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

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

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

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?

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?

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

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.

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 0001 011 010 000 001 – machine equivalent of ADD instruction

History of Computers

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

First Generation Computer made of Vacuum tubes

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.

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

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: 1.328 billion, 2006 42 millions 2,250 Exponential growth Transistor count will be doubled every 18 months  Gordon Moore, Intel co-founder

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.

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.

Number System Binary Number System Decimal Number System Data Representation Number System Binary Number System Decimal Number System

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

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

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

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)

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

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.

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

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

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

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 3x100 + 2x10 + 9x1 = 329

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

Unsigned Binary Arithmetic 10010 10010 1111 + 1001 + 1011 + 1 11011 11101 10000 10111 + 111 11110 carry Base-2 addition – just like base 10 Add from right to left, propagating carry

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

Representation of Signed Integers Cont… Ex: n = 3 Signed magnitude 000 +0 001 +1 010 +2 011 +3 100 -0 101 -1 110 -2 111 -3

Positive integers Negative integers Inference Just like unsigned : zero in most significant (MS) bit 00101 = 5 Negative integers Set MS bit to show negative, other bits are the same as unsigned 10101 = -5 Inference MS bit indicates sign: 0=positive, 1=negative

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: 24 -1 =15 Min. number in signed magnitude form is: -24 -1= -15

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

Example: 1’s Complement How we represent -12 in 1’s complement form Step1: Take +12 in binary representation  01100 Step2: Flip all the bits of the above  10011

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

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

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

Example: + 1 + 1 11011 (-5) 10111 (-9) 00101 (5) 01001 (9) 00101 (5) 01001 (9) 11010 (1’s comp) 10110 (1’s comp) + 1 + 1 11011 (-5) 10111 (-9)

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) 01001 (9) + 11011 (-5) + 10111 (-9) 00000 (0) 00000 (0)

Example:2+(-3) Express -3 in 2’s complement form: 3  00011 3  00011 1’s Complement of 3  11100 2’s Complement of 3  11101 i.e. -3 2  00010 -3  11101 11111

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

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

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

The Decimal Number System The decimal number system is a positional number system. Example: 5 6 2 1 1 X 100 = 1 103 102 101 100 2 X 101 = 20 6 X 102 = 600 5 X 103 = 5000

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.

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

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: 1 0 0 1 1 0 1 26 25 24 23 22 21 20

Total number of unique representations using n bits 1 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.

Converting from Binary to Decimal 1 0 0 1 1 0 1 1 X 20 = 1 26 25 24 23 22 21 20 0 X 21 = 0 1 X 22 = 4 20 = 1 24 = 16 1 X 23 = 8 21 = 2 25 = 32 0 X 24 = 0 22 = 4 26 = 64 0 X 25 = 0 23 = 8 1 X 26 = 64 7710

Converting from Binary to Decimal Class Assignment: Binary Decimal 11101 1010101 100111 (1x24 + 1x23 + 1x22 + 0x21 + 1x20 ) =16 + 8 + 4 + 0 + 1 = 29

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 25 24 23 22 21 20 32 16 8 4 2 1 1 1 0 1 1 1

Procedure for decimal to binary conversion 2 | 55_ 1 (LSB) 2 | 27 1 2 | 13_ 1 2 | 6_ 0 2 | 3_ 1 2 | 1_ 1 (MSB) 0

Converting From Decimal to Binary Class Assignment Decimal Binary 82 107 -14 -329 (82)10=(1010010)2 (107)10=(1101011)2 (-14)10=(10010)2 (-329)10=(1010110111)2

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

(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

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

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 (110010100)2

Binary to Octal (624)8 Group bits (3-bit group) from right to left Convert each 3- bit group to each Octal digit Example 110010100 (624)8

Hexadecimal Number System

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