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CS 550 - Programming Languages

Random Access Machines

Jeremy R. Johnson

Introduction

Objective: To introduce a simple model of a computer thatwill be used to operationally define the semantics of the MiniLanguage. In the following lecture, a compiler will beconstructed that translates Mini Language Programs toequivalent programs that execute on a RAM using RAMassembly language (RAL).

A Random Access Machine (RAM) is an abstract model ofcomputation that resembles a simple idealized computer. It isequivalent in computational power to a Turing machine (canperform any computation). Despite its simplicity it providessome intuition as to how a program executes on a computer.In practice the size of the memory is bounded.

A Random Access Machine

Control Unit

AC

Program

Memory

AC = accumulator

register

Instruction Set

LDA X; Load the AC with the contents of memory address X

LDI

X; Load the AC indirectly with the contents of address X

STA X; Store the contents of the AC at memory address X

STI

X; Store the contents of the AC indirectly at address X

ADD X; Add the contents of address X to the contents of the AC

SUB X; Subtract the contents of address X from the AC

JMP X; Jump to the instruction labeled X

JMZ X; Jump to the instruction labeled X if the AC contains 0

JMN X; Jump to the instruction labeled X if the contents of the AC ;is negative

HLT

; Halt execution

Sample RAM Program

LDI

3; get ith entry from A

ADD 4; add offset to compute index j

STA 5; store index j

LDI

5; get jth entry from B

JMZ 9; if entry 0, go to 9

LDA 3; if entry 1, get index i

STA 2; and store it at 2.

HLT

; stop execution

LDA 1; get constant 1

10. STI 5; and store it in B
    11. LDA 3; get index i 12. SUB 4; subtract limit 13. JMZ 8; if i = limit, stop 14. LDA 3; get index i again 15. ADD 1; increment i 16. STA 3; store new value of i 17. JMP 1;

AC

Memory

constant

answer

Index i

Limit of A

Index j

A

B

Exercises

Modify STOR so that when a computation finishes and theinput sequence contained a duplicate integer, we know whatthat integer was.

Modify STOR so that it uses array indexing when accessingthe array A instead of pointer arithmetic (i.e. the index into Ashould be an array index, starting with 1, rather than anaddress of a location in the array).

Write a RAL program which takes two input integers ataddresses 1 and 2 and multiplies them storing the result ataddress 4.