About Instructions

1. About Instructions Based in part on material from Chapters 4 & 5 in Computer Architecture by Nicholas Carter

2. Instruction Set • One aspect of processor design is to determine what instructions will be supported. • There must be rules (syntax) for how instructions are expressed so that the code can be parsed, one instruction distinguished from the next, the data (operand) separated from the action (operator).

3. Number of operands • An example of syntax would be whether an operator is binary or unary • Binary operators take two operands • e.g. the boolean operator AND • (x<y) AND (i=j) • Unary operator take one operand • E.g. the boolean operator NOT • NOT(x<y) • Some ops are context dependent • - 5 (unary) versus 4-5 (binary)

4. Operation versus Instruction • An operation such as addition, which is binary (takes two operands), can be coded using instructions that are unary (one operand) if there is a default location implied such as Accumulator A. • 5 + 6 becomes • Load 5 (places data in acc. A) • Add 6 (adds number in Acc. A to new number)

5. Where does the answer go? • Whether it’s 5 + 6 or (Load 5, Add 6), there’s the question of what to do with the result. • We can again use the default location of Accumulator A to place the answer in or we can include a third operand that indicates where the result should be placed.

6. Store • Placing the result of an operation in memory is known as storing it. Thus with unary instructions, we would have • Load 5 • Add 6 • Store 7 • The operand of the store is an address indicating where to store the answer, which is held in Accumulator A. • Or one might have three operands • Add 7, 5, 6

7. Addressing Modes • But this raises the question as to what were the operands in the two previous instructions (Load and Add). • For those instructions, the operand might have been the actual numbers one wanted added or the addresses of numbers one wanted added.

8. More than one kind of add • By Add one typically means the latter case on the previous slide. The operand is not the number to be added but the address of the number to be added. • A designer can include a distinct add instruction, Add Immediate, in which the operand is the actual number to be added.

9. Add Indirect • In another version of addition, the operand is an address, and the data at that address is also an address, and the actual number to added is located at the second address.

10. Address Value 0 LOAD 4 1 ADD INDIRECT 5 2 ADD IMMEDIATE 6 3 STOP 4 5 5 6 6 7 7 8 A short program Acc. A: XXX The arrow indicates the program counter, we assume it has not executed the statement it points to.

11. Address Value 0 LOAD 4 1 ADD INDIRECT 5 2 ADD IMMEDIATE 6 3 STOP 4 5 5 6 6 7 7 8 A short program Acc. A: 5 The Load 4 instruction has been executed. The value at location 4 (which is a 5) has been loaded into the accumulator.

12. Address Value 0 LOAD 4 1 ADD INDIRECT 5 2 ADD IMMEDIATE 6 3 STOP 4 5 5 6 6 7 7 8 A short program Acc. A: 12 The Add Indirect 5 instruction has been executed. One goes to location 5 to find a value of 6. That 6 is an address, thus one goes to location 6 to find a value of 7 and that is added to the 5 waiting in the accumulator. The result of 12 is placed in the accumulator.

13. Address Value 0 LOAD 4 1 ADD INDIRECT 5 2 ADD IMMEDIATE 6 3 STOP 4 5 5 6 6 7 7 8 A short program Acc. A: 18 The Add Immediate 6 instruction has been executed. The value 6 is data which is added to the 12 waiting in the accumulator. The result of 18 is placed in the accumulator.

14. The Stop Instruction • Recall that in what is actually executed (machine code) the instructions themselves numbers. • Thus it is crucial to know within an instruction which numbers correspond to an operation and which numbers are operands. • Similarly on the level of the program itself, the processor needs to know where the program ends as there may be data stored after it. • In a machine with an operating system, it is more a notion of returning (control) than of stopping or halting.

15. Recap so far • So there were issues about the number of operands. • Recall that we have a fetch-execute cycle – first an instruction is retrieved from memory and then acted upon. • With unary instructions adding two numbers and storing the result required three instructions, that’s three fetches and three executions. • With ternary instructions it can be done with one instruction, one fetch and one execute. The execution is now more complicated but we have saved time on fetches.

16. Recap so far (Cont.) • More operators means more complicated circuitry, the load and store aspects of the instruction would have to built into each separate instruction. • There is a speed versus complexity issue. And complexity also brings the issue of cost along with it.

17. Recap so far (Cont.) • After determining the number of operands came the issue of what the operands mean. • Are they data, addresses of data or addresses of addresses of data? • Either we can decide to support all of these and choose complexity. Or we can choose to support only some of them and sacrifice efficiency. • For example, you can eliminate Add Immediate if you always store the values you want to add.

18. Data Types • Apart from addressing, another issue is the type of data the operation is acting on. • The process for adding integers is different from the process for adding floating point numbers. • So one may have separate instructions: ADD for addition of integers and FADD for the addition floats. • Furthermore, one may need to include instructions to convert from one type to another. • To add an integer to a float, convert the integer to a float and then add the floats.

19. Ordering of opcodes and operands • Another example of syntax is the ordering of opcode and operand(s). • Postfix: operand(s) then opcode • 4 5 + • Works well with stacks • Prefix: opcode then operand(s) • + 4 5 • Infix: operand opcode operand • 4 + 5

20. Precedence (aka Order of Operations) • Precedence is the order in which operations occur when an expression contains more than one operation. • Operations with higher precedence are performed before operators with lower precedence. • 1 + 2 * 3 - 4 • 1 + 6 - 4 (multiplication has higher precedence) • 7 - 4 (start on the left when operators have the same precedence) • 3

21. Infix to postfix • To convert 1+2*3-4, put in parentheses even though they’re not strictly necessary for this expression • ((1+(2*3))-4) • Convert the innermost parentheses to postfix: 2*3 becomes 2 3 * • ((1+(2 3 *))-4) • Convert the next set of parentheses • ((1 2 3 * +)-4)

22. Infix to postfix • The last step eliminated the innermost set of parentheses. Continue to convert from infix to postfix from the innermost to outermost parentheses. • (1 2 3 * + 4 -) • Note there is one overall set of parentheses that can be thrown away. Also note that the order of the numbers has not changed.

23. Another example • 1+ (2+3) * 4 + (5 + 6) * ((7 + 8) * 9) • Add parentheses • 1+ ((2+3) * 4) + ((5 + 6) * ((7 + 8) * 9)) • Add parentheses • (1+ ((2+3) * 4)) + ((5 + 6) * ((7 + 8) * 9)) • Add parentheses • ((1+ ((2+3) * 4)) + ((5 + 6) * ((7 + 8) * 9))) • Convert innermost to postfix • ((1+ ((2 3 +) * 4)) + ((5 6 +) * ((7 8 +) * 9)))

24. Another Example (Cont.) • ((1+ ((2 3 +) * 4)) + ((5 6 +) * ((7 8 +) * 9))) • ((1+ (2 3 + 4 * )) + ((5 6 +) * (7 8 + 9 * ))) • ((1 2 3 + 4 * +) + (5 6 +7 8 + 9 * *)) • ( 1 2 3 + 4 * + 5 6 +7 8 + 9 * * + )

25. Postfix good for Hardware • Postfix order is better suited for hardware since one must prepare the inputs (a.k.a. the data or operands) before operating on them to get an output. • Postfix is particularly well suited for architectures that use a stack to perform computations.

26. The stack • A stack is a data structure (which may be implemented in hardware or in software) that holds a sequence of data but limits the way in which data is accessed. • A stack obeys the Last-In-First-Out (LIFO) protocol, the last item written (pushed) is the first item to be read (popped).

27. Stack 2 is pushed onto the stack 2 is popped off of the stack 4 2 3 3 1 1 1 1 1

28. Stack Pointer: don’t move all the data just change the pointer

29. Infix Evaluation • 1+ (2+3) * 4 + (5 + 6) * ((7 + 8) * 9) • 1+(5)*4 + (11)*((15)*9) • 1 + 20 + 11*135 • 1 + 20 + 1485 • 21 + 1485 • 1506

30. Evaluating a postfix expression using a stack (1) Enter the postfix expression and click Step

31. Evaluating a postfix expression using a stack (2)

32. Evaluating a postfix expression using a stack (3)

33. Evaluating a postfix expression using a stack (4)

34. Evaluating a postfix expression using a stack (5)

35. Evaluating a postfix expression using a stack (6)

36. Evaluating a postfix expression using a stack (7)

37. Evaluating a postfix expression using a stack (8)

38. Evaluating a postfix expression using a stack (9)

39. Evaluating a postfix expression using a stack (10)

40. Evaluating a postfix expression using a stack (11)

41. Evaluating a postfix expression using a stack (12)

42. Evaluating a postfix expression using a stack (13)

43. Evaluating a postfix expression using a stack (14)

44. Evaluating a postfix expression using a stack (15)

45. Evaluating a postfix expression using a stack (16)

46. Evaluating a postfix expression using a stack (17)

47. Evaluating a postfix expression using a stack (18)

48. Evaluating a postfix expression using a stack (19)

49. Evaluating a postfix expression using a stack (20)

50. Evaluating a postfix expression using a stack (21)