in TAOCP vol3 2nd Edtion's 5.4.1R Replacement Selection, there is a paragraph describing a data structure and example for Replacement Selection as follows:
the algorithm below uses a data structure containing $P$ nodes to represent the selection tree; the $jth$ node $X[j]$ is assumed to contain $c$ words beginning in $LOC(X[j]) = L_0 + cj$, for $0$ $\le$ $j < P$, and it represents both internal node number $j$ and external node number $P + j$ in Fig.63. There are several named fields in each node:
$KEY$ = the key stored in this external node;
$RECORD$ = the record stored in this external node (including $KEY$ as a subfield)
$LOSER$ = pointer to the "loser" stored in this internal node;
$RN$ = run number of the record pointed to by $LOSER$;
$PE$ = pointer to internal node above this external node in the tree;
$PI$ = pointer to internal node above this internal node in the tree.
For example, when P = 12, internal node number 5 and external node number 17 of Fig.63 would both be represented in $X$, by the fields $KEY = 170, LOSER = L_0 + 9c$ (the address of external node number 21), $PE = L_0 + 8c, PI = L_0 + 2c $
for $LOC(X[j]) = L_0 + cj$, 4 questions:
I need TAOCP's $MIX$ machine knowledge for understand this formula?
it seems that $LOC(X[j])$ is not meaning of the array or pointer, its goal is to find $X[j]$'s beginning addrss?
$cj$ is equal to $c * j$?
what's the meaning of $L_0$ ?
$LOC(X = L_0 + 5c, LOSER = L_0 + 9c = LOC(X), PE = L_0 + 8c = LOC(X), PI = L_0 + 2c = LOC(X) $,
what's the meanings about them $LOC(X),LOC(X), LOC(X)$?
according to $LOSER = L_0 + 9c$ indicates that the address of external node number $21$, so that $PE = L_0 + 8c$ indicates the address of external node number $20$, and $PI$'s address of external node number $14$, but int this case of internal number 5 and external number $17$, $20$ and $14$ are unrelated to them?