Problem $1$: Let us say we have an input of size $67$ with nine channels, and the dimensions of weight per channel are $33.$ Let us also assume that the number of filters is one. $(10)$

a$)$ If we have an input buffer of size nine i$.$e$.,$ it can store $9$ elements, output buffer of size $1$ and weight buffer of size $9,$ what is the number of reads$/$writes to the main memory required for the input, weights, and output for convolution in a weight stationary data flow? $(3)$

b$)$ What is the number of reads$/$writes to the main memory required for the input, weights, and output for convolution in an input stationary data flow? Assume the same buffer size as before. $(3)$

c$)$ If we now assume that the number of filters is $9,$ what is the number of input, weights, and output for convolution in an output stationary data flow? For this problem assume that the output buffer is of size $9.(3)$

d$)$ In general, which of the $3$ approaches input, output, or weight stationary is the best for reducing the number of reads$/$writes to memory? $(1)$

Please provide detail analysis with formula to evaluate this in terms of weight input and output