OpenLLM-France/wikimedia huggingface dataset:
# A-level Computing 2009/AQA/Computer Components, The Stored Program Concept and the Internet/Fundamental Hardware Elements of Computers/Gate conversion

Sometimes it is cheaper to create circuits using only one sort of gate, and you might be asked to do so in the exam. These gates tend to be NAND & NOR gates. "But how can you create complex circuits by using only one type of gate?!" you may well ask. We'll now cover how other gates can be made from NAND & NOR gates:
| Step | NOR Gate | Equivalent |
| Diagram | | |
| Description | If you split the same input (A) and feed it into NOR both gate inputs you create a NOT Gate | If you split the same input (A) and feed it into NOR both gate inputs you create a NOT Gate |
| Truth Table | Because: A A $A+A$ ${\overline {A+A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0 | Because: A A $A+A$ ${\overline {A+A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0 |
| Step | NAND Gate | Equivalent |
| Diagram | | |
| Description | If you split the same input (A) and feed it into both NAND gate inputs you create a NOT Gate | If you split the same input (A) and feed it into both NAND gate inputs you create a NOT Gate |
| Truth Table | Because: A A $A.A$ ${\overline {A.A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0 | Because: A A $A.A$ ${\overline {A.A}}$ ${\overline {A}}$ 0 0 0 1 1 1 1 1 0 0 |
* Exercise: Gate Conversion
* Render the following boolean equations using only NAND gates:
* ${\overline {{\overline {A}}.B}}$
* Answer:
* ${\overline {A}}.{\overline {B}}$
* Answer:
* Now try the similar questions using only NOR gates (you might need De Morgan's Law to help you out here, or use a truth table to simplify things)
* $A+{\overline {B}}$
* Answer:
* ${\overline {A}}.{\overline {B}}$
* Answer:
* Why might you want to use only one sort of gate to create a circuit?
* Answer:
* It might be cheaper to make circuits with only one sort of gate, it might make for simpler circuits
# A-level Computing 2009/AQA/Computer Components, The Stored Program Concept and the Internet/Fundamental Hardware Elements of Computers

* From the specification:
* Logic Gate:
* Construct truth tables for the following gates: NOT, AND, OR, XOR, NAND, NOR
* Be familiar with drawing logic diagrams involving one or more of the above gates.
* Boolean Algebra:
* Be familiar with the use of De Morgan’s laws and Boolean identities to manipulate and simplify simple Boolean expressions.
* Logic Gates
* Boolean gate combinations
* Building circuits
* Boolean algebra
** Simplifying boolean equations
** Boolean identities
** De Morgan's Laws
** Gate conversion
* EXTENSION:Uses of gates
# A-level Computing 2009/AQA/Computer Components, The Stored Program Concept and the Internet/Fundamental Hardware Elements of Computers/Building circuits

A common question in the exam is to be given some boolean algebra and be asked to express it as logic gates. Let's take a look at an addition and subtraction example that you should be familiar with:
First we are going to deal with the inner-most brackets
Finally we combine this answer with the $9-$
It will work exactly in the same way for boolean algebra, but instead of using numbers to store our results, we'll use logic gates:
* Example: Building circuits
* $C.(A+B)$
* As with any equation, we are going to deal with the inner-most brackets first$(A+B)$, then combine this answer with the $C.$
* Exercise: Building circuits
* Draw the circuit diagrams for the following. (Remember: do we deal with AND or OR first?):
* $A.B+C$
* Answer:
* $({\overline {A}}+{\overline {B}}).C$
* Answer:
* ${\overline {(A+B)}}.C$
* Answer:
* $(A.{\overline {B}})\oplus (B.C)$
* Answer:
* ${\overline {(A.B).(C+{\overline {D}})}}$
* Answer:
A common question in the exam is to give you a description of a system. You'll then be asked to create a boolean statement from this description, and finally build a logic gate circuit to show this system:
Example: Building circuits
Using boolean algebra describe the following scenario:
A car alarm is set off if a window is broken or if it senses something moving inside car, and the car is not being towed, or the engine is not on.
Where:
A = being towed,
B = window broken,
C = engine on,
D = senses movement
Before you rush into answering a question like this, let's try and break it down into its components. The questioner will often be trying to trick you. The two occasions that the alarm will sound are:
$B+D$ but there is a caveat, the alarm will sound if either of these are true AND two things are also true, namely the engine is NOT on, and the car is NOT being towed:
${\overline {A}}+{\overline {C}}$
Combining both we get (remember the brackets!):
$(B+D).({\overline {A}}+{\overline {C}})$
The next step is to create a diagram out of this: :
* Exercise: Building circuits
* A security system allows people of two different clearance levels access to a building. Either they have low privileges and they have a card and they are not carrying a mobile. Alternatively they have a key and are allowed to carry a mobile.
* The inputs available are:
* A = carrying a card
* B = carrying a mobile phone
* C = carrying a key
* Write down the boolean equation to express this:
* Answer:
* $(A.{\overline {B}})+(C)$
* If you wrote: $(A.{\overline {B}})+(C.B)$ You'd be wrong! The reason being the text says: Alternatively they have a key and are allowed to carry a mobile. This doesn't mean $C.B$, it means they can carry a mobile, or they can choose not to: $C.(B+{\overline {B}})$, which simplifies to: $C.(B+{\overline {B}})=C.(1)=C$.
* Draw the logic gate diagram to solve this:
* Answer:
# Annotations to James Joyce's Ulysses/Circe/556
## Annotations

Introibo ad altare diaboli (Latin) I will go in to the altar of the devil. In the context of the Black Mass which is being parodied here, Father O'Flynn subverts the words of the Prayers at the Foot of the Altar from the Latin Tridentine Mass, which Mulligan quoted on the opening page of the novel. See 003.05. The correct form, however, is: Introibo ad altare Domini Inferi (I will go in to the altar of the Lord of Hell).
Corpus Meum (Latin) My Body. During the Consecration of the Host in the Latin Tridentine Mass, the celebrant elevates the host and says: Hoc est enim corpus meum (For this is my body). In the Black Mass, which is being parodied here, the corresponding words are: Hoc est corpus Jesu Christi (This is the body of Jesus Christ).
In some editions of Ulysses, this phrase is emended to Corpus meum.

## References

* ↑ Gifford (1988) 527. Thornton (1968) 427.
* ↑ Missa Niger.
* ↑ Gifford (1988) 527. Thornton (1968) 427.
* ↑ Missale Romanum 85.
* ↑ Missa Niger.
# Annotations to James Joyce's Ulysses/Circe/557
## Annotations

Exit Judas. Et laqueo se suspendit (Latin) Judas leaves. And he hanged himself with a noose. The first two words parody the stage directions in a Shakespearean play. The last four words are taken from the Vulgate translation of Matthew 27:5:
Matthew 27:5 :
| Et proiectis argenteis in templo, recessit, et abiens laqueo se suspendit | And he cast down the pieces of silver in the temple, withdrew, and going away he hanged himself with a noose. |

## References

* ↑ Gifford (1988) 528. Thornton (1968) 427.
* ↑ Matthew 27:5.
# Advanced Inorganic Chemistry/Normal Modes of Vibration
## Molecular vibrations

Molecular vibrations are one of three kinds of motion, occurs when atoms in a molecule are in periodic motion. Molecular vibrations include constant translational and rotational motion. Translational motion occurs when the whole molecule goes in the same direction while the rotational motion occurs when the molecule spins like a top. Molecule vibrations fall into two main categories of stretching and bending. Stretching changes in interatomic distance along bond axis, while bending changes in angle between two bonds in a molecule.
There are two types of stretching, symmetric stretching and asymmetric stretching as the following figure shows:
There are four types of bend, rocking, scissoring, wagging, and twisting:

## Normal modes of vibration

Each atom in a molecule has three degree of freedom. A molecule with n atoms has 3n degree of freedom. 3n degree of freedom composes of translation, rotations and vibrations. All 3n degrees of freedom have symmetry relationships consistent with the irreducible representations of the molecule's point groups. Non-vibration modes (NVM) include translations and rotations. The vibrational motions of the atoms in a molecule can always be resolved into fundamental vibrational modes for the entire molecule.

### Atomic displacement coordinates

The number of normal modes of vibration:
* 3n-6 for non-linear molecules
* 3n-5 for linear molecules
To indicate the the number of normal modes of vibration:
* Locate a set of three vectors along the Cartesian coordinates at each atom, representing the 3n degrees of freedom
* Find the reducible representation
* Reduce it to irreducible representations, subtract rotations and translations
* The rest of irreducible representations will give the symmetry of the NMVs

## Samples
### vibrations for SO$_2$

| C$_{2v}$ | E | C$_2$ | σ$_{v(xz)}$ | σ’$_{v(yz)}$ | | |
| A$_1$ | 1 | 1 | 1 | 1 | z | x$^2$, y$^2$, z$^2$ |
| A$_2$ | 1 | 1 | -1 | -1 | R$_z$ | xy |
| B$_1$ | 1 | -1 | 1 | -1 | x, R$_y$ | xz |
| B$_2$ | 1 | -1 | -1 | 1 | y, R$_x$ | yz |
| Γ$_{3n}$ | 9 | -1 | 1 | 3 | | |
| N$_i$ | 3 | 1 | 1 | 3 | | |
| X$_i$ | 3 | -1 | 1 | 1 | | |
Reduce
Γ$_{3n}$=3A$_1$+A$_2$+2B$_1$+3B$_2$
Γ$_{trans}$=A$_1$+B$_1$+B$_2$
Γ$_{rotations}$=A$_2$+B$_1$+B$_2$
Γ$_{NMV}$=Γ$_{3n-6}$=2A$_1$+B$_2$
NMVs are also identified by frequency numbers: v$_1$, v$_2$, v$_3$,... The numbering is often assigned systematically in descending order of the symmetry species and among modes of the same symmetry in descending order of the vibrational frequency. Stretching modes have higher frequency than bending modes.
# Annotations to James Joyce's Ulysses/Cyclops/289
## Annotations

tantras (Sanskrit) A tantra is a Hindu religious text. In Theosophy, tantras are mystical and magical words comprising rituals associated with black magic or sorcery.
etheric double (Theosophy) In Theosophy, the double, or Astral Body, is the ethereal counterpart or shadow of a man or animal's physical body.
jivic rays (Theosophy) In Theosophy, jiva refers to Life, as the Absolute. It may also refer to the Monad, the immortal part of man which is reincarnated. The adjectival form jivic appears to be Joyce's own coinage.
prālāyā (Sanskrit) dissolution. In The Theosophical Glossary, Helen Blavatsky defines Pralaya as: A period of obscuration or repose—planetary, cosmic or universal—the opposite of Manvantara. In the context of Theosophy, pralaya refers to the period between death and reincarnation.
In transliterating Sanskrit terms from Devanagari to Roman script, a macron is placed over a long vowel. There are no long vowels in pralaya; Joyce's macrons here and below (lines 16 and 19) are whimsical.
See also 041.04.
tālāfānā, ālāvātār, hātākāldā, wātāklāsāt telephone, elevator, hot and cold [plumbing], water closet. The whimsical spellings and macrons parody the Theosophists' predilection for Sanskrit terms. See prālāyā above.
Māyā (Sanskrit) Illusion. In both Hindu philosophy and Theosophy māyā refers to the idea that the physical world of sense perception is not part of true reality.
In this case, Joyce's whimsical macrons are justified, but it is probably fair to say he would have added them even if they were not.

## References

* ↑ Gifford (1988) 329.
* ↑ Helen Blavatsky, The Theosophical Glossary, p. 296.
* ↑ Helen Blavatsky, The Theosophical Glossary, p. 35. Gifford (1988) 330.
* ↑ Helen Blavatsky, The Theosophical Glossary, p. 153. Gifford (1988) 330.
* ↑ Helen Blavatsky, The Theosophical Glossary, p. 201.
* ↑ Gifford (1988) 330.
* ↑ Helen Blavatsky, The Theosophical Glossary, p.242.
* ↑ Gifford (1988) 330.
* ↑ Helen Blavatsky, The Theosophical Glossary, p. 195.
# Annotations to James Joyce's Ulysses/Cyclops/284
## Annotations

a chara (Irish) friend. This is the vocative case of the noun cara.
the mountain gorse (Ulex Europeus) (Latin) Ulex europaeus is the scientific name for the evergreen shrub variously known in Ireland as the whin, furze or gorse. The leaves are spiny but green, while the flowers are yellow. When they wilt, however, the leaves turn tawny orange in the words of John Betjeman in Cornish Cliffs. In his essay Of Usury, Francis Bacon describes the yellow headgear worn by Jewish moneylenders as orange-tawny. Gorse is found throughout Ireland.
When identifying a species through its scientific name, it is now modern usage to capitalize the genus (Ulex) but not the species (europaeus).

## References

* ↑ Gifford (1988) 320.
* ↑ Cornish Cliffs.
* ↑ The Essays of Francis Bacon, Edited, with Introduction and Notes by Mary Augusta Scott, New York (1908), pp. 187-188.
* ↑ Wildflowers of Ireland.
# Annotations to James Joyce's Ulysses/Cyclops/287
## Annotations

Bi i dho husht (Irish) Be quiet. The correct Irish form is: Bí i do thost. The final word is pronounced [hɔsˠt̪ˠ] (approximately: hawst). The Citizen has clearly confused this with the unrelated English word hush, which implies that he is by no means a fluent speaker of his native tongue.
# Annotations to James Joyce's Ulysses/Cyclops/293
## Annotations

Sinn Fein ... Sinn fein amhain (Errata) This should read: Sinn féin ... Sinn féin amháin. Gabler (1984) did not emend it, however, on the grounds that the errors were Joyce's and not typos. When an early draft of this episode was published in The Little Review, it appeared exactly as it does on the page above.
Sinn féin ... Sinn féin amháin! (Irish) Ourselves ... Ourselves alone! Watchword of Irish nationalists at the turn of the century. According to Gifford these words occur in the refrain of Timothy Daniel Sullivan's patriotic song The West's Awake, though the only song of this name that I am aware of is by Thomas Osbourne Davis, and it does not include these words. Thornton mentions a song called Sinn Fein, Sinn Fein Amhain by O'Higgins.

## References

* ↑ The Little Review, Volume 6, Number 7 (November 1919), p. 50.
* ↑ Gifford (1988) 333. Thornton (1968) 269.
* ↑ Hodgart, Matthew (1959). Songs in the Works of James Joyce. New York: Columbia University Press. p. 202. Retrieved 06-12-2012. {{cite book}}: Check date values in: |accessdate= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)
# Annotations to James Joyce's Ulysses/Cyclops/292
## Annotations

corpora cavernosa (Latin) cavernous bodies. Corpora cavernosa is the anatomical name for two masses of erectile tissue in the penis; a penile erection occurs when the cavities in these bodies (and in a third body, the corpus spongiosum penis) fill with blood and become distended.
in articulo mortis per diminutionem capitis (Latin) at the moment of death caused by the decrease of the head. Bloom's medical Latin is improvised; capitis diminutio is actually a legal term meaning the loss of one's political rights, whereas Bloom means the breaking of the neck (per frangentem cervicis).

## References

* ↑ Gifford (1988) 332.
* ↑ Gifford (1988) 332.
# Adventist Youth Honors Answer Book/Knot/Bowline

* Bowline
* Use: This knot doesn't jam or slip when tied properly. It can be tied around a person's waist and used to lift him, because the loop will not tighten under load. In sailing, the bowline is used to tie a halyard to a sail head.
* How to tie:
* Make the overhand loop with the end held toward you, then pass end through loop.
* Now pass end up behind the standing part, then down through the loop again.
* Draw up tight.
See also Knots/Loop knots/Bowline.
# Adventist Youth Honors Answer Book/Knot/Cat's paw

* Cat's paw
* Use: The Cat's paw is used for connecting a rope to an object.
* Attaching a rope to a hook (or to a post or rail where the load is perpendicular to the post) with more security than a simple girth hitch.
* Joining an eye to a ring.
* Strongly joining eyes in the ends of two lines, where there is access to the end of at least one line.
* How to tie:
* Method 1
* Form a bight in the middle of the line, and pull it back over itself like a girth hitch. This forms two loops, turned in opposite directions. Give each loop one more full turn in the direction that will tend to tighten it (the wrong direction will undo the loop completely). Pass both loops over the hook, rail or post and pull tight, taking care to push the bight up snugly against the turns.
* Method 2
* If working end of the line has an eye in it, and the standing end is accessible, the knot can be tied to a closed ring, another eye, or a rail with inaccessible ends, as follows. Pass the eye around the ring or rail, then pass the standing end through its own eye (this effectively forms a girth hitch). Then pass the standing end through the eye again, and pull up tight, taking care to push the bight up snugly against the turns.
* When using the cat's paw to join two eyes, this process may be repeated several times to give several turns - as many as five in a fine fishing monofilament. Then when tightened, instead of pulling the bight up against the turns, both eyes are pulled equally, to make neat coils of turns in both eyes, meeting halfway between them.
# Adventist Youth Honors Answer Book/Knot/Anchor bend

* Anchor bend
* Use: The Anchor Bend is a knot used for attaching a rope to a ring or similar termination. The round turn and tight application help keep the rope from chafing.
* How to tie:
* Make two turns around a hitch.
* Pass the running end around the standing end and beneath the two turns.
* Finish with a half hitch on the standing end.
# Adventist Youth Honors Answer Book/Knot/Bowline on a bight

* Bowline on a bight
* Use: This makes a secure loop in the middle of a rope which does not slip.
* How to tie:
* A bight is the middle part of the rope (not the ends)
* In the middle of a rope, form a small loop.
* Thread the bight through the loop.
* Spread out the bight a little.
* Pass this down and around the whole knot.
* Continue until it come back to the neck where it started.
* Tighten the bight to complete the knot. Tighten carefully so that you don't get a kind of slip knot.
# Adventist Youth Honors Answer Book/Knot/Bowline on a coil

* Bowline on a coil
* Use: This is used as an impromptu harness, however is not recommended today since there are commercially available pre-fabricated harnesses. This method is preferable to a single loop because it distributes weight across all the loops/wraps.
* How to tie:
* To tie, wrap about 15 feet from the loose end of the rope around your body.
* Form a loop from the (non-loose) end of the rope (like a regular bowline) and slip it under the rope around your body.
* Thread the loose end of the rope through the loop, around the long end, and back through the loop (like a regular bowline).
# Adventist Youth Honors Answer Book/Knot/Care Of Rope

How To Coil a Climbing Rope
If you are storing your rope for a while or stuffing it away in a back pack, coiling a climbing rope is worth the effort and will save you lots of time untangling knots that have mysteriously tied themselves in the middle of it.
Coiling a Climbing Rope
Step 1
Hold the middle of your rope in one hand and loop both strands over your shoulders. Some ropes have a convenient middle marker to make this easy. If yours doesn't, find both ends and hold them together. Then shuffle both the strands of rope through your hands until you get to the middle point.
Step 2
Reach across and grab the rope below your other hand.
Step 3
Pull your hand along the rope, creating enough space to flick the next two strands over your head, so they rest on your shoulders with the first two. Repeat this with your other hand in the opposite direction.
Step 4
Keep draping the rope over your shoulders until there is about four meters left. Use both hands to take the rope off your shoulders, and drape the middle of the loops over your arm.
Step 5
Wrap the two ends of the rope tightly around all the coils near the top. Do this three or four times. It's best to go from the bottom upwards.
Step 6
Push a loop of each end through the top of the main coils as shown.
Step 7
Pass the two ends of the rope through these loops. Pull it all tight and your rope is coiled!
Step 8
If the tails of rope are long enough (at least 1 meter), you can tie the rope on your back. Pull the tails over your shoulders, cross them over your chest, then wrap them in opposite directions around your back. Bring the ends in front of you and tie them together around your waist.
How To Stack a Climbing Rope
Coiling a climbing rope is useful when you need to carry it or pack it away neatly, but you'll need to 'stack' the rope so that it will feed out without tangles while you're climbing. Beginning at one end, simply feed the rope into a pile on top of your rope bag, or a clean area of the ground. Tying the ends of the rope into the straps of your rope bag makes it easier to find them. When preparing to lead climb, the leader will tie into the top end of the rope.
# Adventist Youth Honors Answer Book/Knot/Alpine butterfly

* Alpine butterfly
* Use: The Butterfly Loop has a high breaking strength and is regarded by mountaineers as one of the strongest knots to attach climbers to the middle of a rope, such that they have room to move around even when the main rope goes tight, and they can be supported in either direction from the main rope. The loop is typically attached to a climbing harness by carabiner.
* It can also be used to isolate a worn section of rope, where the knot is tied such that the worn section is used for the center of the loop.
# Adventist Youth Honors Answer Book/Knot/Carrick bend

* Carrick bend
* A fully interwoven diagonally opposed Carrick bend
* Use: The Carrick bend is used for joining two lines. It is particularly appropriate for very heavy rope or cable that is too large and stiff to easily be formed into other common bends. It will not jam even after carrying a significant load or being soaked with water. The Carrick bend's aesthetically pleasing interwoven and symmetrical shape has also made it popular for decorative purposes.
* In the interest of making the Carrick bend easier to untie, especially when tied in extremely large rope, the ends may be seized to prevent the knot from collapsing when load is applied. This practice also keeps the knot's profile flatter and can ease its passage over capstans or winches.
* The ends are traditionally seized to their standing part using a Round seizing. For expediency, a series of double constrictor knots, drawn very tight, may also be used. When seizing the Carrick bend, both ends must be secured to their standing parts or the bend will slip.
* WARNING: The Carrick bend is generally tied in a flat interwoven form shown above. Without additional measures it will capsize (collapse) under load into a secure and stable, although bulky, form. If the knot is allowed to capsize naturally under tension, considerable slippage of line through the knot can occur before tightening. The knot should be upset carefully into the capsized form and worked up tight before actual use.
# Adventist Youth Honors Answer Book/Knot/Clove hitch

* Clove hitch
* Use: This knot is the "general utility" hitch for when you need a quick, simple method of fastening a rope around a post, spar or stake.
* How to tie:
* Make a turn with the rope around the object and over itself.
* Take a second turn with the rope around the object.
* Pull the end up under the second turn so it is between the rope and the object. Tighten by pulling on both ends.