Question $2($b$)$ Assume a set$-$associative mapping with $4$ blocks per set. One implementation of the LRU algorithm is to use a counter associated with each block in the set. Assume the set is empty and assign an initial value of $0$ for each counter.

If the following events occurred in sequence

$1.$ Read miss

$2.$ Read miss

$3.$ Read miss

$4.$ Read hit in the first cache block

$5.$ Read hit in the second cache block

$6.$ Read miss

$7.$ Read miss

$8.$ Read hit in the first cache block

$9.$ Read hit in the first cache block

$10.$ Read miss

Draw a diagram for the set after each event to show how the values of the four counters and the contents of the cache are changed with each event of the above.

For example, the given diagram shows a set with two occupied blocks and two empty blocks. The diagram also shows the contents of the counters associated with each block.