Chapter 1 The Big Picture

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

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.ICs 2 nd Gen.Multi-core processors 3 rd Gen.LSI, VLSI 4 th Gen.Vacuum tubes 5 th Gen.Transistors 4

Practice Flashcards on the text websiteFlashcards 5

Chapter 2 Binary Values and Number Systems

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

Converting Binary to Decimal 8 What is the decimal equivalent of the binary number ? 1 x 2 6 = 1 x 64 = x 2 5 = 1 x 32 = x 2 4 = 0 x 16 = x 2 3 = 1 x 8 = x 2 2 = 1 x 4 = x 2 1 = 1 x 2 = x 2º = 0 x 1 = 0 = 110 in base 10 13

QUIZ: = ??? 10 9

Converting Hexadecimal to Decimal 10 What is the decimal equivalent of the hexadecimal number DEF? D x 16 2 = 13 x 256 = E x 16 1 = 14 x 16 = F x 16º = 15 x 1 = 15 = 3567 in base 10

QUIZ: 2AF 16 = ??? 10 11

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

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

QUIZ: Convert to decimal = ??? 10 AB7 16 = ??? = ??? = ??? 10 14

Addition QUIZ 15 Carry values go here Check in base ten!

Subtraction QUIZ Borrow values Check in base ten!

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

Converting Binary to Octal 18 Mark groups of three (from right) Convert each group is 253 in base 8 17

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

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

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

Converting Octal to Hexadecimal 22 Convert octal 253 into hex A B 253 in base 8 = AB in base 16 18

Quiz on Ch.2 Convert 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:

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?

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

Adding two negative numbers 32 Try these:

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

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

Trick QUIZ What decimal number does this binary number represent?

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: =

QUIZ Convert: =

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: =

QUIZ Convert: =

QUIZ Finite decimal fractions may have infinite binary representation! = Stop after 8 bits!

QUIZ Convert to floating point and to scientific notation: = = 0.0= 41

QUIZ Encode “Hello, world!” in ASCII Decode from ASCII 42

Huffman decoding QUIZ 43 Decode:

QUIZ 44 Explain the similarities and differences between 00FF00 and

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

QUIZ 46 Are these HiColor or TrueColor?

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 × × 1080 Calculate: 1] Data rate (bits per second) for 25 fps 2] Size (bytes) of 2-hour movie 48

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

QUIZ: recognize the gate! 50

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

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 53 Figure 4.7 Various representations of a three-input AND gate

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? 54 Figure 4.7 Various representations of a three-input AND gate

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. 55 Figure 4.7 Various representations of a three-input AND gate

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): 56 Figure 4.7 Various representations of a three-input AND gate

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 in two’s comp. 57 Figure 4.7 Various representations of a three-input AND gate

From gates to circuits 58 Find the logic diagram of the circuit described by the following truth table: Hint: The table is similar to which of the fundamental gates presented last time? 1 0

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 V1 = 0 and V2 = 1. 61

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

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

QUIZ 64 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)

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 how a MUX with only 4 data inputs works Assume S1 = 0, S0 = 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