$25.$ A cache has the following parameters: b block size given in numbers of words $=1$; S number of sets $=8$; N number of ways $=2$; and A number of memory address bits $=32.$

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$($a$)$ In terms of the parameters described, what is the cache capacity in numbers of words?

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$($b$)$ In terms of the parameters described, what is the number of bits required to represent each tag?

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$($c$)$ If b $=1,$ S $=16,$ N $=1($direct mapped cache$),$ A $=32.$ What is the number of bits required to represent each tag?