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== Digital techniques basics ==
For conceptual basics from the atomic level up see ''Semiconductors, Diodes and Transistors'' https://www.youtube.com/watch?v=wPHG0DCWcC0 AND ''An Introduction to Logic Gates'' https://www.youtube.com/watch?t=10&v=95kv5BF2Z9E.

=== Digital gates ===
==== AND ====
The <code>AND</code> gate behaves in the same way as the logical ''and'' operator: Output is ''true'' when both inputs are ''true'' and any otherwise ''false'':
[[File:And.png|140px|thumb|left]]
{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 0
|-
| 0 || 1 || 0
|-
| 1 || 0 || 0
|-
| 1 || 1 || 1
|}

==== OR ==== 

The <code>OR</code> gate behaves like a logical inclusive ''or'': Output is ''true'' if either or both of the inputs are ''true'' and ''false'' if both inputs are ''false'':

[[File:Or.png|140px|thumb|left]]

{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 0
|-
| 0 || 1 || 1
|-
| 1 || 0 || 1
|-
| 1 || 1 || 1
|}
==== XOR ====

The <code>XOR</code> (e'''x'''clusive-'''OR''') gate acts as a logical ''either/or'': the output is ''true'' if the inputs are different, and ''false'' if the inputs are the same:

[[File:Xor.png|140px|thumb|left]]
{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 0
|-
| 0 || 1 || 1
|-
| 1 || 0 || 1
|-
| 1 || 1 || 0
|}

==== NOT ====

A logical inverter, alias <code>NOT</code> gate, has only one input and reverses logic state:

[[File:Not.png|140px|thumb|left]]

{| class="wikitable"
|-
! Input 1 !! Output
|-
| 0 || 1 
|-
| 1 || 0  
|}
&nbsp;

==== NAND ====
A <code>NAND</code> gate works like an <code>AND</code> gate followed by a <code>NOT</code> gate:
[[File:Nand.png|140px|thumb|left]]
{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 1
|-
| 0 || 1 || 1
|-
| 1 || 0 || 1
|-
| 1 || 1 || 0
|}

==== NOR ====

The <code>NOR</code> gate is a combination <code>OR</code> gate followed by an inverter:
[[File:Nor.png|140px|thumb|left]]
{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 1
|-
| 0 || 1 || 0
|-
| 1 || 0 || 0
|-
| 1 || 1 || 0
|}

==== XNOR ====
<code>XNOR</code> (e'''x'''clusive-'''NOR''') gate is a combination of an <code>XOR</code> gate followed by an inverter:
[[File:Xnor.png|140px|thumb|left]]
{| class="wikitable"
|-
! Input 1 !! Input 2 !! Output
|-
| 0 || 0 || 1
|-
| 0 || 1 || 0
|-
| 1 || 0 || 0
|-
| 1 || 1 || 1
|}

=== Universal gates ===

The <code>NAND</code> and the <code>NOR</code> gate can be considered to be "universal" because you can make any of the basic operations out of its combinations: an inverter, an <code>OR</code> gate or an <code>AND</code> gate. Non-inverting gates do not have this versatility since they can not make an invert.

== Wiring notes ==
* Create (or have at hand) a circuit diagram before starting any wiring. Sketchy is okay.
* Use the longer outer rows for +5V on one side and ground on the other side.
* First wire power to the circuit using a common colour (red) for +5V and another (black) for ground.
* Power off while wiring circuits on the board.
* Maintain a clean household. In general designs tend to get complex and can become difficult to debug. The gate circuits are not but serpent definitely qualifies and good practice can not start soon enough (see Morgan's laws).
* Strip insulation off wires no more than necessary to prevent wires from accidentally touching each other. 
* Do not push wires too far into holes to prevent causing open circuits or short circuits.

== Building gate circuits ==

The resistors are sized to insure that the inverter circuit operates in digital mode.

For building the gate circuits, get:
* 2 pn2222 or 2 2n2222 transistors
* 1 ''1 KΩ'' resistor
* 2 ''33 kΩ'' resistor
* 2 LEDs
* 5V power

=== Inverter circuit ===

<pre>
        + 5V ---------------------------+---------------------------->>
                                        |
                                     --------
                                     | 1 KΩ |
                                     --------
                                        |--------------- LED
                                        |
                                        /
                        ---------     |/
         SW 1 ----------| 33 KΩ |-----| pn2222
                        ---------     |\
                                        \
                                        |
         GND ---------------------------+---------------------------->></pre>

=== NAND circuit ===
If another transistor is added in series with the transistor in the inverter circuit, a <code>NAND</code> gate is created. 

<pre>
        + 5V ---------------------------+---------------------------->>
                                        |
                                     --------
                                     | 1 KΩ |
                                     --------
                                        |--------------- LED
                                        |
                                        /
                        ---------     |/
         SW 1 ----------| 33 KΩ |-----| pn2222
                        ---------     |\
                                        \
                                        |
                                        /
                        ---------     |/
         SW 2 ----------| 33 KΩ |-----| pn2222
                        ---------     |\
                                        \
                                        |
         GND ---------------------------+---------------------------->></pre>
=== NOR circuit ===

If another transistor is added in parallel with the transistor in the inverter circuit a <code>NOR</code> gate is the result. IOW, a <code>NOR</code> looks like two <code>NOT</code>s sharing a single pull-up transistor of 1 KΩ.

<pre>
        + 5V ---------------------------+---------------------------->>
                                        |
                                     --------
                                     | 1 KΩ |
                                     --------
                                        |  +------------ LED
                                     ___|__|_
                                   /         \
                   ---------     |/    pn2222 \|     ---------
         SW 1 -----| 33 KΩ |-----|             |-----| 33 KΩ |----- SW 2
                   ---------     |\ pn2222    /|     ---------
                                   \_________/
                                        |
         GND ---------------------------+---------------------------->></pre>

== Boolean algebra ==

=== In plain english ===

If "today is Monday'" is ''true'' then "Not(today is Monday)" is ''false''. This logical expression translates into English as "today is Not Monday" and this makes it easier to see that it is ''false'' if today is indeed Monday. Explanations like that rapidly become convoluted and difficult to follow and this is part of the power of Boolean logic. You can write down arguments in symbolic form. To simplify the handling of complex binary connectives, the mathematician George Boole developed Boolean Algebra, using ordinary algebraic notations AND, OR and NOT. Alternatives that you may encounter are ^ for AND, v for OR, and either over-score or prefix for NOT. 

And ... The Boolean <code>AND</code> is the same as the English use of the term, but the Boolean <code>OR</code> is a little different: If you are asked "coffee OR tea?", in most western households you are not expected to say "yes" to both, while in the Boolean case <code>OR</code> includes both. The Boolean operator that corresponds to the English use of the term "OR" is the <code>XOR</code>.

The above tables next to the digital gates are called ''truth tables''. 
=== Burglary in progress ===
Suppose you want to build a security system which only works at night and responds to a window or the front door being opened. If you have light sensors you can use these for giving off a signal indicating the truth of the statement:

{| class="wikitable"
|-
! Front door open !! Window open !! Burglary in progress
|-
| False || False || False
|-
| False || True || True
|-
| True || False || True
|-
| True || True || True
|}

We can make the propositions as complex as we want:

<pre>(Burglary in progress) = (NOT(It is daytime)) AND ((Window open) OR (Front door open))

                               ---------
        Front door open -----> |       |
                               |  OR   |-----
            Window open -----> |       |    |       ---------
                               ---------    +-----> |       |
                                                    |  AND  |-----> Burglary in progress
                               ---------    +-----> |       |
                               |       |    |       ---------
         It is day time -----> |  NOT  |-----
                               |       |
                               ---------
</pre>

=== Precedence and maintaining order ===

Boolean operations are carried out in a well defined order or "precedence":

{| class="wikitable"
|-
! Operator !! Symbol !! Precedence
|-
| NOT || ' || Highest
|-
| AND || . || Middle
|-
| OR || + || Lowest
|}

Expressions inside brackets are always evaluated first, overriding the default precedence order. The Boolean equation of the ''Burglary in progress'' block diagram in fully bracketed form:
<pre>B = ((T'). ((W) + (F)))</pre>
Using the precedence rules this can be simplified to:

<pre>B = T'. (W + F)</pre>

=== Manipulating boolean expressions ===

==== Unary NOT ====

And there are rules to manipulate Boolean expressions. The most simple are the rules for the unary operator NOT:

<pre>(A')' = A
A' . A = 0
A' + A = 1</pre>

==== General rules for AND and OR ====
For more see Group theory Boolean Algebra http://mathworld.wolfram.com/BooleanAlgebra.html

Associative: 
<pre>(A . B) .C = A . (B . C)
(A + B) + C = A + (B + C)</pre>
Commutative:
<pre>A . B = B . A
A + B = B + A</pre>
Distributive:
<pre>A . (B + C) = A . B + A . C
A + (B . C) = (A + B) . (A + C)</pre>

==== Simplification rules ====

The first group of simplification rules uses one variable:

<pre>A . A = A
A + A = A</pre>

The second group uses Boolean constants:

<pre>A . 0 = 0
A . 1 = A
A + 0 = A
A + 1 = 1</pre>
=== Minimisation with Morgan's laws ===

== K-map groupings ==

== Don't care conditions ==

== Debugging notes ==

* If the errors show patterns of consistency, it's somewhere in the logic.
* If inconsistent, it's probably a loose connection.
* Test each component separately.
* Don't kill friends.
* Check power and GND for all appropriate pins.
* It can be frustrating. Don't kill family members.
* Check pin connections if done as specified in (sketchy) circuit diagram and that they aren't tied together.
* It can be very frustrating. Don't kill any acquaintances either.
* Check minimisations and pinouts.
* On rare occasions it is not me/you/us or what I/you/we did, and it is one of the components (a bent and curled pin, faulty chip, split wire (inside the insulation), faulty test equipment). If that turns out to be the case, don't kill component producer associated people. Or anybody else for that matter.

== Serpent ==

== Resources ==
=== Simulators ===

* SmartSim http://smartsim.org.uk/downloads/manual/smartsim_user_manual.pdf (contains installation and getting started instructions. Because of glibc, I installed the stand-alone version)

=== Breadboards ===
[[File:Cable-bus.png|300px|thumb|right]]

You can buy solderless breadboards in a shop or online. Mind that you pick scalable like the SD-12 so you can hook up breadboards together and they become reuseful for other projects such as prototyping our own embedded water management and short range radio (repeater) systems.

Alternatively, start gathering and collecting IDC ribbon connectors (Floppy drive cables, old HD cables, SCSI cables) to build your own breadboards with. To do this, you will also need a solder iron, hot glue, wire (for example telephone wire will do), a small screw driver, and a clamp. This board will also be scalable. Fine grained scalable. :D

I'll do both. Buy a few, and make a few.

=== Power supply ===

=== Switches for input ===

=== Light emitting diodes (LEDs) ===

=== Transistors ===
Transistors are three pin devices. The amount of current that can flow between the collector and emitter is a function of the current flowing through the base of the transistor. If no current is flowing through the base of the transistor, no current will flow through the collector and emitter. 
* Transistors http://hyperphysics.phy-astr.gsu.edu/hbase/solids/trans.html#c1

With the transistor operating in digital mode, it will be configured to carry the maximum (on) or minimum (off) current from the collector to the emitter that the circuit will allow. 

=== Resistors ===

=== Capacitors ===

=== Chips ===

==== TTL Logic ====

TTL ('''t'''ransistor-'''t'''ransistor-'''l'''ogic) chips were developed with use of transistor switches for logical operations and defines the binary values as:
* 0 V to 0.8 V = logic 0
* 2 V to 5 V = logic 1

The 7400 series logic chips have been manufactured since the 1960s and were used to design and build computers but they are no longer used for that. They still have many uses in teaching digital logic. They are easy to obtain and fairly inexpensive. They draw a lot of power and must be supplied with +5 volts. Individual gates may draw 3 to 4 mA. The low power Schottky versions of TTL chips draw only 20% of the power, but are more expensive. These chips have LS in the middle of their model number. 
* 7400 (Quad 2-Input NAND gate) http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/nand.html#c3
* 7402 (NOR, haven't found it yet) http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/nor.html#c3
* 7404 (Triple voltage regulator) http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/buffer.html#c5
* 7410 (Triple 3-Input NAND gate) http://pdf1.alldatasheet.com/datasheet-pdf/view/7823/NSC/7410.html
* 7420 (Dual 4-Input NAND Gate) http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/nand3.html#c1
* 74151 (Data Selectors/Multiplexers) http://pdf1.alldatasheet.com/datasheet-pdf/view/7831/NSC/74151.html
* 74175 (Hex/Quad D Flip-Flops with Clear) http://pdf1.alldatasheet.com/datasheet-pdf/view/27396/TI/SN74175N.html
* Timer (haven't found one yet) http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/t555.html#c1

==== CMOS Logic ====

CMOS ('''c'''omplementary '''m'''etal '''o'''xide '''s'''emiconductor) chips are lower in power requirements (drawing about 1 mA) and operate with a wide range of supply voltages (typically 3 to 18 volts). The CMOS model number will have a C in the middle of it. A bigh drawback is extreme sensitivity to static electricity - they must be carefully protected from static discharges. 

==== NMOS and PMOS Logic ====

PMOS and NMOS ('''p'''- and '''n'''-channel '''m'''etal '''o'''xide '''s'''emiconductors) offer the advantage of higher component density than TTL chips. They too are sensitive to damage from electrical discharge.

== Related ==
* [[Encrypting everything]]

== References ==