drawing a circuit, nand gates

Question

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?

Edit: My new idea:

^{simulate this circuit – Schematic created using CircuitLab}

Answer 1

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

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.

Answer 2

You want to write your expression using boolean algebra, then convert it (if necessary) using DeMorgan's theorem to a form that you can implement using NAND gates. For example, say you have A + B (A or B). This becomes:

A + B (starting equation) (A'B')' (DeMorgan's format)

You can easily implement (A'B')' using one NAND gate for the purpose of the inverted AND (as expected), and 2 more NAND gates as inverters for A and B.

Use this algorithm with any equation you have in order to get it in terms of NANDS, ANDs (NANDs plus one more NAND after it to invert it), or NOTs (use single NAND to invert)