Part B: Problem $1$: Memory is important when storing images $($texture on a graphics card. Quite often GPU devices have limited memory. We will look at this practical problem of storage space. Consider the following diagram showing a set of animation frames and an image that is scaled for higher resolution.Assume h and w are the same in both examples.

Answer the following questions:

$($a$)$ What is the size needed to store one frame of the original $wh$ image in memory? These images are RGBA values, which mean red, green, blue, and alpha components. Each of these RGBA components is stored as one byte of data $(0-255).$

$($b$)$ What would be the size in memory for $100$ animation frames of the original image, assuming the original image was $512256.($Remember that $1$ kb$=1024$ bytes, $1mb=1024kb,$ and $1gb=1024mb.)$

$($c$)$ What would be the size in memory for an image scaled by $4,$ assuming the original image was $512256?$

$($d$)$ Which operation scales better in terms of memory space efficency? Is more memory needed for adding animation frames or for scaling to a higher resolution image? Analyze this using the Big Theta notation.