TEST 1 NOTES
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The test would consists of 23 multiple choice questions to be written in 45 minutes.
About 30% weight on Representing numbers, 20% on Representing text, 20% on Excel. Other
topics weight about 13%-5% each.
Test starts at the beginning of your lecture time. Bring your York ID (or government issued ID if
you don't have York ID yet), pencils (HB), eraser, and pen. You will write answers on a Scantron
sheet (aka bubble sheet). See an example of filling the Scantron below.
You are required to write the test in your own section (lecture room); otherwise your test will not
be graded.
No calculators can be used. We will provide the power of 2 from 2-5 to 28. See sample cover page
below.
History of Computing
Part 1: Ancient History: up to 1930
- Abacus = first developed calculator in Babylonia, over 5000 years ago, “finger-powered pocket”
calculator
- Algorithm = a finite set of unambiguous instructions to solve problem
- Raised from 9th century mathmatician Muhammad ibn Musa al-Khwarizmi
 Latinized ‘algorithmi’
- Earliest examples – 300 BC
- Early calculating machines
- Either manual or mechanical
 Ie. Slide rule
 Ie. Mechanical calculators (since 1600s)
- Jacquard Loom (1801)
- Used punch cards to define complex patterns woven into textiles
- Punch cards were later used for computer program codes
- George Boole (1815-1864)
- Boolean algebra
- Laid logical foundations of digital computing circuitry
Part 2: Birth of the Electronic Computer (1930-1951)
- Claude Shannon (1916-2001)
 1937: introduced the application of Boolean logic in creating digital computing machines
 1948: published “A mathematical theory of communication” which establishes the
principles for encoding information so it might be reliably transmitted electronically
 Many consider him the father of the modern information age
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Von Neumann Architecture
 “stored program”
 Binary internal coding
 CPU-memory-I/O organization
 “fetch-decode-execute” instruction cycle
 Central processing unit, a memory, mass storage, IO
 Earlier computers (eg. ENIAC) hard-wired to do one task
 Stored program computer can run different programs
 Basis for modern computers
Alan Turing (1912-1954)
 Led the world war 2 research group that broke the (encrypted) code for the (Germany)
enigma machine
 Proposed a simple abstract universal machine model for defining computability – The
Turing Machine
 Devised the “Turing Test” for Artificial Intelligence
 The Enigma Machine
 Invented in 1918, it was the most sophisticated code system of its day, and a
priority for the allies to break it as the Germans believed it was unbreakable
 Contributed to the electronic computing machines in 1940s that helped decrypt
German coded messages
The first electronic general-purpose computer
 ENIAC
 Electronic Numerical Integrator And Computer
o First general purpose electronic digital computer
o Commissioned by the United States Army for computing ballistic firing
missiles
 Noted for massive scale and redundant design
 Used vacuum tubes to control the flow of electronic signals
o Vacuum tubes are large, generate a lot of head and are prone to fail
 Decimal internal coding
 Operational in 1946
 Manual programming of boards, switches and “function table”
o Not “Von Neumann Architecture”
Part 3: Age of the mainframes (1951-1970)
- Since 1950s, computers got smaller over time
- Four generations of vacuum tube computer circuits, showing the reduction in size during 1950s
- Grace Murray Hopper (1906-1992)
- Created first compiler because she was tired of writing machine code by hand. Greatly improved
programming speed and efficiency
- The transistor (The most important invention of the 20th century)
- Transistor replaced vacuum tubes, which were bulky
- Integrated Circuit allowed placement of many transistors onto a small surface
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Lowered cost and decreased space compared to using individual transistors
This enabled computers and other electronic devices to become smaller and cheaper to build and
maintain
- Today exceeding 10 billion transistors in a single package of approximately 25 square
centimeters
A hearing aid
- The first device built with transistors, in 1953
- Zenith royal-T “Tubeless” hearing aid
Transistor Radio
IBM System/360 (1960s)
- Introduced in 1964
- Family of computers, with compatible architecture, covering a wide price range
- Established the standard for mainframes for a decade and beyond
Going to the moon
- Apollo space program depended on computers to calculate trajectories and control guidance
- Trajectories calculated using IBM mainframes
- Onboard guidance computer had less processing power than modern appliances, but had autopilot capabilities
- Margaret Hamilton
 Led the team who coded programming for the guidance computer
 Considered a pioneer in software engineering
Gordon Bell: The “microcomputer” Digital Equipment Corporation (DEC)
- Developed first mini computers, 1960-1983
- Brought computing to small business
- Created major competition for IBM, Univac, who only built mainframes
- DEC PDP Series
 Offered mainframe performance at a fraction of the cost
 PDP-8 introduced at $20,000 vs $1M for a mainframe
Specialized supercomputers
- First developed in the late 1970s
- High-performance systems used for scientific applications (weather forecasting, code breaking)
- Advanced special purpose designs
Supercomputers today: IBM Summit supercomputer
- Used for hydrodynamics, quantum chemistry, molecular dynamics, climate modeling and
financial modeling
Part 4: Age of the personal computers (after 1970)
- Intel 4004 microprocessor (1972)
- First commercially available microprocessor – first used in a programmable calculator
- Made the personal computer possible
- Contained 2300 transistors and ran at 100 kHz
- Desktop and portable computers (1975 and later)
- Use microprocessors
- All-in-one designs, performance/price tradeoffs
- Aimed at mass audience
- Personal computers
- Workstations
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Altair 8080
 First kit micro computer (1975) by MITS
The beginning of Microsoft
- In 1975, Bill Gates and Paul Allen approached Ed Roberts of MITS, the company that developed
the Altair, and promised to deliver a compiler for BASIC language. They did so, and from that
sale, Microsoft was born.
Radio Shack TRS-80 (1978)
- First plug and play personal computer available at retail
- Programmed in BASIC
- Very successful
- Very affordable
- Limited commercial software
- Created a “cottage industry”
Osborne I (1981)
- First “portable” personal computer
- Came with lots of bundled software
- Only weighed around 20 kilos and sold for $1795
IBM PC (1982)
- IBM’s first personal computer
- Significant shift for IBM
- Open architecture
- Established a new standard – legitimized the personal computer
- Operating System (OS) supplied by Microsoft
Xerox Palo Alto Research Center (PARC)
- Contributions to computing include:
 Ethernet networking technology
 Laser printers/copiers
 Object-Oriented Programming (OOP) programming paradigm
 Workstations Alto and Star were the first to use a window-based Graphical User Interface
(GUI)
Xerox Star (1981)
- The first to use a window-based Graphical User Interface (GUI)
Apple Macintosh (1984)
- Second personal computer with GUI interface
- Adapted from the work done at Xerox
- Designed to be a computer appliance for “real people”
- Introduced at the 1984 superbowl
Advanced Research Projects Agency Network (ARPANET)
- Large-area based computer network, established in 1969
- Allowed universities to share data
 University of California, Los Angeles
 University of California, Santa Barbara
 Stanford Research
 University of Utah, CS Dept.
- Communications protocols developed for ARPANET in early 1980s served as the basis for the
internet
Todays price/performance
- Over 3 billion operations per second costs less than $300
- Memory is measured in gigabytes, not megabytes or kilobytes
- Secondary storage is terabytes, soon to be petabytes
- Communication speeds measured in megabits or gigabits per second, not kilobits
Analog vs. Digital Information
Information, Data, Signal
- Information: some knowledge you want to record or transmit
- Ie. Persons weight, current time, picture of a cat
- Data: the presentation of the above
- Ie. Persons weight
 63kg, 139lb, 9 st 13 (“9 stone 13”)
 One average goat, or seven watermelons
- Time
 13:34:16, 1:34:16 PM, 18:34:16 UTC, 183416Z
- Signal: some means to record or transmit the above
- Voltage, current, handwritten note, marking on wood (nat a major factor of this course)
Types of information
- Inherently continuous (infinitely many values in any range)
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- Mass
- Temperature
- Most other physical properties (ie. Body temperature, blood pressure)
Inherently discrete (finite number of values in any range)
- Days in a week
- Current study term
- Names of cities
- Numbers of steps walked
- Number of students on campus today
- Text or any other typed or written symbols
Analog vs. Digital
- 2 main ways to represent information
- Analog data: continuous representation, analogous to the actual information it represents
- Digital data: discrete representation, using a finite number of digits (or any other sets of symbols)
to record the data
- Can we represent continuous information using digital data?
- Spirit (or mercury) thermometer exemplifies analog data as it continually rises and falls in direct
proportion to the temperature
- Digital displays only show (represent) information in a discrete fashion
- What is the current temperature?
- A thermometer provides infinite precision, directly corresponding to actual temperature
- Our reading is limited only by our ability to measure its value
- What time is it?
- 21 hours, 4 minutes, but what about seconds?
 That information has been lost in the digitalization of time
- Computers are finite
- Information often possesses an infinite range of values
 Ie. How many real numbers are in the interval [0…1]?
- However computers are finite and deterministic (ie. Not random)
 They can only operate on a fixed amount of data at a time
 The amount and type of data must be known ahead of time
- How to represent information from an infinite range?
 Represent enough of the range to meet our computational needs
- Conversion of analog to digital data in 2 steps
- Sampling (discretization)
 Converts continuous variation to discrete snapshots
 Ie. Digitalization of video: 24-30 still frames per second
 Dividing a still picture into pixels (ie. HDTV: 1920 x 1080)
 Digitalization of audio
- Quantization (truncation)
 Converts infinite range of values to a finite one
 Examples
o 1/3 = 0.3333333 (some finite number of digits)
o  = 3.14159
o 21.41421
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Discretization of computer variation by sampling
Signal sampling representation. The continuous signal is represented by the green line, while discrete samples
are indicated by the blue vertical lines
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But… the information can be lost?
- YES, some information is allowed to be lost
- BUT
 We decide what can be lost at the very beginning
 There are many mechanisms to determine proper parameters to digitize analog data
(continuous information) with as much precision as necessary
 Nyquist – Shannon sampling theorem (yes, that C. Shannon)
 Quantization error models
 Any losses are completely avoidable after the digitalization is performed
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Bits and Bites
- The basis for representing digital data is the binary digit (bit), with the unit symbol b
- A bit holds one of two values: 0 or 1
- Often combined in groups of eight to represent data
 A group of 8 bits is called a byte, with the unit symbol B
- Can be combined with metric prefixes for larger magnitudes
 Ie. Mb for megabit and MB for megabyte
prefix symbol multiplier (decimal)
multiplier (binary)
kilo
k, K
103 = 1000
210 = 1024 (also, kibi, Ki)
mega
giga
tera
M
G
T
106 = 1 000 000
109
1012
220 = 1 048 576 (also, mebi, Mi)
230 (also, gibi, Gi)
240 (also, tebi, Ti)
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Binary vs. Decimal multipliers
- Decimal
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 Communication (gigabit ethernet: 1 billion bits per second)
 Data transfer (PC3-12800 RAM transfers 12,800,000,000 bytes per second)
 Clock rates (A 2-GHz CPU receives 2,000,000,000 ticks per second)
 Storage, by manufacturers (10TB: 10 trillion bytes)
 Storage, by some operating systems (MacOS, Linux)
 DVD’s
Binary
 Memory capacity (8GB: 8,589, 934, 592 bytes)
 Storage, by some operating systems (Windows, occasionally Linux: 3.63 TB:
4,000,000,000,000 bytes)
 CD’s
So, why digital and why binary?
 Computers cannot work well with analog data
 Discretize the data (ie. Breaking it into discrete samples)
 Quantize the values (or approximate the quantities)
 Problem: large range of values in analog representation
 Low end is limited by noise (electronic, electromagnetic..)
o Low-noise devices are more costly
o Sometimes you hit fundamental limits (ie. Charge of one electron)
 High end is limited by maximum available voltages, strength of electrical
insulation, power consumption, etc.
o High voltages increase sizes and (especially) power consumption
Why do we use binary (and not decimal, etc.)?
 Representing one of only two states benefits cost and reliability
 Benefits of digital in signal transmission (and storage)
 Analog signals continuously fluctuate in voltage up and down
 Digital signals have only a high (1) or low (0) state if binary; or a small number of
easily distinguishable states otherwise
 When transmitted, all electronic signals (both analog and digital) degrade as they
move down a line
o The voltage of the signal fluctuates due to “noise” produced by
environmental effects
o Similar effects when the signals are recorded
 Digital: if the distortion is small enough, can completely regenerate the signal and
regain its original shape
 Analog: degradation of analog signals is permanent; there is no way to determine
if the distortion was not present originally
 Benefits of digital for storage and compression
 Both digital and analogue data can be recorded
o Magnetic audio tapes, vinyl records, pencil drawings, VHS tapes, CDS
and Blu-ray, USB-sticks, SSD..
o Digital copies are always completely identical to the original
o Error-detection and -correction codes exist for digital data
 Most of the data we encounter has some redundancy
o Uniform areas in pictures, silence in sound, values that are changing in a
very predictable way
o Removing this redundancy is much easier with mathematical algorithms
that work with discrete values
Digital Representation: Summary
 Easier to process digital data
 Easier to transmit reliably
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Digital signals can be completely regenerated (if the distortions are not too severe)
Easier storage and compression
Soon, we will look at how numbers, texts, images, audio etc. are stored as digital signals
Representing Numbers
DECIMAL (base 10)
- Numbers
- Natural numbers
 Zero and any number obtained by repeatedly adding one to it
 Ie. 100, 0, 45645, 32
- Negative whole numbers
 Values less than 0, indicated with a “-“ sign before the left-most digit
 Ie. -24, -1, -45645, -32
 Side note: hyphen -, minus - , and M-dash – are four different typographical symbols;
use them correctly in your writing
- Integers
 Values that are either a natural number, or a negative whole number
o Ie. 249, 0, -46545, -32
- Rational numbers
 Values that are integers, or the quotient of two integers
 Ie. -249, -1, 0, 3/7, -2/5
- NOTE: , e, √2, √5... are irrational numbers
- Positional numbers
 48c = forty-eight cents
 $428 = four hundred and twenty-eight dollars
 1820lb = one thousand, eight hundred and twenty pounds
 2108 kg = two thousand, one hundred and eight kilograms
1820
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Positional Notation
- 4
3
2
1
0
- Allows us to count past 10 while using just 10 digits
- Each number in the row above represents a power of the base. This exponent is the order of
magnitude from the column
10000
1000
100
10
1
2
7
9
1
6
= 20000
+
7000
+
900
+
10
+
6
=27916
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Decimal system is based on the number of digits (fingers) we (usually) have
The magnitude of each column is the base, raised to its exponent
The magnitude of the number is determined by multiplying the magnitude of the column by the
digit in the column and summing the products
Binary (base 2)
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Non-decimal number systems
- Numbers can be in any base: 2, 3, 4… 8, 9, 10… 16…
- Decimal is base-10 and has 10 possible digits
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 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Binary is base-2 and has 2 digits
 0, 1
Octal is base-8 and has 8 digits
 0, 1, 2, 3, 4, 5, 6, 7
Hexadecimal is base-16 and has 16 digits
 0, 1, 2, 3, 4, 5, 6, 7, 8, A, B, C, D, E, F
NOTE: for a value to exist in a given base, it can only contain the digits for that base, which
range from 0 up to (but not including) the base
Ie. What bases can these values be in?
 122 = 8 decimal
 198 = 8 decimal
 178 = 8 decimal
 G1A4 = hexadecimal
Positional notation
 An n-digit unsigned integer in base b
 (di is the digit in the ith position in the number)
o The number: (𝑑𝑛−1 𝑑𝑛−2 … 𝑑𝑖 …𝑑1 . . 𝑑0 ) 𝑏
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1 (= 1)
11 (=3)
Examples:
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2
1
0 = 642
(642)10 = 6×10 + 4×10 + 2×10
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3
2
1
0 = 2619
(5073)8 = 5×8 + 0×8 + 7×8 + 3×8
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3
2
1
0 = 11
(1011)2 = 1×2 + 0×2 + 1×2 + 1×2
Binary is base 2 and has 2 digits: 0 and 1
100 (=4)
101 (=5)
111 (=7)
1000 (=8)
1001 (=9)
1010 (=10)
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Binary numbers and computers
- Computers have storage units called binary digits or bits
 For instance,
 Low voltage = 0
 High voltage = 1
 All bits are 1 or 0
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Byte = 8 bits
1 byte
4 bytes (32 bits)
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1 single byte
 = 7, 6, 5, 4 ,3 ,2 ,1 ,0
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27
26
25
24
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128 64
32
16
23
8
22
4
21
2
There is also a representation for zero, giving 256 (28 )
20
1
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- 1 bit: 2 values (0, 1); 2 bits: 4 values (00, 01, 10, 11); …
- Every one bit added doubles the range of values
- 255 is the largest value (in decimal) that can be expressed using 8 bits
Arithmetic in Binary
- Remember that there are only 2 digits in binary, 0 and 1
 0+0=0
 0+1=1
 1 + 1 = 0 with a carry
Octal notation
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Base 8… uses 8 numbers
- 0, 1, 2, 3, 4, 5, 6, 7
- Position represents power of 8
- 15238
 (1 ∗ 83 ) + (5 ∗ 82 ) + (2 ∗ 81 ) + (3 ∗ 80 ) = 512 + 320 + 16 + 3 = 851
Positional notation
For base B, B digit symbols (0~B-1)
Hexadecimal notation
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Base 16… uses 16 symbols
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- Position represents power of 16
- 𝐵65𝐹16 OR 0 x B65F
 (11 ∗ 163 ) + (6 ∗ 162 ) + (5 ∗ 161 ) + (15 ∗ 160 ) = 45056 + 1536 + 80 + 15 = 46687
Representing Text
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Character set : list of characters and the codes used to represent each one
ASCII: American Standard Code for Information Interchange
- Originally 7 bits for each character, 128 unique characters
 33 of them control characters (ie. Used by old printers)
 The rest are decimal digits, English letters, punctuation signs
- Later extended ASCII evolved so that all 8 bits were used
 Represented lines, symbols, and letters with accents
 Several incompatible versions
- First 32 and last one are control characters (or hidden characters); they control how text
appears, but do not appear as text
- Decimal Arabic numbers (ie. 0, 1, 2, etc..) start at code 48 to 57
 Ie. The code for 6 is 48 + 6
- Uppercase letters (A, B, C..) start at 65 to 90
 Ie. Code for J(10th letter) is 65 + (10-1) = 74
- Lowercase letters (a, b, c..) start at 97
 Ie. Code for j (10th letter) is 97 + (10-1) = 106
- Corresponding upper- and lowercase letters are separated by 32 (106-74 = 32)
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Later: a bigger character set table Unicode, 0-127 are same
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Even the extended ASCII is limited
- Symbols
 A lot of common symbols are missing ie. ©, ™, €
- Languages
 Extended portion can be changed sometimes
 Still no way to use multiple languages at the same time (ie. French and Greek)
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Unicode is the superset of ASCII
- The first 128 characters of Unicode character set correspond exactly to ASCII
- Uses 16+ bits per character and can represent more than 1 million characters
Lossless comparison: when some things are redundant
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Data compression
- It is important that we find ways to store and transmit data efficiently, which leads computer
scientists to find ways to compress it
- Data compression is a reduction in the amount of space needed to store a piece of data
- Compression ratio is the size of the compressed data divided by the size of the original data
 Data compression technique can be:
 Lossless; which means data can be retrieved without any loss of the original
information
 Lossy; which means some information may be lost in the process of compaction
 As examples, we look at the following 3 techniques:
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Keyword encoding
o Frequently used words are replaced with a single character
 Ie. As = ^, the = ~, and = +, that = $, must = &
o Note that the characters used to encode cannot be part of the original
text
o Ie.
 349 characters in the original paragraph (including space and
punctuation)…
 314 characters in the encoded paragraph
 349-315 = 35 characters savings
 314/349 = 0.9 x 100 = 90%
 A compression ratio of 90% is not very good
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Run-length encoding (RLE)
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a. Single character may be repeated over and over again in long sequence. This
type of repetition doesn’t generally take place in English text, but often
occurs in large data streams or in images representing paper documents
b. A sequence of repeated characters is replaced by:
i. A flag character,
ii. Followed by the repeated character,
iii. Followed by a single digit that indicates how many times the
character is repeated
c. Example
i. AAAAAAA would be encoded as *A7
d. Ie.
i. Original text contains 51 characters
ii. The encoding string contains 35 characters
iii. 35/51 = 68%
Huffman encoding
a. Why should the blank, which is used very frequently, take up the same
number of bits as the character ‘X’ which is seldom used in text?
b. Huffman code uses variable-length bit strings to represent each character
c. A few characters may be represented by 5 bits, and another few by 6 bits,
and yet another few by 7 bits, and so forth
d. Challenge of variable-length encoding idea
i. Need to know where one symbol ends and other begins
1. Ie. “e” = 01, “q”= 0101.. is “010101” “eee”, “eq”, or “qe”?
e. Solution
i. Prefix-property: no code is a prefix of another code
ii. Enables unambiguous decodability
f. If we use only a few bits to represent characters that appear often and
reserve longer bit strings for characters that don’t appear often, the overall
size of the document will be smaller
g. The idea comes from Morse code
i. Morse code uses variable-length code of dats and dashes (like 0 and
1)
1. Fewer dots and dashes for more frequent letters (a, e, i)
ii. NOTE: no prefix property! (ie. A and J codes)
h. Example of Huffman alphabet
i. Usually different for different input
data
j. Generated during compression step
DOORBELL =
1011110110111101001100100
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Here is why you need prefix property
 No code is a prefix to another code
Input: symbols and their frequency counts
Output: binary-code for each symbol
Huffman
Code
00
01
100
110
111
1010
1011
Character
A
E
L
O
R
B
D
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Property: optimum compression-rate with prefix-property
Huffmans Algorithm
Step 1: sort them in ascending order of frequency
Step 2: replace the 2 minimum frequency symbols by one “combined symbol” and place it in a 2 nd sorted
queue
Step 3: repeat step 2 until only 1 character remains in queue
A binary tree results
Label left branches 0, right branches 1*
The code for each symbol is the binary sequence along the corresponding root-to-leaf path
1) Prefix property
2) Optimum compression ratio
Original = (4 + 6 + 11 + 13 + 17) x 8 = 408 (assume extended ascii)
Compression ratio = 112 / 408 = 27%
Lossless comparison: Summary
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Keyword encoding alone the least effective of the three
Huffman coding the most effective of the three
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Applications:
- Run-length encoding (RLE) is used when compressing data with lots of repetition
 White space in faxes, any data that changes very slowly
 Sometimes combined with others (ie. Hoffman)
- Hoffman encoding is used in a lot of algorithms as building blocks
 JPG, MP3, ZIP
 Huffman encoding is optimal for per-character compression
 Can do it better if consider more symbols at a time during analysis
 (ie. In English, ing, the, ed, wh, gh; keyword encoding?)
Can we compress much better?
- Yes, if (small) losses are acceptable: JPG, MPEG..
Intro to Microsoft Word
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Intro
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Microsoft Word (a member of the Microsoft Office suite) is a very widely-used word processor
Word files have the extensions .doc (with older versions) or .docx (with more recent versions)
Word processors are computer applications used to create, format, store, and print typed
documents e.g., theses
- Other popular word processors include Google Docs, Libre Office, Pages, Zoho Writer,
Notebooks, Corel WordPerfect...
Common features
- Word document is another name for a microsoft word file
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Typically contain following objects and more:
 Text; with attributes including font, size, face, color, etc
 Pictures and drawings
 Tables
 Embedded PDFs and media objects like audio and videos
 Math equations
Word doc window
- Document area = workspace
- Tools contained in tool bar = ribbon
 Represented by icons that describe their functions
 Also reveal tips when you hover over them
- Each ribbon divided into named groups, each group performs related functions
- Caption
 Do not change the caption number as word ‘remembers’ only those numbers it
automatically assigns, so that you have it generate a list of numbered illustrations later
 Also lets you
 change the position of the caption (Usually above tables and below figures), define new
labels (other than figure, table, and equation) for illustrations and its numbering style