Pt1420 Unit 1 Assignment 1

To add new instructions to an existing instruction set or to encode many instructions in short instruction words, processor designers reuse opcode patterns. More specifically, when parameter field $f$ of instruction $I$ does not take specific bit string $s$, new instructions $I'_1, I'_2,...$, whose field $f$ has constant bit string $s$, are added using the same opcode pattern as for instruction
$I$. For example, an irregular instruction set that has extended instructions based on the instruction set in Table \ref{tbl:table} is presented in Table \ref{tbl:table2}. Table
\ref{tbl:table2}'s exclusion condition column means that if one of the exclusion conditions is satisfied by an instruction word, that instruction word is not an instance
of

For example, in the instruction set presented in Table \ref{tbl:table2}, bit string
$01110000$ matches the opcode patterns of instructions B and G.

We extend a decoding entry to triplet $(p_o, l, C_e)$ so that each entry consists not only of pattern $p_o$ and label $l$ but also exclusion condition set $C_e$. If a bit pattern satisfies one of the exclusion conditions, even if the bit pattern matches the opcode pattern, the bit string does not match the decoding entry. An element of the exclusion condition set is pair $(p_m, P_u)$, where $p_m$ is a matching pattern and $P_u$ is a set of unmatching patterns. As an example, the exclusion condition set of instruction A in Table \ref{tbl:table2} is
$\{(\verb|--|00\verb|----|, \{(\verb|------|00), (\verb|------|01)\}),
(\verb|--|11\verb|----|, \emptyset)\}$. In an exclusion condition set, matching condition a=11 is represented by matching

Note that one or more matching conditions is represented by a single matching pattern. For example, matching conditions a==11
$\land$ c==11 would be represented by matching pattern
\verb|--|11\verb|--|11.

The satisfaction of the exclusion condition is checked by
\begin{equation}\label{eqn:exclusions}
\bigvee_{(p_m, P_u) \in C_e}(b \in p_m \land \bigwedge_{p_u \in P_u} b \notin p_u)
\end{equation}
For example, bit string $00000001$ matches both the A and E patterns, but it satisfies one of the exclusion conditions of instruction A: $00000001 \in \verb|--|00\verb|----|\ \land\ 00000001
\notin \verb|------|00\ \land\ 00000001 \notin \verb|------|11$; bit string $00000001$ is not an instance of instruction A but of
instruction