09-07-2020

Evening,

Good progress today too! Five hours of Number Systems completed. 

Incidentally, sir released a video to study for longer hours with the pomodore or some technique. Ironically the thing is I ended up watching five episodes of that two and a half men. Now closed the tab to write this!

Hey few things to be noted in number systems is,

The largest number possible to represent using n digits of base b is (b to the power of n) - 1.

Base is also called radix.

Minimum number of digits required to represent a k digit base b number in base x system is (n) >= k(log b to the base x).

Complementary Number system is mainly proposed to do subtraction using addition circuit already present.

Base b has two types of complements: b-1 's complement and b's complement.

So, how the subtraction (X-Y) works using complements is as below:

For b-1 's complement:

If  X-Y>=1, ignore carry and add 1 to the X+Ycomplement

If X-Y<1, get the b-1 's complement of X+Ycomplement and negate the result to get answer in a familiar form.

For b 's complement:

If  X-Y>=0, ignore carry to the X+Ycomplement

If X-Y<0, get the b 's complement of X+Ycomplement and negate the result to get answer in a familiar form.

Binary numbers are of two types Signed and unsigned.

Signed numbers can be represented in three ways:

1. Sign magnitude form
2. Signed 1's complement 
3. Signed 2's complement

Here we are only talking of integers not other numbers like fractions or real numbers(integers+fractions). Generally integers have decimal point fixed after the least significant number as well as fractions at their most significant number. Hence called Fixed Pointer Representation and as you have gussed the other (integers+fractions or real numbers) have floating point representation since the decimal point/radix point is not fixed. (LOL floating!)

Signing off for today! Good night.

08-07-2020

Hola!

Good progress today, completed yesterday's last hours content and also covered three hours of Sequential Circuits. Will complete another hour also. 

GOAL and DEADLINE is that should complete Number Systems by 10-07-2020 and start notes for DLD. 

As we have seen SR yesterday i.e. Set-Reset FlipFlop, another type is JK FlipFlop which acts same as SR but is also define when JK=11 also unlike SR=11 is invalid JK=11 gives complement of Qpresent. 

JK is again can be modified or seen as two broad types -> T(toggle) and D(delay) FlipFlops. These have an extensive application and role in the construction of counters.

Solve any question by tabling or constructing as follows:

Characteristic Equation -> Function Table-> Characteristic Table-> Excitation Table.

Another important concept is the conversion of a given FF to another FF:

Suppose,

AB is a given/existing/to be used to realize another FF and 

CD is the target FF/new FF/to be constructed using given FF then,

CD should be realized using inputs of given FF AB.

Steps: (Here important thing is to know what is the FF to be constructed using what FF!)

1. Get the characteristic table of the target FF

2. Replace the next state using excitation of the given FF

3. Obtain the expression for the input of given FF and realize them.

Counters are used to provide accurate timing and control signals. Two types: synchronous and asynchronous.

For N states in a state diagram - > Ceil(logN) FFs are needed to realize it.

All the free running counters are Self-starting counters.

Synchronous:

In IC fabrication D-FFs are used. Technically, any flipflop can be used.

Also called shift counters.

Two types: Ring counter I0 = f(QN-1) and Johnson counter I0=f(QN-1 prime).

Johnson counter is also called as switch-tail ring counter. Can be used as gray counter since only one bit changes for every adjacent transition state in the state diagram.

Asynchronous:

In IC fabrication T-FFs are used. Technically, any flipflop can be used.

Also called ripple counters. 

IC-7490 -> decade counter(%10 counter) and IC-7492 -> Hexadecimal counter(%16 counter)

binary-up counter (increasing order states) can be designed.

Hope it is not too technical but it is very important to know how these flipflops work since they are the basic building blocks of memory as well as some control systems like if OS wants to assign a resource through round-robin, then using counters we can make sure that each device is getting the resource for an equal amount of time. Okay! that's it for today.

 

Sayonara!!

07-07-2020

Good Evening,

Completed two hours today with which Design and synthesis of Combinational circuits is completed. 

Now moving on with Sequential circuits. It is 00:12 now and completed almost a hour of that now. SRFlip Flop.

FlipFlop is the smallest building block of memory. It can store a bit of data. Has two stable states 0 or 1 and hence can also be called as "bistate multi-vibrator".

Though it may have the state complement also stored i.e. Q and Qprime it does not mean it can store 2 bits bcoz 11 and 00 cannot be stored. Simple!

Now one of the types is this SR Flip Flop. Mostly SR input is given through a NAND gate (popular representation). 

FlipFlop Circuit - S R have NAND gate before giving it to the inputs of latch.

Characteristic Table - SRQ |||||| 00 Latch ||||||||| 01 Reset |||||||||||| 10 Set ||||||||||| 11 Invalid

Characteristic Equation - Which is used for realization or implemetation -> Qnext = S+Qpresent.Rprime

Excitation Table - What inputs/excitations (SR) should be given for the behavior of Qpresent -> Qnext transition. 

Function Table - Writing the Qnext in terms of Qpresent based on the inputs S and R.

So basically, these are the things we should understand to analyze a flipflop. 

Anyways, I will try to complete another hour today and try to complete notes first man. It's been piling up for a while now. :(

Good night.

05-07-2020

Good Evening,

It is 21.00 now. Completed two hours of videos. Now moving on to Encoders (Non-priority). 

ok. Done with three hours now.

04-07-2020

Good Evening,

I have completed two hours of video today.

03-07-2020

Good evening,

Yesterday, was my uncle birthday attended after like 6 years. I woke up late that day and has barely completed any. 

Today, woke up late but completed some notes and hour lecture. 

Multiplexer, MUX is fully functional gate. i.e. it can realize or implement AND, OR and NOT as well.

1-07-2020

Good morning, 

Today I was forced to play badminton by my neighbor. Noob!

It is 11.05 now. Have to complete notes atleast today. Hey! and IIITH is going to announce results this week. I do not know what will happen. Hope I qualify.

The branching method to minimize the cyclic K-maps is interesting. Bcoz if you want any one of the minimal expression you just chose one and carry on based on that. Whereas if you want to find the number of minimal expressions possible you have to draw the reduced prime implicant chart and then minimize your combinations which cover all the min/max terms.

The procedure if you re not aware is that:

Find the essential prime implicants

Remove the columns of minterms covered by them. If all are covered it is the unique minimal expression possible else, form the reduced prime implicant chart.

If any minterm is having less literals you give priority to that. Else you have liberty to chose any. 

This method of prime implicant can be used till 4 variables to best or 5 to the max. More than that we have a tabular method of K-map minimization, which proves to be efficient.

It is 19.27 and completed an hr notes.