Correct Answer: Option B

Explanation

Convert the binary to base 10 and they convert back to base two

10011₂ + xxxxx₂ + 11100₂ + 101₂ = 1001111₂


(1 × 2⁴ + 0 × 2³ + 1 × 2² + 1 × 2¹ + 1 × 2⁰) + xxxxx₂ +(1 × 2⁴ + 1 × 2³ + 1 × 2² + 0 × 2¹ + 0 × 2⁰) + (1 × 2² + 0 × 2¹ + 1 × 2⁰)

= (16 + 0 + 0 + 2 + 1) + xxxxx₂ + (16 + 8 + 4 + 0 + 0 ) + (4 + 0 + 1)

=(64 + 0 + 0 + 8 + 4 + 2 + 1)

19 + xxxxx₂ + 33 = 79

xxxxx₂ + 52 = 79

xxxxx₂ = 79 − 52

xxxxx₂ = 27₁₀

\( \begin{array}{c|c}
2 & 27 \\
\hline
2 & 13 \text{ rem 1}\\
2 & 6 \text{ rem 1}\\
2 & 3 \text{ rem 0}\\
2 & 1 \text{ rem 1}\\
& 0 \text{ rem 1}\\
\end{array}\uparrow \)

27₁₀ = 11011₂

Therefore xxxxx₂ = 27₁₀ = 11011₂

There is an explanation video available below.

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