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l46kok

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**Boolean Algebra, Logic Diagram, K-Map, Nor gates... HELP!!!!**

## Homework Statement

F(A,B,C,D) = Sigma(2,4,6,10,12)

d(A,B,C,D) = Sigma(0,8,9,13) [Dont Care Functions]

Implement the function using no more than 2 NOR gates.

## Homework Equations

K-map

## The Attempt at a Solution

First of all, I am wondering if this is PHYSICALLY POSSIBLE.

Anyways, if you draw the K-map for it, you get

AB\CD

d 0 0 1

1 0 0 1

1 0 0 0

d d 1 1

As for the grouping, I grouped the Top 4 0s (0100, 1100, 0101, 1101), mid 4 0s (0101, 1101, 0111, 1111) and 2 0s on the right and middle (1011, 1111)

If you're doing Nor implementation.. it's usually easier to group the 0s so

F' = BD + A'D + ABC

(As for the notation, ' are inversion, + is or and * is And EG : AB is A and B)

But we want F.. so we apply the demorgan's theorem

F = (B'D')(AD')(A'B'C')

and that is our function.

I looked at this function and I thought there is no way to solve this problem only by using NOR gates.

Please help!

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