nand/nor gates
The NAND gate is a gate that is an inverted AND gate or not and.The NOR gate is a gate that is an inverted or gate or not or. they are basically AND and OR gates with inverters.
k-mapping
WHAT IS K- MAPPING?
K- mapping is a short for Karnaugh map.It was created by a man named Maurice Karnaugh in 1953 and it is a simpiler way to shorten logic expressions.
To create a K map u must first create a truth table from the inputs ur given.once u have your logic expression transfer that data into the k map.the size of the map will depend on the amount of inputs u are given. You will get 1s, and 0s based on the minterm u entered.Once u have the ones and zeros entered in the map you must group.The groups must be grouped by pairs and u must try to group as much 1s as you can in the smallest amount of groups.After you have done that you get your simplified expression.
K- mapping is a short for Karnaugh map.It was created by a man named Maurice Karnaugh in 1953 and it is a simpiler way to shorten logic expressions.
To create a K map u must first create a truth table from the inputs ur given.once u have your logic expression transfer that data into the k map.the size of the map will depend on the amount of inputs u are given. You will get 1s, and 0s based on the minterm u entered.Once u have the ones and zeros entered in the map you must group.The groups must be grouped by pairs and u must try to group as much 1s as you can in the smallest amount of groups.After you have done that you get your simplified expression.
In this project the trutrh table and the k mapping was done for us.All we had to do was transfer the data to AOI and the NAND/NOR
K-MAPPING VS BOOLEAN
The main reason why k-mapping is better than using boolean algebra is that it is a much shorter way to do it and it is less difficult.When u use boolean u must distrubute and their are certain laws like x+x=1 and u must use certain theorems to simplify the expression.When using k-mapping the only thing u must do after pluging in the inputs into the table is group as much ones by the biggest groups possible.once u have done that u get the simplified minterm and it is ready to be made in to a NAND or NOR design.
The main reason why k-mapping is better than using boolean algebra is that it is a much shorter way to do it and it is less difficult.When u use boolean u must distrubute and their are certain laws like x+x=1 and u must use certain theorems to simplify the expression.When using k-mapping the only thing u must do after pluging in the inputs into the table is group as much ones by the biggest groups possible.once u have done that u get the simplified minterm and it is ready to be made in to a NAND or NOR design.
universal gates
A universal gate is a gate that can be used to create any other gate therefore u can create any circuit.Instead of using manny diffrent gates u only need two.The NAND and NOR gates are considered to be universal cause u can make any other gates from them.Their are AOI(and,or,inverter) equivallents that can be plugged in instead of using 3 diffrent gates.this is an advantage of using NAND and NOR cause it is more flexible and u only use one gate
aoi
This is the original AOI logic.It uses three diffrent types of gates.
converting AOI to nand
The process to converting the AOI versions of the alarm and booth were simple. The first step to coverting from AOI to NAND was to replace the and,or,and inverters to their equivalent NAND gates as seen on the diagram below.
Once u have replaced all of your AOI gates to NAND you must cancle out pairs.You cancle out pairs cause a NAND is a AND gate with an inverter.A notted not AND gate is the same as a normal AND gate therefore you must sumplify.this makes ur design more efficent.
BOOTH NAND
ALARM NAND
multisim nand design(booth/design)
This is the next step is building ur drawn circuit in Multisim.
breadboarding NAND
This is the final step. I have breadboarded NAND design that i created in Multisim.It works accordingly to the truth table for both the booth and alarm and only uses NAND gates.
converting from aoi to NOR
It was the same thing when converting my booth and alarm from AOI to NOR. I just replaced all the AOI gates with the equivalent NOR gates as shown on the digram.
After that i had to simplify my NOR gate designs by cancelling out notted nots.It was a bit diffrent cause in the end the NOR alarm and booth were wired a bit diffrent from the NAND.It was kinda flipped.
nor booth
nor alarm
Multisim nor design(booth/alarm)
This is the multisi NOR design.I had to check if it worked before i breadboarded.
breadboarding nor
This is the final step. I have breadboarded NOR design that i created in Multisim.It works accordingly to the truth table for both the booth and alarm and only uses NOR gates.
why is nand/nor Better
NAND and NOR only designs are better than using AOI for a couple reasons.First AOI requires you to use AND gates,OR gates, and Inverters hence the name AOI.This means that you must use three diffrent gates to get your F1 or output.It might be easy when doing small logic expressions but later on you will have to build much more complex circuits and AOI logic will make every thing much harder to make.NAND and NOR logic simplifies everything. Their is a NAND/NOR equivallent to a and,or,and inverter gate.This means that u will be able to use only one gate to create a whole circuit.This will allow you to make a simpiler circuit and make it easier to read.It is important to compare both NAND and NOR gates cause although u can create whole circuits with both use diffrent amount of gates.In this project i found that the NAND design used 2 less gates then the NOR design.This makes the NAND design a bette and more efficent design.It would cost less to build then a NOR design.