\begin{questions}

    \question Lucy records using her camera. The camera saves the
    audio and video parts of the recording seperately. Lucy transfers
    recording to her computer. The audio file has a size of 19 MB.
    Audio is recorded at a sample rate of 45 kHz. The audio
    resolution is 32 bits.

    \begin{parts}

        \part[5] In minutes and seconds, how long was the recording.

        \begin{solution}
        \begin{align*}
            size &= sample\ rate\times sample\ resolution\times length\\
            18000000 \times 8 &=  45000\times32\times length\\
            18000000 &= 45000\times4\times length\\
            18000 &= 45\times4\times length\\
            18000 &= 180\times length\\
            length &= 100\ seconds\\
            &= 1\ minute\ 40\ seconds\\
        \end{align*}
        \end{solution}

        \vspace{\stretch{1}}

        \part[4] A video file consists of many still frames. Each
        frame is a normal image. The size of a video file can
        therefore be expressed as:

        \begin{align*}
            \mbox{Video file size} = \mbox{Number of frames} \times
            \mbox{Size of each frame}
        \end{align*}

        If each frame is 1920 pixels wide and 1080 pixels high in
        resolution, the bit depth of 24 bits, and her camera records
        30 frames each second. What is the file size of the video
        file, rounded to 3 significant figures, in bytes, with some
        sensible unit prefix?

        \begin{solution}

            Allow error carried forward for time
            \begin{align*}
            size &= length\times frames\ per\ second\times
            resolution\times colour\ depth\\
            &= 100\times 30 \times 1920\times1080\times24\\
            &= 149299200000\ bits\\
            &= 18662400000\ bytes\\
            &\approx 18.7\ GB
            \end{align*}
            Three points for correct calculation. One point for
            correct rounding and unit prefix. Accept other suitable
            unit prefix.
        \end{solution}
        \vspace{\stretch{1}}

        \pagebreak

        \part[1] Lucy combines the audio and video to form a file. She
        then runs a lossy compression algorithm on the resulting file.
        What is lossy compression?

        \begin{solution}
            Reducing the size of a file by removing data.
        \end{solution}
        \vspace{\stretch{1}}

        \part[3] The file size after compression is reduced by 95\%.
        What is the final file size? Use your rounded value for
        video file size. Once more leave your answer rounded to 3
        significant figures, in bytes, with a suitable unit prefix.

        \begin{solution}

            Allow error carried forward for size
            \begin{align*}
                Compressed\ Size &=
                18.7\times 10^9 + 19\times 10^6 * 0.05\\
                &= 935950000\\
                &= 0.93595\ GB\\
                &\approx 0.936\ GB
            \end{align*}
            Two points for correct calculation. One point for
            correct rounding and unit prefix. Accept other suitable
            unit prefix.
        \end{solution}
        \vspace{\stretch{2}}

        \part[1] State an assumption made for part (d).

        \begin{solution}
            There is no metadata or other factor that would influence
            the file size.
        \end{solution}
        \vspace{\stretch{1}}

        \pagebreak

        \part[3] Using your rounded value for the total compressed
        file size, and the length of recording, find a value for the
        size of a compressed video with sound per second.

        Leave your answer rounded to 3 significant figures, with a
        suitable unit and prefix.

        \begin{solution}

            Allow error carried forward for size or time
            \begin{align*}
                Rate &= size \div time\\
                &= 0.936\ GB \div 100\\
                &= 9.36\ MB/s
            \end{align*}
            Two points for correct calculation. One point for correct
            unit and unit prefix. Accept other suitable unit prefix.
        \end{solution}

        \vspace{\stretch{1}}

        \part[3] Lucy wants to record 1 hour of video. Estimate how
        much space this will take on her hard drive when the video and
        audio are combined and compressed, using your answer to (f).

        Leave your answer rounded to 3 significant figures, in bytes,
        with a suitable unit prefix. 
        \begin{solution}

            Allow error carried forward for size or time
            \begin{align*}
                Size &= rate \times time\\
                &= 9.36 \times 60\times 60\\
                &\approx 33.7\ GB
            \end{align*}
            Two points for correct calculation. One point for correct
            unit and unit prefix. Accept other suitable unit prefix.
        \end{solution}

        \vspace{\stretch{1}}

    \end{parts}
    \droptotalpoints
    \pagebreak

    \question Let us say there are some bits:

    \centering
    000110111100000001111111001

    \vspace{1cm}

    \begin{parts}

        \part[2] Using run length encoding represent these bits.
        \vspace{\stretch{1}}

        \part[2] Computers store information in binary. Let us say
        that a run is represented by 5 bits: 4 bits for the length of
        the run, and 1 bit for the bit in the run. For example 00000
        which is 5 zeroes would be 10010, using the first to bits to
        represent the 5 and the final bit to represent the 0.
        Represent your encoding in this format.
        \vspace{\stretch{1}}

    \end{parts}
    \droptotalpoints
    \pagebreak


\end{questions}