Hardware

1
Hardware

• Reading Materials
• Chapter 4-5 of SG
• Optional Chapter 1-2 of A
• OUTLINE
• The Binary Digital Computer
• Binary Numbers
• Data Representation
• Boolean Circuits
• CPU and Program Execution
• Peripherals

2
Hardware

• Educational Goals To learn
• What are computers?
• Hardware machines on which to implement
  algorithms
• How computer are constructed?
• Computers are devices for computing logical
  functions (AND, OR, NOT, etc)
• Simple steps in this construction (eg OR)
• Building complex system from smaller (simpler)
  parts
• Computer are general purpose machines

3
Hardware Chapter Outline

• The Binary Digital Computer
• READING Sect. 4.1 to 4.2 of SG
• Organization of Digital Computers
• Why Binary Numbers / Computers
• Binary Numbers
• Data Representation
• Boolean Circuits
• CPU and Program Execution
• Peripherals

4
The Binary Digital Computer

• Organization of a Computer

5
Analog/Digital Computer

• Up to now, whatever we have discussed could
  equally well be discussed in the context of
  either digital or analog computations
• We shall concentrate on digital computer
• Specifically, binary computers
• BINARY two value (0 and 1) ON/OFF
• Why binary computers?
• Physical components transistors, etc
• Reliability of hardware components

6
Why use Binary Numbers?

• Reliability
• Represent only two values (0 and 1), ON/OFF
• High margin of error
• Nature of Hardware Devices
• Many devices are two-state devices
• Persistence of Digital Data
• Can store and preserve digital data better

7
Why Binary Computers Reliability

• Reliability
• computer store info using electronic devices
• electronic quantities measured by
• voltage, current, charge, etc
• These quantities are not always reliable!
• esp. for old equipments
• Also, the range of voltage changes with advances
  in hardware technology
• What if we want a decimal computer!
• need 10 different, distinct and STABLE levels
• (to represent 0, 1, 2, 3, , 9)
• Eg If voltage is between 0 and 90Volts,

8
Why Binary Computers

• Suppose we want a decimal computer
• Need to represent 10 digits (0, 1, 2, , 9)
• need 10 different, distinct and STABLE levels
• If voltage is between 0 and 90V (volts),
  then may use 0, 10, 20,,90 as digits
• Question How to store 37?
• But, the voltage is NOT reliable,
• eg Even a 10 drop in voltage can cause a
  6 (60V) to be a 5 (54V)!
• Binary numbers give better error margin

9
Why Binary Nature of Hardware Devices

• Many hw devices are two-state devices
• magnetized / demagnetized
• diskettes (3.5 floppy, Zip disks,)
• direction of magnetization (cw / ccw)
• CORE memory (main memory)
• charged / discharged capacitor

10
Why Digital (not Analog) More Durable

• Analog data poses difficulties
• very hard to store real numbers accurately
• or persistently (over time)
• eg old photographs, movie reels, books
• Solution Store them digitally
• CD player uses approximation
• instead of the exact frequency/volume (audio)
• But, the approx is good enough
• Our ears not sensitive enough to tell difference
• Once we have digital data (reliability)
• also, can use various algorithms (eg
  compression) for easier processing of the data.

11
Hardware Chapter Outline

• The Digital Computer
• Binary Numbers
• Decimal and Binary numbers
• From Decimal to Binary
• Adding and Subtracting Binary Numbers
• Data Representation
• Boolean Circuits
• CPU and Program Execution
• Peripherals

12
2. Binary Numbers (vs Decimal Numbers)

• Humans use Decimal number system
• 7809 7?103 8?102 0?101 9?100
• Each digit is from 0,1,2,3,4,5,6,7,8,9
• (we happen to have 10 fingers.)
• Computers use Binary number system
• (1101)2 1?23 1?22 0?21 1?20 13
• Each binary digit (bit) is 0,1
• (IT people have 1 finger/hand)
• Readings Section 4.2 of SG

13
Converting from Decimal to Binary

• Example 43
• Method (repeated divide by 2)
• 43 / 2 ---- Quotient 21 Remainder 1
• 21 / 2 ---- Quotient 10 Remainder 1
• 10 / 2 ---- Quotient 5 Remainder 0
• 5 / 2 ---- Quotient 2 Remainder 1
• 2 / 2 ---- Quotient 1 Remainder 0
• 1 / 2 ---- Quotient 0 Remainder 1
• (43)10 (101011)2

14
Exercise

• In the previous worked example on converting
  decimal numbers to binary, at the end of all the
  dividing-by-two, we collect the digits by going
  backwards! Why?
• Hint Try working this out yourself.
• Try going forward instead. What is the binary
  number you get. Convert it back to decimal and
  see what you will get. Use 6 and 4 as examples.
• Given a decimal number n (a positive integer), if
  we convert it to binary, we will need k digits.
  What is k in term of n?
• Hint Use the above process as a guide. We will
  keep dividing by 2 (and throw away the remainder)
  until we reach 0.

15
Decimal to Binary (2) -- Algorithm

• Algorithm Decimal-to-Binary(n)
• Input Decimal number (n)10
• Output Binary representation
• (n)10 (bk-1 bj b0)2
• let j ? 0
• let num ? n
• while (num 0) do
• bj ? num mod 2 // remainder
• num ? num div 2 // divide by 2
• j ? j 1
• endwhile
• Output B(bk-1 bk-2 b1 b0)

16
Exercise

• Exercise Algorithm Decimal-to-Binary on the
  following inputs. For each input, what is the
  output binary number and the value of k?
• (a) 8 (b) 13

17
For the mathematically inclined

• In General
• (n)10 (bk-1 bi b1b0)2
• where each bit bi is given by
• Number of bits k log2n
• Why is it log2n bits?

18
Rep using Binary Numbers

• More on binary number representation
• with 1 bit, can represent 2 numbers 0,1
• 2 bits ? 4 numbers, 0..3
• 00, 01, 10, 11
• 3 bits ? 8 numbers, 0..7
• 000, 001, 010, 011, , 110, 111
• 4 bits ? 16 numbers, 0..15
• 0000, 0001, 0010, , 1110, 1111
• With k bits ? 2k numbers, 0 .. 2k-1
• Typical computers today work with
• 16 or 32 bit numbers!

19
Add Subtract for Binary Numbers

• Similar to those for decimal (simpler)
• Actually, use the same algorithm!
• For each digit, we have
• 0 0 0
• 0 1 1
• 1 0 1
• 1 1 0 (with carry 1)
• Example
• 101101100
• 110101010

20
Hardware Chapter Outline

• The Digital Computer
• Binary Numbers
• Data Representation
• READ Sect. 4.2 of SG or Sect 1.4, 1.5, 1.7 of
  A
• Representing data numbers, characters
• Approximation for Real Numbers
• Analog Data (audio, video)
• Boolean Circuits
• CPU and Program Execution
• Peripherals

21
3. Representation of Data

• Computers process numbersbut also much more..
• non numeric data and text
• 0 1 9 a b z . (
• special control characters eg CR, tabs
• ASCII (American Standard Code for Information
  Interchange) as-kee
• uses 7 bit code for each character
• Usually, a 0 is added in front
• A is 01000001
• a is 01100001

22
Data Representation (2)

• Using ASCII codes, we can represent
• numbers, letters (as characters)
• Names of people, sentences
• as sequences of characters
• Hello World!
• Question how many chars in above msg?
• Represent instructions (eg ADD, SUB)
• we first assign them codes
• ADD 00
• SUB 01
• and then represent the codes..

23
Data Representation Analog Data?

• What about analog data?
• Why is analog data problematic?
• How to represent (2.1)10 in binary?
• (10.1)2 (2.5)10
• (10.01)2 (2.25)10
• (10.001)2 (2.125)10
• (10.0001)2 (2.0625)10
• (10.00011)2 (2.09375)10
• (10.000111)2 (2.109375)10
• CANNOT represent (2.1)10 exactly in binary!!
• We can only give an approximation.
• Accuracy depends on the number of bits

24
Data Representation..

• Analog data (eg video, audio data)
• can be represented as digital data
• using approximation
• via a digitization process
• Accuracy depends on number of bits!
• the more bits, the more accurate

25
Number Representations

• Read up on
• Signed magnitude numbers
• floating point representation of real numbers
• Mantissa, exponent
• Readings Section 4.? of SG

26
Hardware Chapter Outline

• The Binary Digital Computer
• Binary Numbers
• Data Representation
• Boolean Circuits
• READING Sect. 4.3 to 4.5 of SG Notes
• Basic Gates, Truth Tables
• Combinatorial Circuits
• Sequential Circuits
• CPU and Program Execution
• Peripherals

27
4. Boolean Circuits

• Computer operations based on logic circuits
• Logic based on Boolean Algebra
• Logic circuits have
• inputs (each with value 0 or 1) T/F
• outputs
• state
• Type of Logic Circuits
• Combinational circuits output depends only on
  input
• Sequential circuits output depends also on past
  history (get sequence of output)
• GATES Basic Building Blocks for Circuits

28
Basic Logic Gates (and Truth Tables)

• AND Gate
• OR Gate
• NOT Gate

29
Whats inside a Gate?

• Gate made of physical components
• called transistors
• A transistor is formed by sandwiching a p-type
  silicon between two n-type silicon or vice versa.
• In this course, we do not need to deal with the
  details of whats inside a Gate.

30
Combinational Circuits

• Built using a combination of logic gates
• output depends only on the input
• can also be represented by its truth table
• Examples
• C (A B)
• D AB (A B)
• G A (B C)

31
Combinational Circuits
Logic Circuit
Truth Table
32
Logic Circuits An aside

• Possible Interpretation of G
• Sound the buzzer if
• temperature of engine exceeds 200F, or
• car is in gear and drivers seat-belt is not
  buckled
• We define
• G Sound buzzer
• A Temperature of engine exceeds 200F
• B Car is in gear
• C drivers seat-belt is buckled
• G A (B C)
• HW Give other interpretations

33
Manipulation with Logical Expressions

• Can manipulate logical expression
• subject to Algebraic Laws (Boolean algebra)
• Examples
• Commutative Laws
• (A B) (B A)
• A B B A (Note Shorthand A B as AB)
• Associative Laws
• A (B C) (A B) C
• A (B C) (A B) C
• Distributive Laws
• A (B C) (A B) (A C)
• A (B C) (AB) (AC)

34
Can Prove Laws using Truth Tables

• Can use the truth tables to prove laws
• (AB) (A) (B) DeMorgans Law

35
HW Prove the following laws

• Using Truth tables or otherwise
• (A B) A B DeMorgans Law
• (AB) (AC) A B C Distributive Law
• A A 1 A A 0
• A 1 A A 1 1
• A A B A Absorption Law
• A (A B) A Absorption Law

36
From Truth Table ? Logic Circuits
Output function X A(B)C AB(C)
ABC

• Each row in the table is a logical term
• X A(B)C AB(C) ABC A(B)C AB(C
  C) A(B)C AB

37
More Basic Logic Gates

• XOR Gate
• NAND Gate

38
Logical Completeness

• , , is logically complete
• , is logically complete
• (p q) ( (p) (q) )
• , is logically complete
• , is NOT logically complete
• NAND is logically complete
• (p NAND p) (p)
• (p NAND q) (p q)

39
Design of a One-Bit Adder

• Add two 1-bit numbers
• A B S (with carry-bit C)
• Logic Circuits
• S A ? B C A B

40
Design of an n-bit Full-Adder

• A full n-bit Adder consists of
• consists of n half-adders in stages
• eg A 3-bit Full-Adder
• consists of 3 half-adder
• (An example of design decomposition)

41
Design of A Half-Adder

• Half adder circuit
• Input Ai, Bi, Ci
• Output Si, Ci1
• Design HW problem

42
Sequential Circuits

• Circuits that can store information
• Built using a combination of logic gates
• output depends on the input, and
• the past history (state of the circuit)
• can also be represented by its truth table
• Example
• Initially, SetReset0
• Set1 ? State1
• Reset1 ? State0

43
Basic Sequential Circuit

• Flip Flop (Logical View)
• Memory Element
• State 0 or 1
• Change of state controlled byinput signal at
  each TIME STEP
• Flip Flop
• Initially, Set Reset 0
• If we momentarily let Set1, then Output1
• The value of Output 1 will persist
• even if the value of Set goes back to 0
• If we momentarily let Reset1, Output0
• Value persist even if Reset goes back to 0
• THEREFORE, can use Flip-Flop as Memory Unit
• Stores 1-bit info (State 0 or 1)

44
Hardware Chapter Outline

• The Binary Digital Computer
• Binary Numbers
• Data Representation
• Boolean Circuits
• CPU and Program Execution
• READING Sect. 5.1 and 5.2 of SG
• Memory Unit
• CPU and its Components
• Execution of Stored Program
• Peripherals

45
The Binary Digital Computer

• Organization of a Computer

46
Memory

• the functional unit that stores
• instructions (programs) and
• data
• Primary Memory Types
• RAM (Random Access Memory)
• Read/Write, Volatile
• ROM (Read Only Memory)
• Read only, permanent

47
Memory Unit Organization

• Bit, Byte implemented by flip-flops
• Each flip-flop is a one-bit memory (can be 0 or
  1)
• one Byte is a series of 8 flip-flops (8-bits)
• Memory made up of
• A large array of fixed size cells
• Each cell consists of 8 bits (called bytes)
• Each cell has an address
• Address are represented as bit-strings
• Eg 10-bits can address 210 1K memory cells
• while 20-bit address can rep. 220 1MB memory
• (Recall, k bits can address 2k memory cells)
• Memory and Registers
• registers are similar memory cells
• but built into the CPU (faster access)

48
Memory Unit -- Operations

• Data Transfers
• Need Registers
• MAR (Memory Address Register) for the address
  of the memory being accessed
• MDR (Memory Data Register) for data to be
  written to memory or read from the memory
• Need Instructions
• FETCH instr to read content of a memory
  location
• (fetch some data from memory)
• STORE instr to write a value to a memory
  location
• (store some data into memory)
• implemented via digital circuitry

49
Recap

• Have seen how
• logic gates and flip-flops can be used to form
  combinational and sequential circuits
• Any logic/arithmetic functions (operations) can
  be implemented this way
• But, then the functions will be hard-wired.
• Need a different computer for each new job!!
• Instead, we want a general purpose computer
• computer runs a STORED program
• function of the computer varies according to
  the different STORED program
• the stored program is arbitrary ? general purpose
  computer
• Basic Architecture Von-Neumann Architecture

50
CPU (Central Processing Unit)

• Components of a CPU
• Control Unit the brain of the CPU.
• decoding which operation is to be performed, and
• deciding the next operation to perform
• ALU (Arithmetic Logic Unit)
• consists of logic circuits for addition,
  multiplication, and all other operations
• Buses wire connecting
• wires connecting up different parts of CPU, and
  the CPU to other components
• Each component is built using logic circuits

51
CPU Execution Example W X Y

• To add two numbers stored in X and Y and store
  the result in W
• CPU performs the following steps

• Place address of first number (X) in MAR
• Issue a FETCH command to Memory Unit
• Transfer content of MDR to Register R1
• Place address of second number (Y) in MAR
• Issue a FETCH command to Memory Unit
• Transfer contents of MDR to Register R2
• Issue a ADD command to ALU to perform addition
  of numbers in registers R1 R2 and place result
  in register R3
• Transfer contents of R3 to MDR
• Place address of result (W) in MAR
• Issue a STORE instruction to Memory Unit

52
Functioning of a CPU

• The steps above illustrates
• basic technique for CPU to execute simple
  instructions
• similar technique is used for all other
  instructions
• ANALOGY If we have buttons for the CPU
  functions, then a human can press the appropriate
  button to execute the above step
• In real computers, the
• role of human is performed by the Control Unit,
• role of buttons by using control signals
• Control Unit is also responsible for
• decoding the instruction,
• figuring out the next instruction, etc

53
CPU Instruction Execution

• The CPU repeatedly execution the following
  instruction cycle

• CPU Instruction Execution Cycle
• Fetch instruction from Memory
• Decode the instruction
• Execute the instruction (including determining
  the next instruction to be executed)

54
CPU Instruction Execution (2)

• Fetch instruction from Memory
• Decode the instruction

• PC (Program Counter) contains the address of the
  next instruction
• Place the address on MAR
• Send FETCH command to Memory Unit
• Get the instruction from MDR
• Transfer to Instruction Register (IR)

• Generate list of micro-instructions to be
  executed (see example of ADDING two numbers)

55
CPU Instruction Execution (3)

• Execute the instruction
• including setting up for the next instruction to
  be executed

• The sequencer keeps track of which
  micro-instruction is to be executed in which
  order
• Set up the next instruction to be executed
• Normally, PC ? PC 1
• May be different when if-then-else or
  for/while are used

56
Peripheral Devices

• Other Devices that augments the CPUmemory
• I/O Keyboard, mouse, monitor, printers,
  speakers,
• Storage Cache, Disk drives, CD-drive, Zip-drive,
  tapes
• Communication Network cards, modems,
• Devices communicate with CPU via controllers
• usually some kind of circuit board (eg sound
  cards)
• Also,
• I/O devices vary greatly
• Can Dynamically added/removed devices
• Flexible Design needed to allow easy addition /
  removal / upgrading
• Design may be sub-optimal.
• Flexibility often more important than optimality.

57

• If you are new to all these
• read the textbook
• do the exercises in the book
• The End