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:

1st Gen. ICs2nd Gen. Multi-core processors3rd Gen. LSI, VLSI4th Gen. Vacuum tubes5th Gen. Transistors

4

Practice Flashcards on the text website

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Chapter 2

Binary Values and Number Systems

Converting Binary to Decimal

7

What is the decimal equivalent of the binary number 1101110?

11011102 = ???10

13

Converting Binary to Decimal

8

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

13

QUIZ:

100110102 = ???10

9

Converting Hexadecimal to Decimal

10

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

QUIZ:

2AF16 = ???10

11

Converting Octal to Decimal

12

What is the decimal equivalent of the octal number 642?

6428 = ???10

11

Converting Octal to Decimal

13

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

11

QUIZ: Convert to decimal

1101 00112 = ???10

AB716 = ???10

5138 = ???10

6928 = ???1014

Addition QUIZ

15

Carry valuesgo here

1 0 1 0 1 1 0 +1 0 0 0 0 1 1

14

Check in base ten!

Subtraction QUIZ

16

1 0 1 1 0 0 0 - 1 1 0 1 1 1

15

Borrow values

Check in base ten!

Repeated division QUIZ

17

Convert 4210 to binary

42 2 = rem.

4210 = 2  

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Converting Binary to Octal

18

• Mark groups of three (from right)• Convert each group

10101011 10 101 011 2 5 3

10101011 is 253 in base 8

17

Converting Binary to Hexadecimal

19

• Mark groups of four (from right)• Convert each group

10101011 1010 1011 A B

10101011 is AB in base 16

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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.

10 101 011 1010 1011 2 5 3 A B

253 in base 8 = AB in base 16

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

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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

31

Now you try it

48 (signed-magnitude)

- 147

How does it work inthe new scheme?

Adding two negative numbers

32

Try these: 4 - 4 -4- 3+3 + -3

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. 0100110011 2

40

Stop after 8 bits!

QUIZ

Convert to floating point and to scientific notation:

123.332 =

-0.0034 =

0.0 =

41

QUIZEncode “Hello, world!” in ASCIIDecode 67 83 32 49 49 48 from ASCII

42

Huffman decoding QUIZ

43

Decode:

1011111001010

QUIZ

44

Explain the similarities and differences between 00FF00 and 008800

Extra-credit question

TrueColorA 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 VideoThe 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

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 gateHint: Describe AND first!

52

QUIZ

Draw the gate symbols for:4-input OR5-input NAND3-input NOR4-input XOR

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

QUIZ

Draw the gate symbols for:4-input OR5-input NAND3-input NOR4-input XOR

How many lines does each of the truth tables have?

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

QUIZ

Draw the gate symbols for:4-input OR5-input NAND3-input NOR4-input XOR

How many lines does each of the truth tables have?

Describe in your own words each of the truth tables.

55Figure 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):

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

0 0 0 0 0 0 0 0

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.

57Figure 4.7 Various representations of a three-input AND gate

1 0 0 0 0 0 0 0

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

QUIZThe AND gate is obtained as a NAND followed by an

inverter. Draw its transistor diagram!

60

QUIZDraw 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 S2S1S0 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-creditHow many transistors are needed to build this

MUX?

68