chapter 1
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Chapter 1. The Big Picture. QUIZ. 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. 2. 5. QUIZ. - PowerPoint PPT PresentationTRANSCRIPT
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
5
Chapter 2
Binary Values and Number Systems
Converting Binary to Decimal
7
What is the decimal equivalent of the binary number 1101110?
11011102 = ???10
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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
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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
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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
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Check in base ten!
Subtraction QUIZ
16
1 0 1 1 0 0 0 - 1 1 0 1 1 1
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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
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Converting Binary to Hexadecimal
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• 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?
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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?
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QUIZ
What is the representation for each of these actual numbers? -48 -40 -30 -5
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Let’s use ten’s complement!To perform addition, add the numbers and discard any carry
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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
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QUIZ
Perform the following operation in 8-bit two’s complement:
40 – 13
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Trick QUIZ
What decimal number does this binary number represent?
1001 1110
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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
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QUIZ
Convert:
.10112 = 0. 10
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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
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QUIZ
Convert:
0.310 = 0. 2
39
QUIZ
Finite decimal fractions may have infinite binary representation!
0.310 = 0. 0100110011 2
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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
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Decode:
1011111001010
QUIZ
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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.
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QUIZ
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Are these HiColor or TrueColor?
Extra-credit question
How many bits are needed to represent this palette? Please show your work.
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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