1. Examples with 3-Digit Numbers
10’s complement representation of 247
247 (positive number)
10’s complement of 247
1000 – 247 = 753 (negative number)
Example 2:
10’s complement of 17
1000 – 017 = 983
Example 3:
10’s complement of 777
Negative number because first digit is 7
1000 – 777 = 223
Sign-magnitude value = -223

2. Introduction Basic operations are defined by the hardware
CPU instructions (operations)
Data flow
I/O
Store program: in the memory (von Neumann)
Power: not from complexity, but speed
LMC: MIT 1965; 1979 (Madnick)

3. Goals layout of LMC functionality of LMC LMC instruction set
LMC instruction codes
a simple program
fetch-execute instruction cycle
von Neumann architecture

4. The Little Man Computer

5. LMC Architecture Memory Calculator: Location counter LM
100 mailboxes: (address, content)
Addresses: 00-99
Content: 999
Calculator:
S999; S = + or –
No overflow
Can remember the sign
Location counter LM
I/O: 2 baskets “01”, “02”

6. Instruction Code Format
Instruction mailbox
address
Instruction 5 == LOAD
Code 525 == LOAD value from mailbox 25 onto calculator

7. Instruction Cycle
Fetch: Little Man finds out what instruction he is to execute
Execute: Little Man performs the work

8. Fetch Portion of Fetch and Execute Cycle
1. Little Man reads the address from the location counter
2. He walks over to the mailbox that corresponds to the location counter

9. Fetch, cont.
3. And reads the number on the slip of paper (he puts the slip back in case he needs to read it again later)

10. Execute Portion
1. The Little Man goes to the mailbox address specified in the instruction he just fetched
2. He reads the number in that mailbox (he remembers to replace it in case he needs it later)

11. Execute, cont.
3. He walks over to the calculator and punches the number in
4. He walks over to the location counter and clicks it, which gets him ready to fetch the next instruction

12. von Neumann Architecture (1945)
Stored program concept
Memory is addressed linearly
Memory is addressed by location number without regard to content
Copyright 2013 John Wiley & Sons, Inc.

13. LMC (Basic) Instructions
Notations: Memory = M, calculator=C
LOAD (5)99 from M to C
STORE (3)99 from C to M
STORE (4) XX Store XX to C
ADD (1)99 M to C
SUBTRACT (2)99 M from C
INPUT (9)01 from “01” to C
OUTPUT (9)02 from C to “02”
HALT (0)

14. A Simple Program Mailbox Code Meaning 00 901 Reads from In basket to C
Store C to 99 (op1)
Reads from In basket to C
Add 99 (op1) to C
Output C to output basket
Halt
The logic is: sequential
The program Adds two numbers and Outputs the result

15. Add 3 numbers and Output Result
Mailbox Code Meaning
Reads from In basket to C
Store C to 99 (op1)
Reads from In basket to C
Store C to 98 (op2)
Reads from In basket to C
Add 99 (op1) to C
Add 98 (op2) to C
Output C to output basket
Halt

16. Extended instructions
BRANCH (JUMP) (6)99
BRANCH ON ZERO (7)99
BRANCH ON POSITIVE (8)99
Used to define new types of logic
Branches
Repetitions ([while; for] loops)

17. Primary Programming Constructs
Algorithms
Control structures
Sequence
Branching
Flowcharts
Pseudo-code

18. English vs. Code add two numbers (comments from before)
input first number, input second number,
add them together, output the result
901, 399, 901, 199, 902, 000

19. Program / Algorithm Development
develop concept (in English)
sketch control flow of concept
fill in details
convert into programming language

20. Three Control Structures
Sequence
Branching
Looping

21. Sequence standard operation of a computer
instructions are executed sequentially (from consecutively numbered memory locations)
program counter increments consecutively through memory slots

22. Example of Sequence
How do we get from here to Union Station (using the TTC)?
Directions to get to Union Station are followed in sequence
Get The bus
Get The subway
Leave at Union Station
Directions are an everyday program/algorithm

23. Flowchart for Sequence
start
end

24. Branching allows program execution to depend on input example:
“I Want to wait as little as possible for the Bus”
program:
Is 196 Line too long ?
Go get the 106.

25. Flowchart for Branching
196 Line long?
Get 106
yes no

26. Pseudocode Pseudocode is a brief English description of an algorithm
(the comments from before)
it is not natural English
it does not have complete detail
it is not syntactically correct code

27. Grading Example 85-100 Honors 60-84 Pass Fail start input grade yes no
end

28. Summary Programming == algorithm development + coding
algorithm development requires clarity of thought
coding requires attention to detail

29. Looping
Examples of looping
Structured programming
Writing pseudocode

30. Looping allows program to repeatedly execute a given section example:
deal all the cards from the deck
program:
check to see if there are more cards
deal a card
< repeat >

31. Flowchart for Looping
more cards?
deal a card
yes no

32. Example of Looping Mailbox Code Meaning
<assume that calculator value represents number of remaining cards >
Subtract 99 from C (consider 99 holding the value 1)
if positive, branch to 22
branch to 30 (skip code to deal card)
22… < code to deal cards >
branch to 19 (repeat until no more cards)
30 < remainder of program >

33. Structured Programming
Any program can be written with only the three primary constructs
Branch unconditionally (goto) is not externally available

34. Natural Language to Pseudocode
Use a large sauce pan Bring 4 litres of water to a rolling boil Add salt to taste, if desired
Add contents of package Stir gently
Boil 11 minutes
Remove from heat
Drain well
Serve

35. For A payroll System : Input the employees payroll data
If hours worked is greater than 40 then calculate overtime pay
Calculate gross pay for the employee - Gross Pay = hourly pay times 40 plus overtime
Calculate tax for the employee

36. Summary Natural language is NOT pseudocode
Programming requires great explicitness of thought
Details are easier to fill in after you have the algorithm figured out

37. Program 2 00 IN “01” 901 Input from “01” to C [op1]
01 STO Store from C to M10
02 IN “01” 901 Input from “01” to C [op2]
03 STO Store from C to M11
04 SUB Subtract op2-op1 = r1
05 BRP If r1 > 0 goto M08
06 LDA else load op1 into C
07 SUB op1-op2 = r2
08 OUT “02” 902 Output to “02”
09 HLT
10 Data
11 Data

38. Program 2 00 IN “01” 901 Input from “01” to C [op1]
01 STO Store from C to M10
02 IN “01” 901 Input from “01” to C [op2]
03 STO Store from C to M11
04 SUB Subtract op2-op1 = r1
05 BRP If r1 > 0 goto M08
06 LDA else load op1 into C
07 SUB op1-op2 = r2
08 OUT “02” 902 Output to “02”
09 HLT
10 Data
11 Data

39. How to do C-(A+B) ? 00 Input 901 01 Store 20 320 02 Input 901
03 ADD
04 Store
05 Input 901
06 SUB
07 Output 902
08 Halt 0
Read A
Read B
Sum D=A+B
Read C
Sub C-D

40. Compare A and B. Output Letter C if A greater and D otherwise
00 Input 901
01 Store
02 Input 901
03 Sub (B-A)
04 BRP
05 STVAL (43 hex)
06 Output 902
07 Halt 000
08 STVAL (44 hex)
09 Output 902
10 Halt 0
Read A
Read B
IF A>B
Then Write “C”
Else Write “D”

41. Other Alternative 00 Input 901 01 Store 20 320 02 Input 901
03 Sub (B-A)
04 BRP
05 STVAL
06 Branch
07 STVAL
08 Output 902
09 Halt 0

42. Subtract 10-8 and Add to A (input)
Subtract 10-8 and Add to A (input). If result >10 Output 1 else Output 2
A=10
B=8
C=A-B
Read D
E=D-C
IF E>10 write “1”
Else write “2”

43. Subtract 10-8 and Add to A (input)
Subtract 10-8 and Add to A (input). If result >10 Output 1 else Output 2
00 Stval
01 Store
02 Stval
03 Sub
04 Store
05 Input 901
06 Add
07 Store
08 StVal
Sub
(10 – Result)
10 BRP
11 Staval
12 Branch
13 Stval
14 Output 902
15 Halt 0

44. Multiply A*B Read A Read B C=0 While A>0 Do C=C+B A=A-1 Enddo
Write B

45. 00 Input 901
01 Store
02 Input 902
03 Store
04 Stval
05 Store
06 Staval 1 411
07 Store
08 Load
09 Add
10 Store
11 Load
12 Sub BZ
Store
15 Branch
16 Load
Output 902
18 Halt 0

46. Is the LMC a “real” computer?
CPU instruction set is created using binary numbers rather than decimal
Instructions are performed in a simple electronic way using logic based upon Boolean algebra instead of having a Little Man running around a mailroom.

47. LMC to “real” computer LMC also uses fetch-execute cycles
LMC processes instructions in sequence
Mailboxes are memory
LM and calculator are CPU
Baskets provide I/O

48. Summary LMC is almost real computer! Computers are simple
Programming is easy