(adsbygoogle = window.adsbygoogle || []).push({}); Boolean Algebra, Logic Diagram, K-Map, Nor gates... HELP!!!!

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

K-map

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Boolean Algebra, Logic Diagram, K-Map, Nor gates HELP

**Physics Forums | Science Articles, Homework Help, Discussion**