Yes, we have to include .
We know , size of TAG directory = (No of TAG bit + additional bit)* number of lines in cache
And Size of cache tag directory = Size of tag directory * Number of tag entries
if we assume, Total cache size = 256 KB
Cache block size = 32 Bytes
then, number of cache entries = 256 K / 32 = 8 K = Number of tag entries
Each Cache Tag Directory entry contains :
Address tag bits + valid bits+ modified bits+ replacement bits = Entry size
And Size of Cache directory =No.of Cache Blocks * Entry size
so we have to include tag directory size in cache size .