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Teknik Penyederhanaan Karnaugh Map ( K-Map )

ELEKTRONIKA DIGITAL Misbah , ST, MT. Teknik Penyederhanaan Karnaugh Map ( K-Map ). Dua Variabel Tiga Variabel Empat Variabel. F= A.B + A.B + A.B Hasil dari K-map = F= A + B. Sederhanakan fungsi 2 variabel. B B. A A.

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Teknik Penyederhanaan Karnaugh Map ( K-Map )

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  1. ELEKTRONIKA DIGITAL Misbah, ST, MT TeknikPenyederhanaanKarnaugh Map (K-Map)

  2. DuaVariabel TigaVariabel EmpatVariabel

  3. F= A.B + A.B + A.B Hasildari K-map = F= A + B Sederhanakanfungsi 2 variabel B B A A

  4. Penyederhanaanfungsidaritabelkebenaran 2 variabel Hasil dari K-MAP : F = A’ B + A B’

  5. 1. F= A.B + A.B + A.B 2. F= A.B + A.B + A.B 3. F= A.B + A.B + A.B Soal :

  6. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C SederhanakanFungsi 3 variabel F= A.C + A.B + A.B ATAU F= B.C + A.B + A.B

  7. 1. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C 2. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C 3. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C 4. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C 5. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C Soal :

  8. Penyederhanaanfungsidaritabelkebenaran 3 variabel Hasil dari K-MAP : F = B + A C

  9. F= A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D SederhanakanFungsi 4 variabel F= C.D + A.D + A.B +B.D

  10. 1. F=A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D 2. F=A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D 3. F=A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D Soal :

  11. Penyederhanaanfungsidaritabelkebenaran 4 variabel

  12. 1. F=A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D 2. F=A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D + A.B.C.D 3. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C 4. F= A.B.C + A.B.C + A.B.C + A.B.C + A.B.C Tugas : Tulis tangan di kertas folio

  13. Penjumlahan dari suatu fungsi perkalian. Contoh : F = (A.B.C) + (A.B.C) + (A.B.C) Dapat ditulis dengan F(A,B,C)=∑ {0,3,4} Yang disederhanakan adalah angka ‘1’. SOP (Sum of Product)

  14. Sederhanakan F(A,B,C,D)=∑ {0,1,3,4,7,8,10,11,15} Contoh :

  15. Perkalian dari suatu fungsi penjumlahan. Contoh : F = (A+B+C) . (A+B+C) . (A+B+C) Dapat ditulis dengan F(A,B,C)=∏ {0,3,4} Yang disederhanakan adalah angka ‘0’. POS (Product of sum)

  16. Contoh : • Sederhanakan F(A,B,C,D) =∏{0,1,2,3,6,7,10,11,13,15} F= (A’+B’).(A’+C).(A+B+C).(A+B’+C)

  17. Sederhanakan F(A,B,C,D) = ∏{0,1,3,4,5,10,12,14,15} • Sederhanakan F(A,B,C,D) = ∏{1,2,5,6,8,11,12,14} • Sederhanakan F(A,B,C,D) = ∏{0,2,3,5,6,8,9,11,13,15} Soal :

  18. Don’t care (d) adalah kondisi mengambang dari suatu logika, bisa dijadikan ke logika ‘1’ atau ‘0’. Contoh diberikan tabel kebenaran sbb: Don’t care

  19. F = C’

  20. Sederhanakan F(A,B,C,D) = ∏{0,1,3,4,5,14,15} & d{ 2,11,13} • Sederhanakan F(A,B,C,D)= ∑ {0,1,3,4,7,8,11,15} & d{ 4,10,12,13} Soal :

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