Remove pdfs
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@ -33,7 +33,7 @@ Let's break down each column from the right:
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### More examples to practise with
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![]()
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## Binary multiplication
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Let's remind ourselves of how we do long multiplication within the denary number system:
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@ -17,7 +17,8 @@ When we have completed all the possible intervals between $0$ and $9$, we start
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The principle of counting in decimal:
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Thus each column is ten times larger than the previous column:
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* Ten \[$10^1$\] is ten times larger than one \[$10^0$\]
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@ -53,7 +54,7 @@ $$ 0001, 0010, 0011, 0100 $$
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Counting in binary:
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## Relation to Turing Machines
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@ -66,10 +67,12 @@ Let's convert 6 and into binary:
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If we have before us the binary place values ($1, 2, 4, 8$). We know that 6 is equal to: **1 in the two column and 1 in the 4 column → 110**
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More clearly:
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And for comparison:
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Or we can express the binary as:
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@ -83,6 +86,6 @@ $$ 2^1 + 2^2 $$
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Let's convert 23 into binary:
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@ -9,7 +9,7 @@ tags:
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The reason is straight forward: it is the simplest way on the level of pure engineering of representing numerical and logical values; both of which are the basic foundations of programming. An electronic circuit or transistor only needs to represent two states: on (1) and off (0) which corresponds to the switch on an electrical circuit.
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A single circuit representing the binary values of 1 and 0:
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It would be much more complicated to have to represent ten different states under the decimal number system, although denary computers do exist.
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@ -18,7 +18,7 @@ It would be much more complicated to have to represent ten different states unde
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If we want more digits, we just need to add in more circuits, and we can represent as large a binary number as we need. We just need one switch for every digit we want to represent. The switches used in modern computers are so cheap and so small that you can literally get billions of them on a single circuit board.
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When we use the term 'switch' we actually mean the transistor components of a circuit. We don't need to know the physical details at this level but we can say that a transistor turns a current on and off. They can also be used to amplify the current.
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@ -1,13 +0,0 @@
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---
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tags:
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- Linux
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- arch
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---
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## Pacman, Yay
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|Function|Command / flag|
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|:-------|-------------:|
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|List all installed packages|`-Q`|
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|List all local installed packages|`-Qm`|
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|Remove package|`-R [package_name]`|
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@ -1,16 +0,0 @@
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---
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tags:
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- Theory_of_Computation
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- assembly
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---
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The Little Man was an example of a computer written in machine code → this can be very hard to easily decipher as it functions at such a low level of abstraction. For this reason there are types of programming languages called **Assembly Language**.
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Assembly languages are slightly higher level languages that can easily be converted into machine code. Think of them as one stage up. They are slightly easier to manage and understand. The conversion is carried out by something called an **assembler**.
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The table below is an example of how the LMC machine code could be converted into assembly.
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>
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> While Assembly is rarely used in modern computer programming, it is worthwhile spending a little time experimenting with this set of languages. Programming in Assembly can give you an appreciation for how much complexity is abstracted away by modern languages, and also what are the hardware and software limitations of modern computers. Although programmers nowadays use high-level programming languages, before computers can run them, they must be translated (or compiled) into machine code, which as you have seen is very close to Assembly.
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@ -1,10 +0,0 @@
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---
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tags:
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- Theory_of_Computation
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---
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So far, when talking about binary values we have referred to them as combinations of 1s and 0s or $2^2, 2^3$ etc.
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But actually there are nouns for the different groupings of binary digits:
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