Convert the binary number 10101010 into decimal number.

$\large{\bold{\underline{Solution - \: }}}$

Multiply each digit of the binary number by the corresponding power of two:

→ 1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴+ 1×2³+ 0×2² + 1×2¹+ 0×2⁰

→ 1×128 + 0×64 + 1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1

→ 128 + 0 + 32 + 0 + 8 + 0 + 2 + 0

→ 170

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\tt{\odot\;hence\;Answer\;=\;\bf{\blue{D) 170}}}}}\end{gathered} \end{gathered}\end{gathered}$