100112 2 111002 1012 10011112 - JAMB Mathematics 2015 Question

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 )

        27<sub>10</sub> = 11011<sub>2</sub><br />

       Therefore xxxxx<sub>2</sub> = 27<sub>10</sub> = 11011<sub>2</sub>