Lecture 1 - Random Access Machines | CS 281, Papers of Computer Science

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Systems Architecture I

Lecture 1: Random Access Machines

Jeremy R. Johnson

Introduction

• Objective: To develop a simple model of computation that

provides insight into how a program executes on a computer.

• A Random Access Machine (RAM) is an abstract model of

computation that resembles a simple idealized computer. It is

equivalent in computational power to a Turing machine (can

perform any computation). Despite its simplicity it provides

some intuition as to how a program executes on a computer.

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 (unconditional jump)
• 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

**1. LDI 3; get i-th entry from A

2. ADD 4; add offset to compute index j
3. STA 5; store index j
4. LDI 5; get j-th entry from B
5. JMZ 9; if entry 0, go to 9
6. LDA 3; if entry 1, get index i
7. STA 2; and store it at 2.
8. HLT ; stop execution
9. 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

1 constant

2 0 answer

3 6 Index i

4 9 Limit of A

5 0 Index j

A

B

Exercises

• Modify STOR so that when a computation finishes and the

input sequence contained a duplicate integer, we know what

that integer was.

• Modify STOR so that it uses array indexing when accessing

the array A instead of pointer arithmetic (i.e. the index into A

should be an array index, starting with 1, rather than an

address of a location in the array).

• Write a RAL program which takes two input integers at

addresses 1 and 2 and multiplies them storing the result at

address 4.