- #1
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Boolean Algebra, Logic Diagram, K-Map, Nor gates... HELP!
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.
K-map
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!
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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