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Published: Tuesday, 04 April 2023 17:33

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Memory Testing:

We learned in previous section on VLSI that all logic gates on silicon are tested via DFT (Design for Testability). Same would apply to sram memory on silicon too.Here we are talking about 6T SRAM meory, but the memory testing has to be applied to all kinds of memories inclusinfg DRAM, NAND, etc. We are limiting to to SRAM meories since these are the memories that are found on 99% of the chips as CPU, GPU, embedded chips and other digital/analog chips.

However memory can't be tested in traditional way of testing other gates. Reason is there are tons of memory bits (i.e there are 1M memory cells for 1Mbit mem). If we test each bit for stuck at 0 and stuck at 1, it will take a long time. First, we've to apply the addr to choose the intended bit, then write a 0, and then read out a 0. Then we write a 1, and read out a 1. Then we move to the next addr, until all the addr are exhausted. But we are not done here. Memory bits being in close proximity to each other have effect on each other, where writing a 0 or 1 in one bit, may perturb the value of other bit. So, we have to test all other bits when we have written a 0 or 1 to a single bit. And repeat this process million times for million bits. Assuming clk running at 1GHz, and memory of 1 Mbit, and rd/wrt time of 1 cycle only, reading 1M bits would need = 1M/1G=0.001sec. Now we repeat it million times, implying total time of 0.001sec*1M=1000sec. This is impractical and cost prohibitive.

BIST (Built in Self Test)

So, memory folks over the years observed the failing pattern of memories on silicon, and figured out what kind of interactions occur among different bits, and what kinds of patterns are going to give you the highest failure rate. Not all patterns need to be applied exhaustively. On top of that, instead of having a software program read/write memories, they built in hardware support for testing memories. Here in comes the BIST. It involved adding a state machine which would go thru all addresses of memories, rd/wrt appr values, compare the read values to expected values, and then generate a signature at end. Different kind of memory testing algorithms popped up. The most popular among them is 14N MARCH algorithm.

Memory Repair:

Since memory bits are placed very densely together, and are relatively less stable than logic cells across PVT (process, voltage and temperature), they are more likely to have failures. If we have to throw away the whole chip because of some defect in one of the memory bits, that would be pretty costly. So, redundancy was added in the memories, where few failing rows or columns may be swapped with spare rows and columns. These spare rows/columns were added to same meory array, but were just marked unused. When a failure was detected by the BIST engine above, these rows/columns would be swapped automatically by the BIST repair engine, and locked via some "fuse" bits, so that the next time chip powered up, it would be using the swapped rows/columns for failing bits. This was all transparent to the user, as everything was handled by hardware internally.

This memory test and repair is usually done everytime the chip powers up.

Diagram:

This is simplistic diagram of how memory logic looks like in presence of BIST.

CAD Tools:

In the past, BIST hardware was designed individually by each company to be used on their chips, since they had their own custom memories. Now, with memory compilers available from major CAD vendors, there's no need for designing your own custom memories. These CAD vendors alos supply BIST solutions to go along with their memories, so no need to code your own bist engine.

Synopsys Star Builder also knows as SMS (Star Memory System):

Star Builder is a tool by Synopsys which can add "test and repair logic" at RTL level to memories in your design. STAR stand for "Self Test And Repair". They also include the whole set of suites to verify the design at RTL level as well as diagnose memory in silicon, once these are added to design. In order for their SMS to work with other 3rd party memories, Synopsys developed a memory description language called MASIS. Using MASIS, you may specify your memory view, which will be used by SMS to integrate STAR logic in your design. MASIS is very simple text file, which specifies a "tag" for all i/p and o/p ports as Clock, Data, TestData, Address, TestAddress, ReadEnable, TestReadEnable, WriteEnable,, TestWriteEnable, BistEn, etc. It also has additional strutural details about rows, columns, etc. As per synopsys , SMS works better with Synopsys compiled memories, since then they can integrate the critical SMS logic within the hard memory macro allowing for better timing and area. SMS can be used with SRAM, DRAM, NAND or any other embedded or custom memory.

Star Builder has a GUI which has options to customize adding BIST. Or you may also use the command line tool called "buildersh" which is a Star Builder Shell to automate the process via scripts. SMS is added to RTL in multiple separate steps as shown below:

Here's a link for various steps: https://www.synopsys.com/dw/doc.php/memoriesandlogiclibraries/doc/latest/apnt0256.pdf

1. Add memory wrappers around all memories in RTL design. These wrappers add extra ports for BIST purpose, and add muxes so that original functional operation of memories is not affected. For 3rd party memories, MASIS view has to be provided, so that tool can figure out where to place bist test ports.
2. Now add SMS processor (or state machine) that will control these BIST ports on memories. You may configure to have one SMS processor for each memory or group multiple memories under one SMS processor.
3. Once these SMS processors and memory wrappers have been added at block level, we can now have a master SMS server that connects to all these SMS processors for each block, and communicate to them via IEEE1500 protocol. We can have an optional TAP logic at top chip level, that can communicate with this SMS server and initiate STAR tests for memories when needed. We usually also have an interface on the SMS server for software to write into it's registers which will allow software to control BIST and repair too.

Once SMS is added, we can verify new RTL by inbuilt tests provided. Once silicon data is available, the yield Accelerator tool can analyze memory failures and provide guidance for yield improvement.

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Published: Sunday, 26 March 2023 23:48

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Astronomical Science

I'm including Astronomical Science as it's included in US middle School Curriculum. Astronomy is the study of planets and the universe. It's good to know about it.

Khan Academy videos:

Middle School Earth and Space Science: https://www.khanacademy.org/science/middle-school-earth-and-space-science

Cosmology and Astronomy (unit 1, 2 and 3): https://www.khanacademy.org/science/cosmology-and-astronomy

Most of the material below is from Khan Academy lectures above, with supplementary material from elsewhere.

Units of time:

Since we'll be talking in units of billions of years, it's better to have a unit for large number of years. One commonly accepted in Ga (Giga annum) or Gy (Giga years). All of these refer to 1 Billion years (giga in science means 10^9 or billion). Ga is the most commonly used. Gya (Giga year ago) is used to refer to timeline in Billions, while Mya (Million year annum) is used for millions.

Big Bang

Assuming, big bang is what happened, we start from there. Big Bang Theory => https://en.wikipedia.org/wiki/Big_Bang

According to "Big Bang Theory" widely accepted, a big bang (explosion) happened 14 Billion years ago (14 Gya) from one point. That is considered the beginning or the birth of the Universe. Big Bang Theory is the best theory out there explaining the birth of Universe, but also sounds very unimaginable. Sal explains on Khan Academy on how this Universe is expanding, and has no end or edges, as it can be considered to be a 4 dimensional sphere with 3 dimensional surface, which is hard to imagine. But the question that begs is what was there before big bang? Well, the theory says that there was nothing before big bang, because there was no time. Time started when "Big Bang" happened (i.e time=0 was when Big Bang happened). Where did this matter come for "Big Bang" to happen? Physicists claim that something came out of nothing, and after billions of years, when the last star dies, everything will get into a black hole with nothing left. So, we started from nothing and will go back to nothing. There's a good article on bbc over here: https://www.bbc.com/future/article/20220105-what-existed-before-the-big-bang

Starting from Big Bang, a full chronology of events is provided here: https://en.wikipedia.org/wiki/Chronology_of_the_universe

During the first microsecond of Big Bang, a substance called Quark-Gluon Plasma was the only matter that existed. First the plasma that consisted of quarks and gluons was separated by the hot expansion of the universe. Then the pieces of quark reformed into so-called hadrons. A hadron with three quarks makes a proton, which is part of atomic cores. Neutrons also formed at this time.

The very first elementary particles formed are explained via the standard model here: https://en.wikipedia.org/wiki/Standard_Model

The standard model is theory used to describe 3 fundamental forces out of the 4 fundamental forces that exist. They also describe elementary particles which are sub atomic and are used to form components of atoms. There are two fundamental classes of subatomic particles: fermion and boson

1. Fermion: Fermion is a particle that follows Fermi Dirac statistics. These have one half integer spin as 1/2, 3/2 etc. Fermions have 12 elementary particles of spin 1/2. They have antiparticle too for each of these 12 particles. All ordinary matter that exists in universe is made of Fermions. Fermions are classified according to how they interact. There are 2 categories:
   1. Quark and antiquark: The defining property of quarks is that they carry color charge, and hence interact via the strong interaction. There are 6 quarks, and 6 anti quarks. 6 quarks are up, down, charm, strange, top and bottom. Quarks can form color-neutral composite particles called Hadrons that either contain a quark and antiquark (mesons) or 3 quarks (baryons). Protons and neutrons are the lightest baryons that we see in atoms.
   2. Lepton and antilepton: Leptons do not have color charge. There are 6 leptons and 6 antileptons. Out of 6 leptons, 3 of them carry charge (electron, muon and tau) and hence interact electromagnetically. The remaining 3 (neutrino versions of charged ones - i.e electron neutrino, muon neutrino and tau neutrino) do not carry electric charge either, so their motion is directly influenced only by the weak nuclear force and gravity, which makes them notoriously difficult to detect.
2. Boson: Boson is a particle that follows Bose-Einstein statistics. These ave integer spin as 0, 1, 2, etc. Bosons, unklike fermions, don't make up matter but instead are force carriers, which either give rise to forces between other particles, or in one case give rise to the phenomenon of mass. There are 5 elementary bosons.
   1. Scalar Boson (spin=0): Higgs Boson is the only particle here. It gives rise to the phenomenon of mass via Higgs mechanism.
   2. Vector Boson (spin=1): These are Gauge bosons, and act as force carrier. There are 4 of these => Photons, Gluons, neutral weak boson and charged weak bosons (2 types)

Within about 3 minutes after the Big Bang, conditions cooled enough for these protons and neutrons to form hydrogen nuclei. This is called the era of nucleosynthesis. Some of these nuclei combined to form helium as well, though in much smaller quantities (just a few percent). But after about 20 minutes, nucleosynthesis ended and no further nuclei could form. The problem at this point was that electrons couldn’t stay in orbit around any atomic nucleus because of the immense heat and radiation still flooding the universe. Shortly after any neutral atoms would form, they were knocked apart again by energetic radiation. 

Galaxies and Stars:

At around 100,000 years, after the neutral helium atoms form, helium hydride is the first molecule. (Much later,  hydrogen and helium hydride react to form molecular hydrogen (H2) the fuel needed for the first stars) Finally, after 380,000 years or so, the universe had again expanded and cooled enough for conditions to favor electrons staying in orbit around atomic nuclei. This is when recombination occurred — neutral hydrogen (and helium) finally appeared (along with traces of lithium, Beryllium and Boron) because they could “recombine with” (hold on to) electrons without easily losing them to stray radiation. Hydrogen was 75%, Helium was 25% and other atoms were in negligible quantity. This is also the time when the cosmic microwave background was generated, because the atoms that formed entered their lowest energy state quickly after, releasing excess energy in the form of photons that could finally travel freely through the universe without knocking into anything along the way. This is the light that makes up the cosmic microwave background. From 370,000 years until about 1 billion years, the clouds of hydrogen collapsed very slowly to form stars and galaxies, so there were no new sources of light.

Birth of stars:

Stars were a mystery until early 20th century. Scientists were puzzled onto how energy is created in stars.  Gradually they figured out that stars are initially a big cloud of Hydrogen. These Hydrogen atoms being very close to each other, start fusing into one mass under this very high pressure and high temperature of 10 millions of Kelvin. Over time, the core of the star getting more hot, starts fusing 4 Hydrogen atoms (1 proton, and no neutron) into Helium atoms (2 protons and 2 neutrons). This is the fusion reaction where some mass is lost, which is converted into energy as per Einstein's equation E=mc^2. The core then becomes smaller (as Helium atoms pack neutrons and protons even closer than what hydrogen packed protons in), even hotter (100M Kelvin) and then helium fuses into even heavier elements as carbon, oxygen, etc. Intermediate heavier elements are made too, but carbon and oxygen are predominant among the heavier elements. Many stars are made of about 90 per cent hydrogen, with most of the remainder being helium and a very small fraction of heavier elements. 

From the end at about 1 billion years (i.e 13Gya), the universe gradually transitioned into the universe we see around us today, but denser, hotter, more intense in star formation, and more rich in smaller (particularly unbarred) spiral and irregular galaxies, as opposed to giant elliptical galaxies. Galaxy is a system of millions or billions of stars, together with gas and dust, held together by gravitational attraction. The majority of giant galaxies contain a supermassive black hole in their centers, ranging in mass from millions to billions of times the mass of the Sun. The black hole mass is tied to the host galaxy bulge or spheroid mass.

There are fundamentally two types of galaxies.

1. Blue star-forming galaxies =>These are groups that are more like spiral types. When a galaxy forms, it has a disk shape and is called a spiral galaxy due to spiral-like "arm" structures located on the disk. Spiral galaxies are quite thin, dense, and rotate relatively fast. The galaxy that our solar system is in is called Milky way, and is a Spiral galaxy
   
2. Red non-star forming galaxies => These are more like elliptical galaxies. The stars in elliptical galaxies have randomly oriented orbits.
   

Hertzsprung–Russell diagram (or H–R diagram)

We saw above that dense regions within molecular clouds, collapse and form stars. Hydrogen fuses to form Helium in the core, and then hydrogen is only at the surface. These stars get much cooler at the surface, but huge at the same time. Stars go thru phases where they burn brightly at birth to just being a core of elements at their death. The fate and journey also depend on the size that it started with. Observations indicate that the coldest clouds tend to form low-mass stars, observed first in the infrared inside the clouds, then in visible light at their surface when the clouds dissipate, while giant molecular clouds, which are generally warmer, produce stars of all masses.

There's H-R diagram of all the stars that was developed by Hertzsprung and Russell in early 1900's. It is a scatter plot of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their classification or temperatures. Each star is represented as a point with an x-coordinate of effective temperature and a y coordinate of luminosity. Very big stars called supergiants have very high luminosity and high temperature. White dwarfs are stars which have low luminosity but high temperature. Main sequence stars are the stars that are still active in their lifecycle, and that is where most of the stars are. Sun is a main sequence star with a luminosity of 1, and temperature of 5000 Kelvin. 

Here's the wiki link => https://en.wikipedia.org/wiki/Hertzsprung-Russell_diagram

This is the HR plot => https://en.wikipedia.org/wiki/Hertzsprung-Russell_diagram#/media/File:HRDiagram.png

Red Shift:

The universe at the beginning was very hot and very compact, and since then it has been expanding and cooling down. To prove that Universe is expanding, we should see a red shift of light emitted from objects such as distant stars. Red shift of visible light happens when light sources are moving away from you at very fast speeds. Red shift is exactly what we see which proves the "Expansion of Universe". Other Observation that proves "Big Bang" and expansion of Universe is the "Cosmic Microwave background radiation" that we observe coming from all directions. These are light waves emitted shortly after the birth of Universe, when photons emitted could travel. These photons are coming from all directions to earth, but because these light sources are moving away from us, we see  massive shift in Frequency, and instead of being red, they go even more into low frequency range, and appear as radio waves.

Hubble's Law:

Hubble came up with a law of how fast Universe is expanding. As of now, it says that things are moving at speed of 70.6km/s per megaparsec (1 megaparsec is 3 million light years) . i.e things that are 1 megaparsec away are moving away at 70.6km/s, while things which are 2 megaparsec away are moving at 141.2km/sec and so on. So, all things in universe are moving further and further away from each other.

According to wikipedia, the actual estimate for the radius of the observable universe is 14000 Mpc (or 14 Gpc), so the velocity of the expansion at this distance would be 14000 * 70.6 = 988,400 Km/s! Way beyond the light speed limit! If we wanted to know the distance that an object in space must have in order to move away at the speed of light (rounded at 300,000 km/s), we should do:
300,000 / 70.6 = 4,249,291,784 parsec (4.29 Gpc)-> approximately 14 billion light years. May be that is how Huble came up with this Constant so that start time is at 14 billions years ago, as nothing can move faster than speed of light.

Formation of Earth:

At around 4.5Gya, earth was formed, though mostly molten, and with some atmosphere but no oxygen. Over time, the Earth cooled, causing the formation of a solid crust, and allowing liquid water on the surface.

Life started forming around 4Gya. More details about evolution of life are in "Classification of Life" in Biology section. Around this time is when Moon is supposed to have been formed by Earth's collision with a giant planet sized body called Theia. In Astronomy section, we will focus on how different bodies in space evolved from Big Bang to until now.

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Published: Sunday, 26 March 2023 14:22

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Elementary and Middle School Science

In US Curriculum, there is no Science study in Elementary School, except for basic introduction. In middle school too, there is very little science material. All of biology, chemistry and Physics are combined into one as Science. All Science material until Middle School can be covered within a couple of weeks with 20 hours of dedicated study per week. This is in contrast to Science in Indian Schools, where Physics, Chemistry and Biology have vast material in 11th and 12th grade. Even before that up to 10th grade, the material is not easy in Indian Science curriculum.

Khan Academy has very nice sets of videos on Basic Science (unit 1 and 2): https://www.khanacademy.org/science

In Texas, Science test is taken as part of STAAR in 5th grade (when you pass Elementary school) and in 8th grade (when you pass middle school). After 8th grade, there is no more Science material in High School. There is a biology test that you take in High School, but the material is that of middle school. You could take a look at the STAAR test questions here for last couple of years (look under 5th and 8th grade for Science).

https://tea.texas.gov/student-assessment/testing/staar/staar-released-test-questions

I'm listing the topics that are considered for passing the Science STAAR test in texas. Here's a link for Science Topics that TEA (Texas Education Agency) lists:

https://tea.texas.gov/academics/subject-areas/science

I've simplified and summarized everything below for all Science material until 8th grade:

1. Astronomical Science: Various aspects of Astronomy starting from origin of Universe to planets in solar system, stars, etc.
   1. Origin of Universe: Big Bang Theory, evolution of planets, and timeline.
   2. Galaxies: compare spiral, elliptical, irregular, dwarf, and active galaxies.Learn about our Milky way galaxy and other galaxies
      
2. Earth Science:
3. Physics:
4. Chemistry:
   1. Matter: Learn about Atoms, molecules, ionic and covalent bonding. Know about Electrons, protons and neutrons.
   2. Periodic Table: Know about how many elements are there and how they are arranged in periodic table. How their chemical properties are determined by their valence electrons. Radioactive elements and isotopes.
5. Biology:

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Published: Friday, 24 March 2023 18:17

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ChatGPT

ChatGPT is a revolutionary Genrative AI chat Bot developed by openai.com. GPT stands for "Generative Pre-trained Transformer".

chatGPT link: https://chat.openai.com/chat

You will need to make an account, before you can use it. openai.com has a lot of other tools too, such as

I've a separate section for chatGPT, as looks like it can give answers to all your questions, no matter how badly you phrase it. It's amazing, as to what is causing it to understand questions, and then respond in a human way, not just "matching answers" from it's database.

Here are few basic questions that chatGPT gets totally messed up.

Maths:

1. Simple Geometry question: Given 3 coordinates of a parallelogram, find it's 4 coordinate. Here the trick is that if you solve it in not so smart way, the process may be very long. First you find equations of 2 parallel sides, name . Then you find eqn of 3rd side, and use that to find eqn of 4th side. Then you find intersection of 3rd and 4th side which are not parallel, the solution of which gives you the coordinates. However, simpler solution is to find the midpoint of the parallelogram using 2 of the coordiantes, and then use that midpoint to find other coordiante.

Question: If 3 coordinates of parallelogram as (3,4), (5,7) and (9,0), what's the 4th coordiante?

Answer: chatGPT first uses the complex eqns to determine the solution. It messes up trying to the find the intersection of 2 parallel lines, solves for x as follows (which is total garbage):

3/2 * x - 1/2 = 3/2 * x - 27/2

=> 27/2 - 1/2 = 0

=> x = 2

When you say it's wrong, it tries the midpoint formula and comes up with one possible solution pretty fast. If you ask for other solutions" it says :

"No, there is only one solution for the fourth vertex of the parallelogram given three of its vertices. The fourth vertex is uniquely determined by the geometry of the parallelogram, as it is determined by the intersection of the two diagonals of the parallelogram."

When you confront by saying that the vertices can be in any order, then it comes up with all 3 possible solutions.

Score: PASS

Physics:

1. Simple Charge question: Given 2 equal charges of opposite magnitude (+Q1 and -Q1) in a gravity free environment, and the initial distance between them thrown with some initial velocity, how long will it take for them to collide? For the solution, we just need to solve differential equation for electrostatic force between the two charges, and the resulting acceleration between them, and then solve for distance r=0.