# How to convert boolean expression from AND and OR to NAND only

I have a task that drives me crazy because I don't know where to start.

The task is as follows: Convert the given boolean expression so that it contains only NAND operations and no negations.

``````c * b * a + /c * b * /a
```

```

I guess this is possible: D but I have no idea how to do it and spent a few hours just spinning in circles.

Can anyone point me in the right direction?

Regards,

Update:

thanks to the answers, I think I found a solution:

``````c*b*a = /(/(c*b*a)*/(c*b*a)) = A;

/c*b*/a = /(/(/(a*a)*b*/(c*c))*/(/(a*a)*b*/(c*c))) = B;

c*b*a+/c*b*/a = A + B = /(/(A*A)*/(B*B))
```

```
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It has a breakdown of how to build other logic gates via NAND. There should be a simple application:

eg. C = A AND B is equivalent

``````C = NOT (A NAND B)
or
C' = (A NAND B)
C = C' NAND C'   (effectively NOT'ing A NAND B)
```

```
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For a good in-depth discussion on how to create boolean expressions with only one kind of function / logic gate (NOR in this case, but changing it to NAND is easy), take a look

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``````c * b * a + /c * b * /a
```

```

NAND only

``````/( /(c * b * a)  *  /( /(c * c) * b * /(a * a) ) )

NAND( NAND(c,b,a) , NAND( NAND(c,c), b, NAND (a, a)))
```

```

So, you need two 3-gate NAND, three 2-gate NAND.

NOT (A) = NAND (A, A)

A OR B = NAND (NAND (A, A), NAND (B, B))

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