Address-format code for X=(P+Q)×(R+S)

Assumptions: the operands are memory locations, R1, R2, ... are CPU registers, T1, T2, ... are temporary memory locations, and X receives the result. Multiplication and division are done before addition and subtraction, and equal-priority operators go left to right.

Fully bracketed: X = (P+Q)*(R+S). Postfix (reverse Polish) form: P Q + R S + *.

Three-address instructions (OP dest, src1, src2)

ADD R1, P, Q   ; R1 = P + Q
ADD R2, R, S   ; R2 = R + S
MUL X, R1, R2  ; X = R1 * R2

Number of instructions: 3. Shortest program, but each instruction is long (three addresses).

Two-address instructions (OP dest, src; dest = dest OP src)

MOV R1, P   ; R1 = P
ADD R1, Q   ; R1 = R1 + Q
MOV R2, R   ; R2 = R
ADD R2, S   ; R2 = R2 + S
MUL R1, R2  ; R1 = R1 * R2
MOV X, R1   ; X = R1

Number of instructions: 6. A MOV is needed first because the destination operand is overwritten.

One-address instructions (accumulator AC is the implied operand)

LOAD P    ; AC = P
ADD Q     ; AC = AC + Q
STORE T1  ; T1 = AC
LOAD R    ; AC = R
ADD S     ; AC = AC + S
MUL T1    ; AC = AC * T1
STORE X   ; X = AC

Number of instructions: 7. Intermediate results that cannot stay in AC are saved in memory temporaries.

Zero-address instructions (stack machine)

PUSH P  ; push P
PUSH Q  ; push Q
ADD     ; pop two, compute, push result
PUSH R  ; push R
PUSH S  ; push S
ADD     ; pop two, compute, push result
MUL     ; pop two, compute, push result
POP X   ; X = top of stack

Number of instructions: 8. Only PUSH and POP carry an address; ADD, SUB, MUL, DIV work on the top two stack items, so the program follows the postfix form directly.

Summary: 3-address = 3, 2-address = 6, 1-address = 7, 0-address = 8 instructions. Fewer addresses per instruction means shorter instructions but more of them.