## DIGITAL LOGIC CIRCUITS (PART 2)

In the previous article, the half adder was introduced, in this article, I am mainly going to be focussing on the full adder. Before moving forward I would for you to go back and do a little revision of the half adder.

The full adder unlike the half adder can add larger binary numbers, it takes in three inputs and gives out a sum and a carry output. The  major difference between the full and half adder is the fact that the half adder is only used to add least significant bits (LSB)  without accounting for the carryout of the previous addition. While the full adder is used to add up most significant bits (MSB) and  LSBs and also taking into account the carry out from the previous additions.

At this point it will be wise for us to recall the procedures for adding larger binary numbers; firstly, we begin with the addition of the LSBs of the two numbers, we record the sum under the LSB column and take the carry, if any to the next higher column bits. As a result, when we add the next adjacent higher column bits, we would be required to add three bits if there were a carry from the previous addition. We continue with the same procedure of adding the next two LSBs and the carry if there is, until we get to the MSB. Therefore, if want a hardware that can add larger binary numbers, it is therefore of utmost importance that the full adder circuit must be implemented. The truth table and equations coupled with the circuit is shown below;

 A B Cin Sum Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1
Fig.1.  Truth Table

Fig.2. CIRCUIT DIAGRAM

The full adder described above forms the basic building block of binary adders. However, a single full adder circuit can be used to add one bit binary numbers only. A  cascade arrangement of these adders can be used to construct adders capable of adding binary numbers with a large number of bits. A five bit binary adder would require four full adders.
This brings us to the end of this part, if you want the video on how to simulate the full adder to add larger number of bits, please comment below for the link.

## Atomic Structure: Definition, History and theories

Introduction of Atom

Define of Atom:-

The Greek philosopher Democitus (460B.C – 370 B.C) was among the first to suggest the existence of Atoms (from the Greek word “atoms” means indivisible).

He believed that atoms were indivisible and indestructible. His ideas dis agree with later scientific theory, but did not explain chemical behaviour, and was not based on the scientific method, but just philosophy.

Dalton’s Method:-

John Dalton took what was known about chemical reactions at his time and proposed the first atomic model.

Conservation of Mass

• Law of Multiple Proportions
• Law of Definite Composition

Billiard Ball Model:-

Dalton combined the observation into one theory which stated that all matter was composed of small indivisible particles that he called atoms.

Demitri Mendeleev used this theory when he constructed the first working periodic table.

Dalton’s Atomic Theory (experiment based):-

1. All elements are composed of tiny indivisible particle called atoms
2. Atoms of the same element are identical.
3. Atoms of any one element are different from those of any other element.
4. Atoms of different elements combine in simple whole-number  rations to form chemical compounds. E.g CO2

In chemical reactions, atoms are combined, separated, or rearranged, but never changed into atoms of another element.

Sizing up to the Atom:-

Elements able to be subdivided into smaller and smaller particles, those are the atoms, and they still have properties of that element
If you could line up 100,000,000 copper atoms in a single file, they would be approximately 1cm long.

Despite their small size, individual atoms are observable with instruments such as scanning tunnelling microscopes.

Cathode Ray:-

Crookes worked in the areas of chemistry and physics. He had many accomplishments, one of which was the discovery of cathode rays.

Crookes Tube:-

A source of high potential difference was placed across the cathode of a glass tube that had gas at a very low pressure inside.
Noticed a glow coming from the negative terminal.

Properties of Cathode Ray:-

A wide variety of cathodes (different metals) were tested and all produced same results.

Magnetic fields deflected the rays.
The rays produced some chemical reactions similar to those produced by light.

The rays travelled in straight lines, perpendicular to the surface of the cathode.

History:-

Electron means “amber” in Greek
Properties discovered by the Greek Thales of Miletos 600 BC. Rubbed the mineral amber with cat fur and attracted feathers.

J. J. Thomson discovered the electron while experimenting with cathode rays. In 1897, J. J. Thomson used a cathode ray tube to deduce the presence of a negatively charged particle: The Electron.

Cathode Ray:-
Thompson showed that the production of the cathode ray was not depend on the type of gas in the tube, or the type of metal used for the electrodes. He conludes that these particles were part of every atom.

Thomson’s Charge to Mass Ratio:- It was noticed that the beam of electrons be bent by a magnetic field. This means that: Fnet = Fm
So,
mv2 = Bqvr
so, q/m = v/Br.

## DIGITAL LOGIC CIRCUITS (PART I)

COMBINATIONAL CIRCUITS

Arithmetic Circuits
Arithmetic circuits are circuits that performs arithmetic operations on binary numbers. In a computer, these operations are performed in the arithmetic and logic unit (ALU). This is a part of the central processing unit (CPU) of a computer. The ALU is responsible for performing two operations; the arithmetic and logic operations.
The arithmetic operations includes; Addition, Subtraction, Multiplication(process of repeated additions) and Division(process of repeated subtraction); while the logic operations include AND, OR, NAND, NOR, NOT .etc.
The fundamental building blocks that forms all hardware used to perform all the arithmetic operations on binary numbers mentioned above includes; Full adder, Half adder, Full subtractor, Half subtractor and Controlled inverter.

It can be said to be the arithmetic circuit block that can be used to add two bits (which are called the inputs) to produce to outputs; the sum and the carry outputs.
The truth table for the half adder can be seen below;

 A B Sum Carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1
fig .1. Truth table of the half adder
fig .2.block symbol of the half adder
The circuit diagram of the half adder can drawn from the equation which can be gotten from the truth table above;

fig .3.
As can be seen in the picture above, the sum of the half adder can either be obtained by using the NOT, AND and the NOR gates or simply using the EXOR gate. While the carry can simply be realised by using the AND gate.

The circuit of the half adder can be seen below;

fig. 4.
The complete video on how to simulate this will be available soon, please comment below if you have any questions.

## Principles Of Current Limiting Reactors

INTRODUCTION

In electrical Engineering, a current limiting reactor is an inductive coil having a large inductive reactance in comparison to their resistance and are used to reduce short circuit current which result from plant expansions and power source additions to a level that can be adequately handled by existing distribution systems.
Reactors are used to limit the short circuit current which can lead the damage of the power system equipment.

PRINCIPLES OF CURRENT LIMITING REACTORS
The inductive reactance is chosen to be low enough for an acceptable voltage drop during normal operation but high enough to restrict a short circuit to the rating of the switch gear.

If the resistance of a circuit during fault is 'X' and 'E' voltages are given, then the short circuit current can be calculated as; Isc =E/X, i.e , the reactant is inversely proportional to the current. If 'X' increases, Isc decreases and vice-versa.

Short circuit current depend on the generating capacity, fault point voltage and the reactance of the circuit.

The rating of the reactors are given in KVA and the formula for percentage reactance is

%X = KVdrop / KV(phase voltage).

PRIMARY FUNCTIONS OF CURRENT LIMITING REACTORS

The primary functions of current limiting reactors are;

• To reduce the flow of current into a short circuit so as to protect the power system apparatus and parts of the system from excessive mechanical stress and over heating.
• To localise the faults by limiting the current that flows into the fault from other healthy feeders or part of the system.

• To reduce the duty imposed on switching equipment during short circuits.

REACTOR RATING

The rating of the reactor is usually expressed in terms of percentage and on a three phase system operating at 11KV +20% is one which will have a voltage drop of 1,270 volts across it with full load flowing through it.

Other ratings include;
• Continuous Rated Current
It is the r.m.s. value of current which the reactor can carry continuously with the temperature rise of current carrying parts within specified limits. (e.g 100A).

• Rated Short-Time Current
It is the symmetrical r.m.s value of fault current which the reactor can carry for specified short time duration (e.g, 60KVA for 1second).

• Rated Voltage
This is the line to line service voltage to which the reactor is designed.

• Short Circuit Rating
This refers to the amount of mechanical and thermal stress during short circuit conditions the reactor can withstand for a specified period of time.

So here's a little exercise to try yourself.

1. The figure below shows a power system where load at bus 5 is fed by generators at bus 1 and bus 4. The generators are rated at 150MVA, 11KV with sub-transient  reactance of 25%. The transformers are rated each at 150MVA, 11/112KV and have a leakage reactance of 8%. The lines have an inductance of 1mH/phase/km. Line L1 is 100Km long while lines L2 and L3 are each of 50Km in length. Find the fault current and MVA for a 3-phase fault at bus 5.

 fig. 1. Please comment below if you need a detailed solution to the exercise.

## Biology: Mitosis vs Meiosis, definition and differences.

Mitosis

This is the process by which cells increases in number and achieves growth. Mitosis occurs in five stages namely; Interphase, prophase, metaphase, anaphase and telophase.

Mitosis occurs in somatic or body cell such as skin, bone marrow, lymph nodes and injured places as well as meristematic tissues in plant.

i) Interphase: In this phase,
• chromosone becomes elongated and forms a network of fine thread called chromatid.
• The nuclear membrane is nearly visible.
• The nucleolus is also visible.

ii) Early prophase: In this phase,
• Chromosone becomes visible as the chromatid thread condenses.
• Chromosone are lone and thin.
• The nucleolus starts to shrink.
• There is a formation of spindle fibres.

Late Prophase: In this phase,
• chromosone becomes faster, thinner and very visible.
• The nuclear membrane disappears.
• The nucleolus disappears entirely.

iii) Metaphase: In this phase,
• The chromosome arranges themselves along the equator.
• The chromatids are attached to the spindle be the centromeres.

1v) Anaphase: In this phase,
• The chromatids separate.
• The chromatids start migrating to the poles.
• The chromatids eventually get to the poles.

v) Telophase: In this phase,

• The cell starts dividing into two.
• The chromosone now loses their thick appearance.
• The spindle structure disappears.
• The daughter cells are formed.

Importance of mitosis

1. It ensures that the diploid condition of the cell is retained from generation to generation.
2. It helps in growth of multi-cellular organisms.
3. It helps in asexual reproduction of animal and plant.
4. Mitosis ensures that the exact copy of DNA (deoxyribose nucleic acid) are transmitted to daughter cell.

Meiosis

It is a two-successive cell division with my one duplication of chromosones. Meiosis is a reduction in cell division and the resulting in daughter cells.

For example,
• Ovules and pollen grains in plants.
• Ovaries and testes in animals.

In animals, meiosis occurs in the formation of gametes sex cells such as eggs and spermatozoa. The process of gametes formation is called gametogenesis. The process involved in the production of spermatozoa by testes is called spermatogenesis, while the process of producing eggs by the ovaries is known as Oogenesis.

Importance of Meiosis

• It aids formation of sperm in animals.
• It aids formation of eggs or ova in female animals.
• It aids the formation of pollen grains in flowering plants.
• It aids the formation of ovules in flowering plants.

Differences between Mitosis and Meiosis

 Mitosis Meiosis a) It occurs during the growth of somatic cells and asexual reproduction. It occurs during gamete’s production. b) Two daughter cells or off springs are formed Four daughter cells or off springs are formed. c) Chromosone number of daughters and parent’s cells are equal.                                         cells Is half the number The chromosone number of daughter cells is half the number in the parents’. d) Off-springs produced by mitosis is the exact replicate of the parents Off-springs produced by meiosis will show Variation.

## Chemistry: What is Hydrogen? It's Uses, physical properties, chemical properties and methods of preparation

Hydrogen is found in group one of the periodic table. Though, it is non-metal, it is usually placed in group one because it has one valence electron.

Physical Properties of Hydrogen
•  It is a colourless, odourless and tasteless gas.
• It is neutral to litmus paper.
• It is insoluble in water.
• It is the lightest substance known.
• It has a very low boiling point of (-253-degree Celsius).
• It is less dense than air.

Chemical Properties of Hydrogen

1. It reacts with metals to found hydrides.

2Na + H2 ---> 2NaH

2. It burns in air to produce steam.

H2O + O2 ---> 2H2O

3. It reacts with halogens to produce halides

H2 + Cl ---> 2Hcl
H2 + 2Br ---> 2HBr

4. Acts as a Reducing agent: It reduces oxides to their respective metals

CuO + H2 ---> Cu + H2O

Uses of hydrogen
• It is used in the hydrogenation of oil.
• It is used to manufacture soap and margarine (saponification).
• It is used in filling balloons.
• Liquid hydrogen is used for rocket fuel.
• It is used for welding metals.

Isotopes of hydrogen

Hydrogen has three naturally occurring Isotopes. There are;
• Protium – ( 11H )
• Deuterium – ( 12H )
• Tritium - ( 13H )
“Deuterium oxide” is commonly known as heavy water because it is about 1.1 times heavier than water.  “Protium” has no neutrons, it is the ordinary isotope of hydrogen. “Tritium” is radioactive and rarely found in ordinary hydrogen.

Laboratory Preparation of hydrogen

Hydrogen can be prepared in the laboratory by;

* Action of dilute acid on metal.
* Action of cold water on sodium.
* Action of steam on red hot iron

Laboratory preparation of hydrogen by the action of dilute acid on metal.

AIM – To prepare hydrogen.

APPARATUS – Round bottom flasks, delivery tube, glass jar, thistle funnel, trough etc.

METHOD
• Place some pieces of zinc metal in a round bottom flasks
• Set up the apparatus.

• Add dilute sulfuric acid (H2SO4) to zinc metal through the thistle funnel.
• Collect the gas formed over water.

OBSERVATION – As soon as the metal effervescence occurs, gas liberated is collected over water.

CONCLUSION – Hydrogen can be prepared in the laboratory

Industrial preparation of hydrogen

Hydrogen can be prepared in large quantities in the industries by the following ways;
• Water Gas
• Hydrocarbon
• Electrolysis

By Water Gas

When steam is passed over red hot coke at a temperature of about 1100 degree Celsius. The mixture of carbon (ii) oxide or hydrogen gas is produced and this is known as water gas.

H2O + C ---> CO + H2

The product obtained is mixed with excess steam and passed over iron(iii)oxide or Uranium (iii) oxide as a catalyst at a temperature of 450 degree Celsius.

During this process, carbon (ii) oxide in water gas is converted to carbon (iv) oxide and the liberation of excess hydrogen.

CO + H2 + H2O ---> CO + H2

Questions? Comment below.