Thursday 5 October 2017

drawing a circuit, nand gates


Task: Construct an AND circuit with 8 inputs, a circuit which implements the expression a∧b∧c∧d∧e∧f∧g∧h.


Condition: Use only NAND-Gates with two inputs to solve this task.


Could anyone explain to me how to solve this question?



Thanks.


Edit: My thought would be to do sth. like this:


https://crcit.net/c/df53a1d9


Could that be right?


enter image description here


Edit: My new idea:


schematic


simulate this circuit – Schematic created using CircuitLab



Answer



Since you seem to be a bit lost. read https://en.wikipedia.org/wiki/De_Morgan's_laws#Engineering



enter image description here let me show one way. Often we use X or Y or Z for outputs or f(ABCDEFGH)=...


\$Y=((A\cdot B)\cdot (C\cdot D))\cdot ((E\cdot F)\cdot (G\cdot H))\$


Since you must solve using 2in-NAND gates , I will use ! to indicate an inverted logic. (sometimes you will find ! used before or after brackets, but you must be consistent!)


AND = \$(A\cdot B)!! = (A\cdot B) \$ with both inputs of a NAND gate joined to make it an inverter (INV).


\$Y=(~~(A\cdot B)!!\cdot (C\cdot D)!!~~ )!!\cdot ((E\cdot F)!!\cdot (G\cdot H)!!)!!\$


Cleaner notation removes the dot for AND but leaves + for OR.


\$Y=~((AB~!!)(CD)!! ) ~ ((EF)!!(GH)!!)!!\$


I should have labelled the inputs with ABC etc but I was too lazy.


Here is what it looks like with my simulator that denotes H,L for 1,0 where you can carefully click on any input ( without disconnecting it by dragging the mouse click ;)


So you see output is H only when all inputs are H.



enter image description here


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