Turing Complete - User contributions [en]

Building Circuits with Words

2024-08-21T00:04:25Z

Poppi-Sama: In the Introduction's first paragraph, 2nd sentence, between "the gates" there were 2 spaces instead of just 1, so I got rid of the 2nd space.

{{guide|narrow=1}}
=== Introduction ===
This small guide is for players who are completely new to binary logic. It shows how the names of the gates correspond to words in a sentence and how they can be used to create circuits by simply describing what you see in a truth table.

This concept might be perceived as obvious for people with background knowledge, but is still something that each of us had to learn at some point.

=== Step 1: Describe the green outputs ===
Let's take a look at the XOR level and its truth table

[[File:XOR_Gate_TruthTable.png]]

'''We want to describe each combination, that turns the desired output''' {{On}}

What's the idea? If we make sure that our circuit outputs {{On}} in all relevant cases, then it automatically outputs {{Off}} in all other cases. So we only have to focus on the {{On}} and get the {{Off}}s for free.

Start like this:

[[File:Guide_words_description1.png]]

There are 2 columns, that turn the desired output to {{On}}.

Let's start with the first and expand our descriptive sentence.

[[File:XOR_Gate_TruthTable_Column1.png]]

[[File:Guide_words_description2.png]]

Nice! Okay that's the first column - now let's add the second.

[[File:XOR_Gate_TruthTable_Column2.png]]

[[File:Guide_words_description3.png]]

We now have a complete description when our circuit outputs {{On}}

=== Step 2: Replace 'Red' with 'Not Green' ===
We only focus on {{On}} signals, that's why we try to avoid using the {{Off}} symbol in our description.

Here is the trick: When something is {{Off}}, we can also say it is '''<nowiki>'</nowiki>not {{On}}<nowiki>'</nowiki>'''.

So let's replace every {{Off}} symbol:

[[File:Guide_words_description4.png]]

=== Step 3: Highlight the gate names ===
The connecting words in our sentence are also the name of gates!

Let's highlight all words, that are also names of gates and see what it looks like:

[[File:Guide_words_description5.png]]

''Notice, that i also added some brackets, since AND is a stronger connection than OR.''

=== Step 4: Build the circuit ===
Now we can build a circuit that exactly matches our description, using the same gates that we highlighted in our sentence:

[[File:XOR_Gate_Circuit1.png|650px]]

This technique works for every truth table.

----

The structure of the resulting circuit is called ''Canonical Disjunctive Normal Form (CDNF)'' which can usually be optimized to require fewer gates (there are several techniques to achieve this).

=== More phrases ===
By using phrases that contain only AND, OR, and NOT, you can build any circuit you want, by simply describing each combination for each {{On}} output. But there is more...

You can use the following phrases and translate them into gates:

==== NOR gate ====

[[File:NOR_Gate_TruthTable_Description_Circuit.png]]

==== XOR gate ====

Phrases like ''"...different values"'' or ''"...not the same"'' translate into an '''XOR''' gate

[[File:XOR_Gate_TruthTable_Description_Circuit.png]]

==== XNOR gate ====

Phrases like ''"...equal values"'' or ''"...the same"'' translate into an '''XNOR''' gate

[[File:XNOR_Gate_TruthTable_Description_Circuit.png]]

==== Conditions ====

Phrases like ''"...under the condition that..."'' or ''"If...then"'' translate into an '''AND''' gate or a '''SWITCH'''

[[File:COND_Description_Circuit.png]]

Component/Switch (word)

2024-08-21T00:01:43Z

Poppi-Sama: Added a description to the 8 Bit Switch, linked the 1-bit switch, and added a part about circuit dependency.

The 8-bit switch is a device that can enable or disable the output, similar to the [[1-bit Switch|1-bit switch]]. It has a 1 byte input, 1 byte output, and a bit toggle switch. When the bit toggle switch is 1 or {{On}}, it outputs the input. When the bit toggle is 0 or {{Off}}, the output is disabled. Because the output is fully disabled, this mean you can connect the output to other types of output wires without causing a circular dependency.

Component/Mux

2024-08-20T23:42:33Z

Poppi-Sama: Added an example image of the mux using the input 1/2.

[[File:Mux example.png|thumb|Example of a 8 Bit Mux switching between input 1 and input 2.]]
An 8-bit multiplexer (MUX) is a digital device that has a one bit input (select 1 / 2), two byte inputs (input 1, input 2), and one byte output. The bit input determines the byte output. If the bit input is {{Off}} or 0, it outputs the first byte input. If the bit input is {{On}} or 1, it outputs the second byte input.

File:Mux example.png

2024-08-20T23:40:04Z

Poppi-Sama:

A mux device that outputs input 1, or outputs input 2, depending on if the select input is off or on.

Component/Mux

2024-08-16T00:21:32Z

Poppi-Sama: Added {{on}} and {{off}}

An 8-bit multiplexer (MUX) is a digital device that has a one bit input (select 1 / 2), two byte inputs (input 1, input 2), and one byte output. The bit input determines the byte output. If the bit input is {{Off}} or 0, it outputs the first byte input. If the bit input is {{On}} or 1, it outputs the second byte input.

Component/Mux

2024-08-16T00:00:06Z

Poppi-Sama: Added a description to the 8 Bit Mux, and how it generally works.

An 8-bit multiplexer (MUX) is a digital device that has a one bit input (select 1 / 2), two byte inputs (input 1, input 2), and one byte output. The bit input determines the byte output. If the bit input is 0 (or off), it outputs the first byte input. If the bit input is 1, it outputs the second byte input.