Chapter 1 The Big Picture QUIZ Explain the

Chapter 1 The Big Picture

QUIZ Explain the abstractions we normally apply when using the following systems: DVD player Registering for classes on Duck. Trax Walking In each case, explain what is the internal view and what is the abstract view. 2 5

QUIZ Explain the abstraction applied in browsing the WWW: • What is the internal view? • What is the abstract view? 3

QUIZ Connect each generation of computer hardware with its defining technology: 1 st Gen. 2 nd Gen. 3 rd Gen. 4 th Gen. 5 th Gen. ICs Multi-core processors LSI, VLSI Vacuum tubes Transistors 4

Practice Flashcards on the text website 5

Chapter 2 Binary Values and Number Systems

Converting Binary to Decimal What is the decimal equivalent of the binary number 1101110? 11011102 = ? ? ? 10 7 13

Converting Binary to Decimal What is the decimal equivalent of the binary number 1101110? 1 x 26 = 1 x 64 = 64 + 1 x 25 = 1 x 32 = 32 + 0 x 24 = 0 x 16 = 0 + 1 x 23 = 1 x 8 = 8 + 1 x 22 = 1 x 4 = 4 + 1 x 21 = 1 x 2 = 2 + 0 x 2º = 0 x 1 = 0 = 110 in base 10 8 13

QUIZ: 100110102 = ? ? ? 10 9

Converting Hexadecimal to Decimal What is the decimal equivalent of the hexadecimal number DEF? D x 162 = 13 x 256 = 3328 + E x 161 = 14 x 16 = 224 + F x 16º = 15 x 1 = 15 = 3567 in base 10 10

QUIZ: 2 AF 16 = ? ? ? 10 11

Converting Octal to Decimal What is the decimal equivalent of the octal number 642? 6428 = ? ? ? 10 12 11

Converting Octal to Decimal What is the decimal equivalent of the octal number 642? 6 x 82 = 6 x 64 = 384 + 4 x 81 = 4 x 8 = 32 + 2 x 8º = 2 x 1 = 2 = 418 in base 10 13 11

QUIZ: Convert to decimal 1101 00112 = ? ? ? 10 AB 716 = ? ? ? 10 5138 = ? ? ? 10 6928 = ? ? ? 10 14

Addition QUIZ 1010110 +1 0 0 1 1 Carry values go here Check in base ten! 15 14

Subtraction QUIZ Borrow values 1011000 - 110111 Check in base ten! 16 15

Repeated division QUIZ Convert 4210 to binary 42 2 = 4210 = rem. 2 17 19

Converting Binary to Octal • Mark groups of three (from right) • Convert each group 10101011 10 101 011 2 5 3 10101011 is 253 in base 8 18 17

Converting Binary to Hexadecimal • Mark groups of four (from right) • Convert each group 10101011 1010 1011 A B 10101011 is AB in base 16 19 18

Counting Count from 5 to 17 in binary. Place the numbers in a table. 20

Converting Octal to Hexadecimal Convert octal 253 into hex. 21 18

Converting Octal to Hexadecimal Convert octal 253 into hex. 10 101 011 2 5 3 253 in base 8 1010 1011 A B = AB in base 16 22 18

Quiz on Ch. 2 Convert 201023 to decimal

Chapter 03 Data Representation

Quiz A video file is originally 3. 5 GB long. We compress it to 490 MB. What is the compression ratio? 25

Quiz A digital thermometer has a scale from 50 to 100 degrees (F). The temperature is represented on 7 bits. What is the smallest temperature difference that it can measure? 26

QUIZ How many bits are needed to represent all the courses you’re planning to take in college? 27

QUIZ Given the following representations, find in each case what actual number is being represented: 51 52 96 47 28

EXTRA-CREDIT QUIZ If the representation is 76, what actual number is being represented? 29

QUIZ What is the representation for each of these actual numbers? -48 -40 -30 -5 30

Let’s use ten’s complement! To perform addition, add the numbers and discard any carry Now you try it 48 -1 47 (signed-magnitude) How does it work in the new scheme? 31

Adding two negative numbers Try these: 4 -4 - 3 +3 + -3 32

QUIZ What is the 8 -bit two’s complement representation of these numbers? -13 40 33

QUIZ Perform the following operation in 8 -bit two’s complement: 40 – 13 34

Trick QUIZ What decimal number does this binary number represent? 1001 1110 35

Converting fractions from binary to decimal Easy! Just multiply with the powers of 2, as we did for unsigned binary. Only difference is that now the powers are negative. Example: . 10012 = 0. 10 36

QUIZ Convert: . 10112 = 0. 10 37

Converting fractions from decimal to binary Remember the repeated division algorithm? We apply it for the integer part of the number. To covert the fractional part, we use the repeated multiplication algorithm! Example: 0. 43510 = 0. 2 38

QUIZ Convert: 0. 310 = 0. 2 39

QUIZ Finite decimal fractions may have infinite binary representation! 0. 310 = 0. 010011 2 Stop after 8 bits! 40

QUIZ Convert to floating point and to scientific notation: 123. 332 = -0. 0034 = 0. 0 = 41

QUIZ Encode “Hello, world!” in ASCII Decode 67 83 32 49 49 48 from ASCII 42

Huffman decoding QUIZ Decode: 1011111001010 43

QUIZ Explain the similarities and differences between 00 FF 00 and 008800 44

Extra-credit question True. Color A 24 -bit color depth: eight bits used for each number in an RGB value How many different colors can be represented in True. Color? Please show your work. 45

QUIZ Are these Hi. Color or True. Color? 46

Extra-credit question How many bits are needed to represent this palette? Please show your work. 47

3. 6 Representing Video The problem: huge amount of data! Example: In HDTV, the Frame size is defined as the number of horizontal pixels × number of vertical pixels: 1280 × 720 1920 × 1080 Calculate: 1] Data rate (bits per second) for 25 fps 2] Size (bytes) of 2 -hour movie 48

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

QUIZ: recognize the gate! 50

QUIZ: elementary properties A AND 0 = ? A AND 1 = ? Etc. 51

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! 52

QUIZ Draw the gate symbols for: 4 -input OR 5 -input NAND 3 -input NOR 4 -input XOR Figure 4. 7 Various representations of a three-input AND gate 53

QUIZ Draw the gate symbols for: 4 -input OR 5 -input NAND 3 -input NOR 4 -input XOR How many lines does each of the truth tables have? Figure 4. 7 Various representations of a three-input AND gate 54

QUIZ Draw the gate symbols for: 4 -input OR 5 -input NAND 3 -input NOR 4 -input XOR How many lines does each of the truth tables have? Describe in your own words each of the truth tables. Figure 4. 7 Various representations of a three-input AND gate 55

QUIZ A computer represents numbers in 8 -bit two’s complement. Design a circuit that will detect the number zero (the output of the circuit becomes 1 if and only if all 8 bits are 0): 0 0 0 0 Figure 4. 7 Various representations of a three-input AND gate 56

Extra-credit QUIZ A computer represents numbers in 8 -bit two’s complement. Design a circuit that will detect the number -128 Hint: -128 is 1000 0000 in two’s comp. 1 0 0 0 0 Figure 4. 7 Various representations of a three-input AND gate 57

From gates to circuits 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 presented last time? 58

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: Draw the diagram: 59

QUIZ The AND gate is obtained as a NAND followed by an inverter. Draw its transistor diagram! 60

QUIZ Draw its switch diagram. Show the states of all switches for V 1 = 0 and V 2 = 1. 61

De. Morgan’s law QUIZ Apply De. Morgan’s Law directly on the gate diagrams below to obtain equivalent circuits: 62

QUIZ The XOR operation can be implemented with AND, OR and NOT gates: =A’B+AB’ How many transistors are required for the XOR gate? 63

QUIZ Connect the MUX input to implement a prime number detector (i. e. the output F is 1 iff S 2 S 1 S 0 are the binary code of a prime number) 64

S – R latch “forbidden” inputs What happens if both S and R are activated (made 0) at the same time? 65

Use a MUXes as “lookup tables” to implement the 1 -bit adder 66

Show a MUX with only 4 data inputs works Assume S 1 = 0, S 0 = 1. Draw the equivalent circuit in this case and explain the value of the output q. 67

Extra-credit How many transistors are needed to build this MUX? 68