Instructions & addressing formulas

Smallest $k$ with $2^k\ge n$. Applies to an opcode field ($n$ instructions), a register field ($n$ registers) or an address field ($n$ addressable locations).

$N_2$, $N_1$, $N_0$ are the numbers of two-, one- and zero-address instructions. The two-address format has a $(W-2A)$-bit opcode; each unused two-address code gives $2^A$ one-address codes, and each unused one-address code gives $2^A$ zero-address codes. Assumes every instruction is exactly $W$ bits, every address field is $A$ bits, and $W>2A$.

$R$ is the index register (indexed), the base register (base) or the PC (PC-relative); $D$ is the displacement field. For PC-relative, $D$ is signed.

$P{C}_{\text{after fetch}}$ is the address of the instruction AFTER the branch (branch address + branch length), unless a question says the branch's own address is used. $D$ is the signed displacement in bytes, unless the ISA scales it.

Range in displacement units relative to the base PC. If the displacement counts instructions of $s$ bytes, multiply by $s$ to get the byte range.