Difference between revisions of "Arcane mixing techniques"

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Integrated circuits have many individual circuit components in a single package. For example, the 7400 chip has 4 NAND gates. See resources.
 
Integrated circuits have many individual circuit components in a single package. For example, the 7400 chip has 4 NAND gates. See resources.
  
−
In the below circuit <code>AB + BC</code> 3 chips are used: the 7400, 7402 and 7404. All three inverters are on one chip. Both NAND's are too. The chips are IC1, IC2 and IC3 in the diagram, the order in which they will be placed on the breadboard. That is also why the pins are numbered as they are (no need to look up datasheets).  
+
In the below circuit <code>AB + BC</code>, 3 chips are used: the 7400, 7402 and 7404. All three inverters are on one chip. Both NAND's are on the same chip too. The chips are IC1, IC2 and IC3 in the diagram, the order in which they will be placed on the breadboard. That is also why the pins are numbered as they are (no need to look up datasheets).  
  
 
[[File:Labeling.png|800px|thumb|center]]
 
[[File:Labeling.png|800px|thumb|center]]

Revision as of 19:03, 4 September 2015

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 AND gate behaves in the same way as the logical and operator: Output is true when both inputs are true and any otherwise false:

And.png
Input 1 Input 2 Output
0 0 0
0 1 0
1 0 0
1 1 1

OR

The OR 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:

Or.png
Input 1 Input 2 Output
0 0 0
0 1 1
1 0 1
1 1 1

XOR

The XOR (exclusive-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:

Xor.png
Input 1 Input 2 Output
0 0 0
0 1 1
1 0 1
1 1 0

NOT

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

Not.png
Input 1 Output
0 1
1 0

 

NAND

A NAND gate works like an AND gate followed by a NOT gate:

Nand.png
Input 1 Input 2 Output
0 0 1
0 1 1
1 0 1
1 1 0

NOR

The NOR gate is a combination OR gate followed by an inverter:

Nor.png
Input 1 Input 2 Output
0 0 1
0 1 0
1 0 0
1 1 0

XNOR

XNOR (exclusive-NOR) gate is a combination of an XOR gate followed by an inverter:

Xnor.png
Input 1 Input 2 Output
0 0 1
0 1 0
1 0 0
1 1 1

Universal gates

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

Labeling diagrams

Integrated circuits have many individual circuit components in a single package. For example, the 7400 chip has 4 NAND gates. See resources.

In the below circuit AB + BC, 3 chips are used: the 7400, 7402 and 7404. All three inverters are on one chip. Both NAND's are on the same chip too. The chips are IC1, IC2 and IC3 in the diagram, the order in which they will be placed on the breadboard. That is also why the pins are numbered as they are (no need to look up datasheets).

Labeling.png

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

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

NAND circuit

If another transistor is added in series with the transistor in the inverter circuit, a NAND gate is created. 

        + 5V ---------------------------+---------------------------->>
                                        |
                                     --------
                                     | 1 KΩ |
                                     --------
                                        |--------------- LED
                                        |
                                        /
                        ---------     |/
         SW 1 ----------| 33 KΩ |-----| pn2222
                        ---------     |\
                                        \
                                        |
                                        /
                        ---------     |/
         SW 2 ----------| 33 KΩ |-----| pn2222
                        ---------     |\
                                        \
                                        |
         GND ---------------------------+---------------------------->>

NOR circuit

If another transistor is added in parallel with the transistor in the inverter circuit a NOR gate is the result. IOW, a NOR looks like two NOTs sharing a single pull-up transistor of 1 KΩ. 

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

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 AND is the same as the English use of the term, but the Boolean OR 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 OR includes both. The Boolean operator that corresponds to the English use of the term "OR" is the XOR.

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:

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: 

(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  |-----
                               |       |
                               ---------

Precedence and maintaining order

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

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: 

B = ((T'). ((W) + (F)))

Using the precedence rules this can be simplified to: 

B = T'. (W + F)

Manipulating boolean expressions

Unary NOT

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

(A')' = A
A' . A = 0
A' + A = 1

General rules for AND and OR

For more see Group theory Boolean Algebra http://mathworld.wolfram.com/BooleanAlgebra.html

Associative: 

(A . B) .C = A . (B . C)
(A + B) + C = A + (B + C)

Commutative: 

A . B = B . A
A + B = B + A

Distributive: 

A . (B + C) = A . B + A . C
A + (B . C) = (A + B) . (A + C)

Simplification rules

The first group of simplification rules uses one variable: 

A . A = A
A + A = A

The second group uses Boolean constants: 

A . 0 = 0
A . 1 = A
A + 0 = A
A + 1 = 1

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

Breadboards

Cable-bus.png

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.

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 (transistor-transistor-logic) 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.

CMOS Logic

CMOS (complementary metal oxide semiconductor) 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 metal oxide semiconductors) offer the advantage of higher component density than TTL chips. They too are sensitive to damage from electrical discharge.

Related

References

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