1. CS/COE0447 Computer Organization & Assembly Language
Pre-Chapter 2

2. “C Program” Down to “Numbers”
void swap(int v[], int k) {
int temp;
temp = v[k];
v[k] = v[k+1];
v[k+1] = temp; }
swap:
muli $2, $5, 4
add $2, $4, $2
lw $15, 0($2)
lw $16, 4($2)
sw $16, 0($2)
sw $15, 4($2)
jr $31
compiler … … … … … … …
assembler

3. “Numbers” in Memory … … … … … … …

4. Stored Program Concept
program fetch
data load/store
program A
program A
disk I/O
program
counter
data A
program C
program B
program B
data B
processor
hard disk
main memory

5. Stored Program Concept
Programs (instructions) are stored in memory as a stream of bits (numbers)
Indistinguishable from data
More than one programs can reside in memory at the same time
Programs can be modified by the processor or I/O just as data can be modified
Instructions are fetched by the processor, are decoded and they determine processor actions
Program Counter determines which instruction is fetched next

6. Stored Program Concept
In fact, one of the great ideas in computer science is the idea that programs could be stored just as data was stored.
Before that, people envisioned the hardware running a fixed program, and data being stored in memory.

8. …

12. Addresses and Contents shown in Hex

13. Number Systems Actual machine code is in binary
O, 1 are high and low signals to hardware
Hex (base 16) is often used by humans (code, simulator, manuals, …) because
16 is a power of 2 (while 10 is not); mapping between hex and binary is easy
It’s more compact than binary
We can write, e.g., 0x in programs rather than

14. Base 10 (Decimal) Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (10 of them)
Example:
3217 = (3103) + (2102) + (1101) + (7100)
A shorthand form we’ll also use:

15. Numbers and Bases in General
Number Base B  B unique values per digit
Base 10: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Base 2: {0, 1}
Base 16: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
(Unsigned) number representation
d31d30…d1d0 is a 32-digit non-negative number
Value = d31B31 + d30B30 + … + d1B1 + d0B0
N-digit base B  BN unique values

16. Example: Base 2 (Binary)
Digits: 0, 1 (2 of them)
“Binary digit” = “Bit”
Example:
11010two = (124) + (123) + (022) + (121) + (020) = = 26ten
Choice for machine implementation!
1 = on, 0 = off

17. Base Conversion Let’s do decimal-to-binary conversion
Aten = dn-1dn-2…d1d0two
Given a base-10 number A, come up with n-digit binary number that has the same value!
X = the number
Let N be the largest power of 2 that fits into X
Put a 1 in that position
X = X – 2^N
Repeat until you are done!

18. Base Conversion, cont’d
From binary to decimal
From decimal to binary
From binary to hexadecimal
From hexadecimal to binary
From decimal to hexadecimal? (more complicated; later)

19. Base Conversion, cont’d
Binary to hex (base 16), or hex to binary base conversion:
Take 4 bits in binary and convert them into one hex digit and vice versa
Since binary notation tends to be long, hex notation is frequently used in assembly language (and in C programs).
More on binary number representation will be discussed when we study arithmetic

20. Before moving on to chapter 2….
We’ll mention some concepts in program performance, so you have ideas in mind
The text covers this in the Chapter 1 questions and in Chapter 4. We’ll wait until Chapter 4 to cover this more fully.

21. Program Performance Program performance is measured in terms of time!
Program execution time has to deals with
Number of instructions executed to complete a job
How many clock cycles are needed to execute a single instruction
The length of the clock cycle (clock cycle time)

22. Clock, Clock Cycle Time Circuits in computers are “clocked”
At each clock rising (or falling) edge, some specified actions are done, usually within the next rising (or falling) edge
Instructions typically require more than one cycle to execute
Function block
(made of circuits)
clock cycle time
clock

23. Program Performance time = (# of clock cycles)  (clock cycle time)
(# of instructions executed) 
(average cycles per instruction)
We’ll do specific calculations when we get to Chapter 4.
But now, let’s move on to Chapter 2