Question

For these problems, words are assumed to be 4 bytes, and the references are word-addresses. Thus, the words in memory are located in word-addresses 0, 1, 2, ... As a comparison, note that byte-addresses for words are multiples of 4. Thus, the byte-addresses for words are 0, 4, 8, 12,.... Note that the caches have a cache-line of two-words. We can write a 2-word block as follows (0,1), (2,3), etc are blocks 0, 1, ... Problem B (1 pts). Assume a fully associative cache with least recently used replacement. The cache has 2- word blocks and total size of 4 words. In the table below, indicate if the reference is a HIT ("Y" for yes, "N" for no). 2 3 11 16 3 11 10 3 2 10 4 22 4 10 Ref HIT? List the final contents (references) in the cache:

Answer 1

wood = 4bytes hiven ond Caches Cache ine of two-cwoads have and to tal size of 4 cods (bytes) block 22 Loods) 4 13 5 3 2 dock 1 C2 oods Tog obytes 2 3 Cache s empty intially ASSUME and is toyte addsesable main memoy Ceae fetchin 2 nd byte it coill be miss will be eplaced in Cache (o to 7byłes) So first blocK and Newt if we ase fetching 30d byte pseviously loaded fcm (o to 7 bytes f we fetch Il-th byte it coill be miss Nent IS bytes) i be deplaced and in 2nd block (8 to by tes of mcin memošy. Since Cai th 8 to 1s this block is decenty Used .

16 th byte t i oe miss Next f C>e fetch in first bloCk (o to bytes) in Cache Since and in 2nd block (s to 1s bytes)ase pdesent block 1is deplaced buith 16 to 23 bytes So Since biock 1 is e least ecently USed 3 Yd byte itcill also miss Next if ue fetb and to IS 2nd block i be eplaced Jith Cto ytes Since 2nd b lock is las ecentty USed Net f we fetch Ith byte it is also miss and 6 to 23) 1St block will be replaced cith B to Is) by tes o the by te if is ahit. Next f we fetch Next if we fetch 3 od byte Since 2nd bloc is having Co-7) bytes . Next 2nd jte fetching also a nit is also hit foth byte fetching is als0 a hit. Next th byte fetching is also Next hit L2 block Nert 22nd byte fetching fails and 1St block s Teplased with (16 to 23) bytes since 1st block is Jast resertly sed e4th by te fetching is again a hit . ast tot byte fetchig is miss and deplaced first, blocx fom (8 to 1s)

32lo 22 I0 Ref 6 11 3 2 yN NYYy yyN N N N HIT yN final Cootents o Cache - tog L4 3 2 O tog s 14 3 12