$3.$ Directory protocols are more scalable than snooping protocols because they send explicit request and invalidate messages to those nodes that have copies of a block, while snooping protocols broadcast all requests and invalidates to all nodes. Consider the eight$-$processor system illustrated in Figure $5\mathrm{.}37$ and assume that all caches not shown have invalid blocks. For each of the sequences below, identify which nodes $($chip$/$processor$)$

receive each request and invalidate.

a$.$ P$0,0$: write

b$.$ P$0,0$: write

c$.$ P$0,0$: write

d$.$ P$1,0$: write Figure $5\mathrm{.}37$ Multichip, multicore multiprocessor with DSM$.($a$)$ P$0,0$: write In this case, P$0$ sends a write request to Chip$0$ and Chip$1.$ Chip$0$ receives the request and invalidates its block, while Chip$1$ receives the request and invalidates its block.

$($b$)$ P$0,0$: write In this case, P$0$ sends a write request to Chip$0$ and Chip$1.$ Chip$0$ receives the request and invalidates its block, while Chip$1$ receives the request and invalidates its block.

$($c$)$ P$0,0$: write In this case, P$0$ sends a write request to Chip$0$ and Chip$1.$ Chip$0$ receives the request and invalidates its block, while Chip$1$ receives the request and invalidates its block.

$($d$)$ P$1,0$: write In this case, P$1$ sends a write request to Chip$2$ and Chip$3.$ Chip$2$ receives the request and invalidates its block, while Chip$3$ receives the request and invalidates its block.

$4.$ Exercise $3$ asked you to add the Owned state to the simple MSI snooping protocol. Repeat the question, but with the simple directory protocol above.