1. Today's Agenda What is Computer Architecture?
What is Computer Organization?
Brief history of Computers
Introduction to Binary Number Systems

2. Layers of Abstraction: from application program to execution of program
High Level Language
main() {
int i,b,c,a[10];
for (i=0; i<10; i++)…
a[2] = b + c*i; }
Compiler …
lw r2, mem[r7]
add r3, r4, r2
st r3, mem[r8]
ISA
Assembler

3. Where ISA is positioned in entire Abstraction layers
Application
Operating
System
Compiler
Firmware
Instruction Set
Architecture
Instr Set Proc.
I/O system
Datapath & Control
Digital Design
Circuit Design
Layout

4. Architecture
Architecture is those attributes visible to the programmer
Instruction set
Number of bits used for data representation
I/O mechanisms
Memory addressing techniques
Architecture Question:
Is there a multiply/division instruction available?

5. Organization Organization is how features are implemented
Control signals
Interfaces between computer and peripherals
Memory technology used
Organization Question:
Is multiplication is implemented by separate hardware or is it done by repeated addition?

6. Architecture & Organization
All Intel x86 family share the same basic architecture
The IBM System/360 family share the same basic architecture
This gives code compatibility
At least backwards
Organization differs between different versions

7. Computer Architecture & Organization
Architecture refers to those attributes of the system visible to the programmer.
Organization refers to the operational units and their interconnections.
Examples of architectural attributes are
Instruction set, number of bits used to represent datatypes like number, character etc
Examples of organizational attributes are
Processor design including control signals, register file, their interconnection.
Memory Technology, interfaces between processor and I/O devices.

8. Example Processor: LC3 Addressability is 16 bit – 216 address space
8 Registers each 16 bit – it requires 3 bits to represent each register
Opcode is 4 bit long – 16 different instructions can be there
Addressing Modes
Example instruction:
ADD R3,R4,R2
– machine equivalent of ADD instruction

9. History of Computers

10. First Generation Computer: Vacuum Tubes
Decimal machine rather than a binary machine
Mainly used for large calculations.
It had to be programmed manually by setting switches and plugging and unplugging the cables.
A ring of ten vacuum tubes represented each digit.
Very large machines
Vacuum Tube

11. First Generation Computer made of Vacuum tubes

12. Second Generation: Transistors
Made up of Silicon
Silicon:
Insulator
It is made Semiconductor by Doping
All the electronic devices are semiconductor devices
And most of them are made up of transistors.
Boolean logical gates are made of transistors.
Combinational and sequential circuits – logic gates
Integrated circuits – are made up of these circuits.
Microprocessor is made up of these integrated circuits.

13. Moore’s Law Size of transistor is decreasing
Number of transistors are increasing exponentially.
Moore’s Law:
Number of transistors doubles every 18 months to 2years.
Gordon Moore: Co-founder of Intel

14. Core 2 Duo (Conroe) 291 millions, July 2006
Moore’s Law
Core 2 Duo (Conroe) 291 millions, July 2006
P4 Extreme Ed.
178 millions w/ 2MB L3
IBM POWER5 has
276 million transistors
Intel Dual-Core Xeon (P4-based Tulsa) w/ 16MB unified L3: billion, 2006
42 millions
2,250
Exponential growth
Transistor count will be doubled every 18 months
 Gordon Moore, Intel co-founder

15. Stored Program Concept
Von Neumann Model
Program is first stored in the memory and each instruction is then executed one by one by the processor.

16. Third Generation: Integrated Circuits
In second generation, discrete components such as transistors , resistors etc were manufactured separately and soldered on the circuit board.
This made the entire manufacturing process from transistor to circuit board cumbersome and expensive
Then Integrated circuits were introduced.
SSI circuits
LSI circuits
VSLI circuits
Later generations used LSI, VLSI and new technology.

17. Number System Binary Number System Decimal Number System
Data Representation
Number System
Binary Number System
Decimal Number System

18. What kinds of data do we need to represent?
Numbers – signed, unsigned, integers, floating point, complex, rational, irrational, …
Text – characters, strings, …
Images – pixels, colors, shapes, …
Sound - numbers
Logical – true, false
Instructions – strings of characters 18

19. How do we represent data in a computer?
At the lowest level, a computer is an electronic machine.
Works by controlling the flow of electrons
Easy to recognize two conditions:
Presence of a voltage – we’ll call this state “1”
Absence of a voltage – we’ll call this state “0” 19

20. Computer is a binary digital system
Finite number of symbols
Decimal Number system:
10 symbols, [0,9]
Binary (base two) system:
Has two symbols representing two stable states: 0 and 1 20

21. Physical devices used to store and process data in computers are two state devices like
semiconductor switches (ON/OFF)
Magnetic surface alignment (N-S,S-N)
Flip-flops ( low voltage, high voltage)

22. Bits and bytes Bits – binary digits (binary: only two possible values)
Byte – collection of bits
1 Byte = 8 Bits

23. Bits, Bytes, and Words A bit is a single binary digit (a 1 or 0).
A byte is 8 bits
A word is 32 bits or 4 bytes
Long word = 8 bytes = 64 bits
Quad word = 16 bytes = 128 bits
Programming languages use these standard number of bits when organizing data storage and access.

24. Bits, Bytes Unit Symbol Number of Bytes kilobyte KB 210 = 1024
MB 220 (over 1 million)
GB 230 (over 1 billion)
TB 240 (over 1 trillion)
Unit Symbol Number of Bytes
kilobyte
megabyte
gigabyte
terabyte

25. Bit Permutations
1 bit 1
2 bits 00 01 10 11
3 bits
000
001
010
011
100
101
110
111
4 bits
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Each additional bit doubles the number of possible permutations

26. Representation of Numbers
Binary Numbers
Unsigned Integers
Signed Magnitude
1’s Complement
2’s Complement

27. Unsigned Integers 101 329 Weighted positional notation
like decimal numbers: “329”
“3” is worth 300, because of its position, while “9” is only worth 9
101 22 21 20
1x4 + 0x2 + 1x1 = 5
most
significant
least
329
102
101
100
3x x10 + 9x1 = 329

28. Unsigned Integers (cont.)
An n-bit unsigned integer represents 2n values: from 0 to 2n-1. 22 21 20 1 2 3 4 5 6 7

29. Unsigned Binary Arithmetic
10111
+ 111
11110
carry
Base-2 addition – just like base 10
Add from right to left, propagating carry

30. Signed Integers With n bits, we have 2n distinct values.
Assign about half to positive integers (1 through 2n-1) and about half to negative (- 2n-1 through -1)
That leaves two values: one for 0, and one extra

31. Representation of Signed Integers Cont…
Ex: n = 3
Signed magnitude

32. Positive integers Negative integers Inference
Just like unsigned : zero in most significant (MS) bit = 5
Negative integers
Set MS bit to show negative, other bits are the same as unsigned = -5
Inference
MS bit indicates sign: 0=positive, 1=negative

33. Question
Given n bit string, What is the Maximum number we can represent in Signed Magnitude form? 1 .
2n-1
2n-2 22 21 20
The Max. value is : 2n-1 -1
The Min. value is : - 2n-1 -1
Ex: Given 5 bits,
Max. number in signed magnitude form is: =15
Min. number in signed magnitude form is: = -15

34. 1’s Complement Representation
Positive numbers representation is same as signed integers.
Negative numbers represented by flipping all the bits of corresponding positive numbers
For Example:
+5 is represented as 00101
-5 is represented by 11010

35. Example: 1’s Complement
How we represent -12 in 1’s complement form
Step1: Take +12 in binary representation 
Step2: Flip all the bits of the above 

36. Inference -12 representation in 1’s complement form: 10011

37. Limitations! Problems with sign-magnitude and 1’s complement!
Two representations of zero (+0 and –0)
Arithmetic circuits are complex to implement above representation

38. Two’s Complement Representation
If number is positive or zero
Normal binary representation
If number is negative
Start with positive number
Flip every bit (i.e., take the one’s complement)
Then add one

39. Example: + 1 + 1 11011 (-5) 10111 (-9) 00101 (5) 01001 (9)
00101 (5) (9)
11010 (1’s comp) (1’s comp)
11011 (-5) (-9)

41. Advantage of 2’s complement
Two’s complement representation is developed to make circuits easy for arithmetic.
For each positive number (X), assign value to its negative (-X), such that X + (-X) = 0 with “normal” addition, ignoring carry out
00101 (5) (9)
(-5) (-9)
00000 (0) (0)

42. Example:2+(-3) Express -3 in 2’s complement form: 3  00011
1’s Complement of 3 
2’s Complement of 3  i.e. -3
2 
-3 
11111

43. Interpret the result 11111 Look at MSB  1  the result is negative
What is the decimal equivalent of the result
Take 2’s complement of 11111
Flip the bits to get 1’s complement 0000
Add 1, we get 0001, hence the number is -1

44. 2’s Complement Signed Numbers23 22 21 20 1 2 3 4 5 6 7 23 22 21 20 1 -8 -7 -6 -5 -4 -3 -2 -1

45. Base conversion Convert a number from one number system to another
Binary to Decimal and Decimal to Binary
Decimal to Octal and Octal to Decimal
Octal to Binary and Binary to Octal
Binary to Hexadecimal and Hexadecimal to Binary

46. The Decimal Number System
The decimal number system is a positional number system.
Example:
X 100 =
X 101 =
6 X 102 = 600
5 X 103 = 5000

47. The Decimal Number System
The decimal number system is also known as base 10.
The values of the positions are calculated by taking 10 to some power.
Why is the base 10 for decimal numbers?
Because we use 10 digits, the digits 0 through 9.

48. The Binary Number System
Uses two symbols 0 and 1 to represent numbers
Hence base 2

49. The Binary Number System (con’t)
The binary number system is also a positional numbering system.
Example of a binary number and the values of the positions:

50. Total number of unique representations using n bits1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Total number of unique representations using n bits
A sequence of n bits has 2n possible unique representations.

51. Converting from Binary to Decimal
X 20 = 1
X 21 = 0
1 X 22 = 4
20 = = X 23 = 8
21 = = X 24 = 0
22 = = X 25 = 0
23 = X 26 =

52. Converting from Binary to Decimal
Class Assignment:
Binary Decimal
11101
100111
(1x24 + 1x23 + 1x22 + 0x21 + 1x20 )
= = 29

53. Converting Decimal Number to Binary Number
Make a list of the binary place values up to the number being converted.
Perform successive divisions by 2, placing the remainder of 0 or 1 in each of the positions from right to left.
Continue until the quotient is zero.
Example: 5510

54. Procedure for decimal to binary conversion
2 | 55_ 1 (LSB) 2 | | 13_ 1 2 | 6_ 0 2 | 3_ 1 2 | 1_ 1 (MSB) 0

55. Converting From Decimal to Binary
Class Assignment
Decimal Binary 82
107
-14
-329
(82)10=( )2
(107)10=( )2
(-14)10=(10010)2
(-329)10=( )2

56. HexaDecimal Number System
Base 16
16 distinct symbols
0-9,A,B,C,D,E,F
Convert binary number to hexadecimal number

57. (624)8 Decimal to Octal Example Divide the magnitude by 8
Record the remainder
Keep on dividing the quotient and record the remainders
Write the remainders in reverse order
Same as Decimal to Binary Conversion
Example
(404)10
(624)8

58. Octal to Decimal (6 X 82) + (2 X 81) + (4 X 80) Result is (404)10
Method is same as Binary to decimal conversion
Only the base changes to 8
Verify previous example
(624)8
(6 X 82) + (2 X 81) + (4 X 80)
Result is (404)10

59. Octal to Binary (110010100)2 Method I Method II Example
Convert Octal to Decimal
Then convert Decimal to Binary
Method II
Write 3-bit binary equivalent of each Octal digit in Octal Number
Example
(624)8
( )2

60. Binary to Octal (624)8 Group bits (3-bit group) from right to left
Convert each 3- bit group to each Octal digit
Example
(624)8

61. Hexadecimal Number System

63. Exercise Convert Hexadecimal Number to Binary Number ADF6 DB69 CA36
5678
DABC