Preface

Prerequisites

Learning ethics

ASCII

What are Information management concepts?

Why do Information management concepts matter to you?

Research

Ecosystem

Standards, jobs, industry, roles, …

Story

FAQ

Worked examples

Chapter Name

Subsection

Subsubsection

Exercises

1. Logic. Mathematics. Code. Automatic Verification such as Lean Proven or Frama-C.

2. Languages in Anki.

Projects

Summary

FAQ

Reference Notes

Information theory Overview

0.13 Number systems

0.130 Positional number systems

Assume $(0)_b=0$ and $(1)_b=1$

Convert from $b$-base to decimal. If $b\geq 2,$ then

Convert from decimal to $b$-base.

def a(number, k):
    return math.trunc(number / math.pow(10, k)) % 10


def length(number):
    return math.trunc(math.log10(number)) + 1


def from_base_to_decimal(number, b):
    acc = 0
    for k in range(length(number)):
        acc +=def from_decimal_to_base(number, base):
    return acc

def from_decimal_to_base(number, base):
    base_number = ""
    q = number
    while q > 0:
        qk = trunc(q/base)
        ak = q - base*qk
        base_number = str(ak)+base_number
        q = qk
    return base_number

function from_base_to_decimal(number, base) {
    return String(number).
			split('').
			map((n)=> parseInt(n, base)).
			reduce((acc, current, index, array) => {
			   console.log(`${current}+${base}*${acc}=${current+base*acc}`);
			   return current+base*acc;
			});
}

function from_decimal_to_base(number, base) {
    if (base <= 1) {
        return;
    }
    base_number = ""
    q = number
    while (q>0)
    {
        qk = Math.trunc(q/base)
        ak = q - base*qk
				console.log(`${base * qk + ak}=${base}*${qk}+${ak}`);
        base_number = ak.toString(base).toUpperCase()+base_number
        q = qk
    }
    return base_number
}

function from_any_base_to_any_base(number, start_base, end_base) {
	console.log(`from base ${start_base} to decimal`);
	const start_number = from_base_to_decimal(number, start_base);
	console.log(`from decimal to base ${end_base}`);
	return from_decimal_to_base(start_number, end_base);
}

Fast algorithm.

http://www.opentextbookstore.com/mathinsociety/2.4/HistoricalCounting.pdf

https://www.gcu.ac.uk/media/gcalwebv2/gcuoutreach/NUMBERS & NUMBER SYSTEMS.pdf

https://www.radford.edu/~wacase/Number Systems Unit Math 116.pdf

https://www.cl.cam.ac.uk/teaching/1415/CompFund/NumberSystemsAnnotated.pdf

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/comps-programming/mud5.pdf

https://en.wikipedia.org/wiki/Numeral_system

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-01-unified-engineering-i-ii-iii-iv-fall-2005-spring-2006/comps-programming/number_systems.pdf

https://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/study-materials/MITRES_18_008_supp_notes01.pdf

https://www.cs.princeton.edu/courses/archive/spr15/cos217/lectures/03_NumberSystems.pdf

http://www.unitconversion.org/unit_converter/numbers-ex.html

COMS W3827 Fundamentals of Computer Systems

0.1311 Binary and boolean function

Binary vs boolean and bits

Ecosystem

0.132 Nonpositional Number Systems

0.14 Data Storage

0.140 Data Types

0.141 Storing Numbers

Method of complements

Nine's complement

Ten's complement

One's complement

One's complement is an operation to invert bits.

Worked examples.

$m=-56,C(56)=2^8-56-1=199$

Two's complement

There is only one zero in two’s complement notation.

One's complement + 1. Because $(0)_{one's complement}=(1)_2$, but $(0)_{two'scomplement}=(0)_2$

Worked examples.

$m=-56,C_{8 bits}(56)=2^8-56=200$

Trick.

https://www.csestack.org/how-to-find-2s-complement/

Example. $11100110$ two's complement format to integer.

How to encode negative numbers in binary number systems?

• Gray code

• Base −2

• 8–4–2–1 code is also called BCD (Binary coded Decimal)

• Sign and magnitude

• Offset binary, also called excess-K or biased representation

  Excess-8 (biased)

  Zig-zag encoding

  Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3), shifted binary or Stibitz code. https://en.wikipedia.org/wiki/Excess-3

• Complements

  • Ones' complement

  • Two's complement

    Two's complement is the easiest to implement in hardware, which may be the ultimate reason for its widespread popularity. Choo, Hunsoo; Muhammad, K.; Roy, K. (February 2003). "Two's complement computation sharing multiplier and its applications to high performance DFE". IEEE Transactions on Signal Processing. 51 (2): 458–469. doi:10.1109/TSP.2002.806984.

How to encode real numbers in binary number systems?

• Fixed-point

  https://planetcalc.com/862/

• Floating-point

  IEEE 754 format

  three parts: a sign, a shifter, and a fixed-point number.

0.142 Storing Text

A character is an element of grammar (English, Spanish, ...) + accepted human-computer interface by convention (backspace, delete, escape, @, ...), i.e. a code. $code=\{character | character \in grammar \text{ or } character \in \text{ human-computer interface} \}.$

For example, English grammar is $\{A,B,C,...,Z\}\cup \{a,b,c,...,z\} \cup \{.,;,-,+,!,...,*\} \cup \{0,1,2,3,...,9\}$ and human-computer interface in ASCCI is$\{NUL,SOH,Space,...CAN\}$.

We can represent each character with a bit pattern of n bits (bit pattern length=n). If we have a $code=\{A\}$, his cardinality $|code|=1$. Then computer understands $\text{computer code}=\text{bit patterns =}\{0\}$ and $\text{bit pattern length}=1$

$code=\{A,B\},|code|=2,\text{bit pattern}=\{0,1\},\text{bit pattern length}=1$ .

$code=\{A,B,C,D\},|code|=4,computer=\{00,01,10,11\},\text{bit pattern length}=2$.

$|code|=8,\text{bit pattern length}=3,lg(8)=3$.

Therefore, $\text{bitPatternLength}=lg(|code|)$.

0.1421 ASCII Code and UNICODE

IEEE milestones.

ASCII.

UNICODE. Emojis.

printf "\r12345\n\r6\n"; printf "\r5\n"

printf "\r12345"; printf "\r5\n"

https://stackoverflow.com/questions/3091524/what-are-carriage-return-linefeed-and-form-feed

Hex Code.

How works internally?

https://www.w3schools.com/tags/ref_urlencode.ASP

https://onlineunicodetools.com/convert-unicode-to-hex

https://en.wikipedia.org/wiki/List_of_Unicode_characters

Mackenzie, Charles E. (1980). Coded Character Sets, History and Development (PDF). The Systems Programming Series (1 ed.). Addison-Wesley Publishing Company, Inc. pp. 6, 66, 211, 215, 217, 220, 223, 228, 236–238, 243–245, 247–253, 423, 425–428, 435–439. ISBN 978-0-201-14460-4. LCCN 77-90165. Archived (PDF) from the original on May 26, 2016. Retrieved August 25, 2019.

https://stackoverflow.com/questions/12747722/what-is-the-difference-between-a-line-feed-and-a-carriage-return

https://pjb.com.au/comp/diacritics.html

ASA standard X3.4-1963

https://stackoverflow.com/questions/1761051/difference-between-n-and-r

0.143 Storing Audio

0.144 Storing Images

0.145 Storing Videos

0.15 Operations on Data

0.150 Logic Operations

0.151 Shift Operations

0.152 Arithmetic Operations

Sum of naturals.

Rules. 0+0=0, 0+1=1, 1+0=1 and 1+1=10

Binary Addition Algorithm. (2015, July 06). Retrieved from https://chortle.ccsu.edu/assemblytutorial/zAppendixE/binaryAdd.html

Subtraction of naturals (No complements).

Rules. 0-0=0, 1-0=1, 1-1=0, 0-1=10-1=1

https://www.calculator.net/binary-calculator.html

Subtraction of naturals (Two's complement)

$91-46=91+(-46)=45$

https://www.exploringbinary.com/twos-complement-converter/

Why does char - '0' successfully convert a char to int in C?

https://www.quora.com/Why-does-char-0-successfully-convert-a-char-to-int-in-C/answer/Greg-Kemnitz

Nine's complement

Pascaline.

0.153 Bitwise operations in C

Bitwise Operators in C and C++

x & 1 is equivalent to x % 2 (no sign).

if x&1 is true, then x is an odd number.

First of all, an example:

5(00000101)& 1(00000001)
00000101 &
00000001
00000001 (1 True)

Informal Proof. For non-complement binary number. Where $n$ is position left to right.

std::list<int> v = { 1, 2, 3, 4, 5, 6 };
    auto it = v.begin();
    while (it != v.end())
    {
        // remove odd numbers.
        if (*it & 1)
        {
            // `erase()` invalidates the iterator, use returned iterator
	            it = v.erase(it);
        }
            // Notice that the iterator is incremented only on the else part (why?)
        else {
            ++it;
        }
    }

x >> 1 is equivalent to x / 2

https://www.cprogramming.com/tutorial/bitwise_operators.html

0.154 Boolean Algebra and Digital Logic: Arithmetic Logic Unit

https://www2.southeastern.edu/Academics/Faculty/kyang/2018/Spring/CMPS375/ClassNotes/CMPS375ClassNotesChap03.pdf

Summary

Floating numbers

IEEE 754

File classification

In Unix, everything is a file, so what is a directory? a file, what is a process? a file, what is a driver? a file. If you don’t separate how looks and how does it, you have blobs.

Blobs and plain text.

Blobs tracking in Git, databases, spreadsheets

Blobs and byte arrays

https://security.stackexchange.com/questions/220560/rsa-key-string-vs-hex-vs-base64-vs-byte-array-represantational-form

Binary-to-text encoding

Split a file into chunks

Images

How can you see an image? and process it? OpenCV

PACS

PACS (picture archiving and communication system)

DICOM

Raster images

png, jpg, webp

Vector images

SVG and canvas

High-performance images and animations

WebGL, OpenGL, directx, vulkan

Computer graphics

QR Code

By field

Myers Automatic Booth

(LAS, Geology)

(G-code, Manufacturing)

(EDF, Neuroscience)

(FASTA, Genetics)

GIS (Geographic Information System)

Financial Information eXchange (FIX)

(XML, JSON and YAML, Information Technology)

https://www.npmjs.com/package/serialize-javascript

https://docs.python.org/3/library/pickle.html

(PDF, Standard)

https://www.youtube.com/watch?v=48tFB_sjHgY&ab_channel=Computerphile

SWIFT

DICOM Standard

https://pydicom.github.io/

DICOM networking protocol

File as Programming

CSS, JS, HTML, WASM

Internet media type (MIMES)

Video

The filmmaker’s handbook

Hex editing

We tell you that files are binary, right? But, how we can you show that if you don’t feel it? And yes, you could write your programs in hex — ”since C and assembly are too high-level” you’re thinking and yes you could do reverse engineering to software.

In Unix, you have different options to edit and show files as hex. Some choices are xxd, hexdump [2], and so on [4]. We’re going to use xxd and vim.

Write a plain text in Unix with “Hello World” and vim. Change to mode xxd.

But, how can show a “Hello World” in binary? xxd -b

Writing a binary file

Unicode. UTF-8. Emojis.

References

[1] hexdump(1) - Linux manual page. (2022, December 19). Retrieved from https://man7.org/linux/man-pages/man1/hexdump.1.html

[2] Explains, F. S. (2021, December 24). Writing binary files: a tutorial in C and Python (security@cambridge screencast). Youtube. Retrieved from https://www.youtube.com/watch?v=jAu0oyxsP20&list=PLbyW0t9gkXg2lcU_T4LgZryxrcJBdP_iF&index=6&ab_channel=FrankStajanoExplains

[3] Hex dump. (2023, January 14). Retrieved from https://vim.fandom.com/wiki/Hex_dump

[4] Top Hex Editors for Linux. (2021, May 17). Retrieved from https://www.tecmint.com/best-hex-editors-for-linux

Data type size

Extended ASCII

https://www.gnu.org/software/emacs/manual/html_node/emacs/User-Input.html

Threads

Overflow

Automation and insights

Drawing.

Ofimatics. Spreadsheet programming.

Spreadsheets Are An Awesome Functional Programming Tool | Lucas Reis' Blog. (2018, December 29). Retrieved from https://lucasmreis.github.io/blog/spreadsheets-are-an-awesome-functional-programming-tool

Conference, S. L. (2014, September 21). "Spreadsheets for developers" by Felienne Hermans. Youtube. Retrieved from https://www.youtube.com/watch?v=0CKru5d4GPk&ab_channel=StrangeLoopConference

Editor

Keyboard remapping

Exercises

1. Logic. Mathematics. Code. Automatic Verification such as Lean Proven or Frama-C.

2. Languages in Anki.

Projects

PDF

Is standard?

Is it capable to render HTML, JS?

Summary

FAQ

Reference Notes

References

http://neerc.ifmo.ru/wiki/index.php

https://tug.org/texshowcase/cheat.pdf

Explains, F. S. (2021, March 19). Touch typing: why you MUST learn it ASAP. Youtube. Retrieved from https://www.youtube.com/watch?v=0FUsiyiWWw8&list=PLbyW0t9gkXg2OjpTqGig1nWCqzxwrF8h5&ab_channel=FrankStajanoExplains

Next steps

Problems

From LeetCode, HackerRank, ...

• Given a signed 32-bit integer x, return x with its digits reversed. If reversing x causes the value to go outside the signed 32-bit integer range [-231, 231 - 1], then return 0.

  https://math.stackexchange.com/questions/480068/how-to-reverse-digits-of-an-integer-mathematically

Assume the environment does not allow you to store 64-bit integers (signed or unsigned).

1. Multiply

2. Divide

3. Length