QUIZ. What do these bits represent?

Transcription

1 QUIZ What do these bits represent?

2 QUIZ What do these bits represent? Unsigned integer: Signed integer (2 s complement): Fraction: IBM 437 character: Latin-1 character: Huffman-compressed text: Red-color level: 2

3 QUIZ What do these bits represent as Huffmancompressed text?

4 QUIZ What do these bits represent as Huffmancompressed text? L D? Bits from the next byte 4

5 QUIZ: Audio Formats MP3 analyzes the frequency spread and discards information that can t be heard by MOST humans (>16 khz) How many MP3 samples are there in a 4-minute song? After Huffman encoding, the average bits-per-sample has decreased from 8 to 5. What is the total size of the file? 5

6 All hail the HARDWARE! Chapter 4 Gates and Circuits (with some transistors thrown in for good measure)

7 Abstractions and more abstractions You are here 7

8 Abstractions and more abstractions Computers Made of lots of different circuits (CPU, memory, controllers, etc.) Circuits Made from gates combined to perform more complicated tasks Gates Devices that perform basic logical operations on electrical signals. They re built out of transistors Transistors Very small electronic switches 8

9 There are 3 layers of computer abstraction that we examine in this chapter: Circuits Gates Transistors 9

10 4.2 Gates There are six basic gates: NOT AND OR XOR NAND NOR Real-life logic diagrams are black and white with gates distinguished only by their shape We use color for emphasis (and fun) in this text 10

11 How do we describe the behavior of gates and circuits? 1. Boolean expressions Uses Boolean algebra, a mathematical notation for expressing two-valued logic 2. Logic diagrams A graphical representation of a circuit; each gate has its own symbol 3. Truth tables A table showing all possible input value and the associated output values 11

12 NOT Gate (a.k.a. inverter) A NOT gate accepts one input signal (0 or 1) and returns the opposite signal as output Figure 4.1 Various representations of a NOT gate 12

13 AND Gate An AND gate accepts two input signals If both are 1, the output is 1; otherwise, the output is 0 Figure 4.2 Various representations of an AND gate 13

14 QUIZ: AND Gate The inputs to an AND gate have the values A = 1 and B = 0. What is the output? 14

15 QUIZ: AND Gate The input B to an AND gate has the value B = 0. What is the output? 15

16 QUIZ: AND Gate The input B to an AND gate has the value B = 1. What is the output? 16

17 Conclusion: the AND gate has the following interesting properties A AND 0 = 0, irrespective of B A AND 1 = A 17

18 OR Gate An OR gate accepts two input signals If both are 0, the output is 0; otherwise, the output is 1 Figure 4.3 Various representations of a OR gate 18

19 XOR Gate If both inputs are the same, the output is 0; otherwise, the output is 1 XOR is called the exclusive OR Pronunciations: zor, ex-or 19

20 QUIZ: recognize the gate and draw its symbol! 20

21 QUIZ: elementary properties A AND 0 =? A AND 1 =? 1 AND B =? A OR 1 =? A XOR 0 =? A XOR 1 =? 21

22 Quiz XOR For the following circuit diagram: Find the Boolean expression Find the truth table NOT X X = 22

23 Quiz For the following circuit diagram: Find the Boolean expression Find the truth table X X = 23

24 Quiz For the following circuit diagram: Find the Boolean expression Find the truth table X X = 24 EOL 1

25 Quiz For the following circuit diagram: Find the Boolean expression Find the truth table X X = 25

26 NAND Gate If both inputs are 1, the output is 0; otherwise, the output is 1 Compare to AND:

27 Quiz Can we make a AND gate out of an NAND and an INVERTER? 27

28 Quiz Can we make a NAND gate out of an AND and an INVERTER? (A B) (A B) = A B 28

29 QUIZ Can we build an inverter (NOT) from a NAND gate? 29

30 QUIZ Can we build an inverter (NOT) from a NAND gate? Figure 4.7 Various representations of a three-input AND gate 30

31 NOR Gate If both inputs are 0, the output is 1; otherwise the output is 0 Compare to OR: 31

32 Quiz Can we make an OR gate out of a NOR and an INVERTER? 32

33 Not in text Whatever happened with the inverted XOR? It s called XNOR, pronounced [ex-nor] 33

34 Review of Gates A NOT gate inverts its single input An AND gate produces 1 iff both input values are 1 An OR gate produces 0 iff both input values are 0 A XOR gate produces 0 iff input values are the same If and only if All inverted gates have the opposite outputs It s OK to put the gate representations on your memory-sheet, but you should be able to remember the word descriptions above! 34

35 Quiz What are the 3 ways we use to describe gates and circuits? Use the 3 ways to describe the NAND gate Hint: Describe AND first! 35

36 Gates with More Inputs A three-input AND gate produces an output of 1 iff all input values are 1 36

37 QUIZ Draw the gate symbols for: 4-input OR 5-input NAND 3-input NOR 37

38 QUIZ Draw the gate symbols for: 4-input OR 5-input NAND 3-input NOR How many lines does each of the truth tables have? 38

39 QUIZ Draw the gate symbols for: 4-input OR 5-input NAND 3-input NOR How many lines does each of the truth tables have? Describe in your own words each of the truth tables. 39

40 Extra-credit QUIZ 40 EOL 2

41 Remember: There are 3 layers of computer abstraction that we examine in this chapter: Circuits Gates Transistors 41

42 4.3 Constructing Gates Transistor = device that acts either as a wire that conducts electricity or as a resistor that blocks the flow of electricity, depending on the voltage level of an input signal Made of a semiconductor material Neither good conductor of electricity nor a good insulator but with a little help can be either! Acts like a switch, but w/o moving parts: Switch open Switch closed 42

43 How transistors operate as switches High voltage, a.k.a. + Base or gate Low voltage, a.k.a. - When 1 is applied on the base/gate, the switch closes When 0 is applied on the base/gate, the switch opens 43

44 Transistors Figure 4.8 The connections of a transistor A transistor has three terminals: A collector/source, typically connected to the positive terminal of a power source (5 volts, 3.5 volts, etc.) An emitter/drain, typically connected to the ground (0 volts) A base/gate, which controls the flow of current between source and emitter 44

45 The names of transistor terminals -setting the record straight FYI- Bipolar Junction Transistor (BJT) Collector, Base, Emmiter Field-Effect Transistor (FET) Drain, Gate, Source Mongrel transistor (our text) 45

46 The easiest gates to create are the NOT, NAND, and NOR We can explain their operation for any combination of inputs! We do this by replacing the transistors with switches! 46

47 If there is no path from output to Ground, V out = 1 If there is a path from output to Ground, V out = 0 47

48 QUIZ The AND gate is obtained as a NAND followed by an inverter. Draw its transistor diagram! 48

49 QUIZ: Transistors What gate do we have below? 49

50 QUIZ: Transistors What gate do we have below? 50

51 To do for next time: Read pp of text Answer in notebook the end-of-chapter questions: 1 through 11 EOL3 51

52 QUIZ: Review of Gates A NOT gate An AND gate An OR gate A XOR gate All inverted gates 52

53 QUIZ: Based on the switching behavior of transistors, verify the truth table of the OR gate Remember: connection to Ground means logical zero! 53

54 4.4 Intro: From gates to circuits We can go either way between gates and circuits, e.g. Analysis Find the truth table for the circuit: X 54

55 From gates to circuits Design Find the logic diagram of the circuit described by the following truth table: 1 0? Hint: The table is similar to which of the fundamental gates? 55

56 SOLUTION Having only one 0 in the output column, the circuit most resembles the OR gate! It is different from the OR gate only in this respect: Write the Boolean expression: 56

57 SOLUTION Write the Boolean expression: Draw the circuit diagram: X = A + B 57

58 SOLUTION Write the Boolean expression: Draw the diagram: X = A + B 58

59 4.4 Circuits Combinational circuit The input values explicitly determine the output Remember: We describe the circuit operations using Boolean expressions Logic diagrams Truth tables 59

60 Combinational Circuit AB+AC Three inputs require 2 3 = 8 rows to describe all possible input combinations Boolean expression is: 60

61 Another Combinational Circuit 61

62 Another Combinational Circuit Consider the following Boolean expression A(B + C) Does this truth table look familiar? 62

63 Circuit equivalence: Two circuits that produce the same output for identical input are called equivalent Boolean algebra allows us to apply provable mathematical principles to help design circuits: A(B + C) = AB + AC (distributive law) so circuits must be equivalent 63

64 Each property (law) of Boolean Algebra translates directly into a property of equivalent circuits! Null elements A 0 = 0 A + 1 = 1 Idempotency A A = A A + A = A Double complement (A ) = A 64

65 De Morgan s Laws Null elements A 0 = 0 A + 1 = 1 Idempotency A A = A A + A = A Double complement (A ) = A 65

66 DeMorgan s law applied directly to gates 66

67 DeMorgan s law QUIZ Apply DeMorgan s Law directly on the gate diagram below to obtain equivalent circuits: 67

68 DeMorgan s law QUIZ Apply DeMorgan s Law directly on the gate diagram below to obtain equivalent circuits: 68

69 QUIZ: Write the circuit forms for all Boolean properties in this table! (left and right) Null elements A 0 = 0 A + 1 = 1 Idempotency A A = A A + A = A Double complement (A ) = A 69

70 Extra-credit QUIZ 70

71 Very Useful Combinational Circuit: the Adder At the digital logic level, addition is performed in binary Addition operations are carried out by special circuits called adders 71

72 Half-Adder truth table The result of adding two binary digits could produce a carry value Recall that = 10 in base two Half adder A circuit that computes the sum of two bits and produces the correct carry bit Truth table Do you recognize these outputs? 72

73 Half Adder Circuit diagram Boolean expressions Sum = A B Carry = A B How many transistors are here? 73

74 Full Adder This adder takes the Carry-in value into account! Do you recognize these circuits? 74

75 Adding multiple bits - Ripple Carry Adder - 75

76 SKIP Multiplexers EOL4 76

77 There are 2 basic types of circuits Combinational circuit The input values explicitly determine the output Sequential circuit The output is a function of the input values and the existing state of the circuit 77

78 4.5 Circuits as Memory a.k.a. Sequential Circuits A sequential circuit is one whose output depends not only on the current values of its inputs, but also on the past sequence of those inputs (history). It can be used to store information, i.e. as memory. 78

79 The S R latch There are several ways to build S R latches using various kinds of gates, but there s always feedback. Figure 4.12 An S-R latch How many transistors are here? 79

80 The S R latch Figure 4.12 An S-R latch 80

81 S R latch The value of X at any point in time is considered to be the state of the circuit Figure 4.12 An S-R latch If X is 1, we say that the circuit is storing a 1; if X is 0, the circuit is storing a 0 As long as S = R = 1, an S-R latch stores a single binary digit,1 or 0. The design guarantees that the two outputs X and Y are (almost always) complements of each other. 81

82 Set means make 1, Reset means make 0 To make X = 1, make S = 0 (while keeping R = 1). To make X = 0, make R = 0 (while keeping S = 1). 82

83 QUIZ: S R latch What happens if both S and R are made 0 at the same time? 83

84 Integrated Circuit (a.k.a. IC or chip) = A piece of silicon on which multiple gates have been embedded Silicon pieces are mounted on a plastic or ceramic package with pins along the edges that can be soldered onto circuit boards or inserted into appropriate sockets 84

85 Integrated Circuits Integrated circuits (IC) are classified by the number of gates contained in them 3 rd gen. 4 th gen. 5 th gen. VVLSI (?) more than 1B 85

86 Integrated Circuits Figure 4.13 An SSI chip containing NAND gates How many transistors are here? VLSI chip: AMD Phenom II CPU contains 768 million transistors 86

87 As of 2014, the highest transistor count in a commercially available CPU is over 4.3 billion transistors, in Intel's 15-core Xeon IvyBridge- EX. On August 7, 2014, IBM announced their second generation SyNAPTIC chip, which contains the most transistors in a Neurosynaptic chip to date: 5.4 billion. Xilinx currently holds the "world-record" for a FPGA containing more than 20 billion transistors. Pricing ranges from $1200 to $6800 per chip and with up to 8 per server, that can get costly but is only part of the puzzle. Each chip can address up to 1.5TB of memory meaning that in an 8 processor configuration one could get up to 12TB of RAM. Source: Source: 87

88 The most important integrated circuit in any computer is the Central Processing Unit, or CPU motherboard CPU Each CPU chip has a large number of pins through which communication takes place in a computer system 88

89 Each CPU chip has a large number of pins (Pin Grid Array = PGA) through which communication takes place Image source: 89

90 Extra-credit Image source: 90

91 Image source: Image source: Latest packaging technology: Ball Grid Array = BGA 91

92 Chapter review questions Identify the basic gates and describe the behavior of each Includes the inverted gates! Describe how gates are implemented using transistors Combine basic gates into circuits Analysis vs. design Describe the behavior of a gate or circuit using Boolean expressions, truth tables, and logic diagrams 92

93 Chapter review questions Write demorgan s laws in Boolean form and in circuit form Compare and contrast a half adder and a full adder Explain how an S-R latch operates Describe the characteristics of the four (five?) generations of integrated circuits What is the CPU? 93

94 Homework due Wednesday, March 2 End-of-chapter 37, 48, 49, 50, 62, 66, 70, 72, 73 Thought question #4 94