I am trying to find the flip-flop input equations. I found the sum of minterms f

Question

I am trying to find the flip-flop input equations. I found the sum of minterms from my state table, And I am trying to figure out how to do this Karnaugh map for these specific sum-of-minterms. The problem, I have 2 D flip flops, 4 inputs and 4 outputs in my state table. From what I know, that give me a 6 variable K-map. And that is 64. That is too large. Is there a way to simplify this K-map correctly?

Da(A,B,T,S,G,W) = (2,4,5,7)
Db(A,B,T,S,G,W) = (1,3,5,7)
E(A,B,T,S,G,W) = (0)
G(A,B,T,S,G,W) = (3)
W(A,B,T,S,G,W) = (4)
P(A,B,T,S,G,W) = (5)

Explanation / Answer

  To simplify hte equations Da = A'B'T'S'GW' + A'B'T'SG'W' + A'B'T'SG'W + A'B'T'SGW Da = A'B'T('S'GW' + SG'W' + SG'W + SGW) Da = A'B'T' [ S'GW' + SG' + SGW ] Da = A'B'T' [ S'GW' + S(G' + GW) ] Da = A'B'T' [ S'GW' + SG' + SW) ] Da = A'B'T'S'GW' + A'B'T'SG' + A'B'T'SW Db = A'B'T'S'G'W + A'B'T'S'GW + A'B'T'SG'W + A'B'T'SGW Db = A'B'T' [S'G'W + S'GW + SG'W + SGW] Db = A'B'T' LS'W(G'+G) + SW(G'+G)] Db = A'B'T' [ S'W + SW ] Db = A'B'T' [ W(S'+S)] Db = A'B'T'W Da = A'B'T' [ S'GW' + SG' + SW) ] Da = A'B'T'S'GW' + A'B'T'SG' + A'B'T'SW Db = A'B'T'S'G'W + A'B'T'S'GW + A'B'T'SG'W + A'B'T'SGW Db = A'B'T' [S'G'W + S'GW + SG'W + SGW] Db = A'B'T' LS'W(G'+G) + SW(G'+G)] Db = A'B'T' [ S'W + SW ] Db = A'B'T' [ W(S'+S)] Db = A'B'T'W Db = A'B'T'S'G'W + A'B'T'S'GW + A'B'T'SG'W + A'B'T'SGW Db = A'B'T' [S'G'W + S'GW + SG'W + SGW] Db = A'B'T' LS'W(G'+G) + SW(G'+G)] Db = A'B'T' [ S'W + SW ] Db = A'B'T' [ W(S'+S)] Db = A'B'T'W

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