Lista3 Miguel Ali Termos (1) (1)

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<p>UDC Monjolo</p><p>Ciência da Computação</p><p>Ali Mohamad Termos</p><p>Projeto de Sistemas Digitais – Lista 03</p><p>Prof. Miguel Diogenes Matrakas</p><p>Foz do Iguaçu</p><p>2024</p><p>3 Simplificação de circuitos</p><p>3.1 Álgebra de Boole</p><p>1. Simplifique as expressões utilizando Álgebra de Boole:</p><p>(a) Sa = AB~C + ~A~BC + ABC + ~ABC + ~AB~C</p><p>= AB~C + ABC + ~ABC + ~A~BC + ~AB~C</p><p>= AB(~C + C) + ~AB(C + ~C) + ~A~BC</p><p>= AB + ~AB + ~A~BC</p><p>= B + ~A~BC</p><p>(b) Sb = ABC + ~AB~C + A~BC + AB~C + ~ABC</p><p>= ABC + AB~C + ~AB~C + ~ABC + A~BC</p><p>= AB(C + ~C) + ~AB(~C + C) + A~BC</p><p>= AB + ~AB + A~BC</p><p>= B + A~BC</p><p>(c) Sc = A~B~C + ABC + ~A~BC + A~BC + ~AB~C + AB~C + ~ABC + ~AB~C + ~A~B~C</p><p>= A~B~C + ABC + A~BC + AB~C + ~A~BC + ~ABC + ~AB~C + ~AB~C + ~A~B~C</p><p>= A~B~C + ABC + A~BC + AB~C + ~A~BC + ~ABC + ~AB~C + ~A~B~C</p><p>= A~B~C + A~BC + ABC + AB~C + ~ABC + ~AB~C + ~A~BC + ~A~B~C</p><p>= A~B(~C + C) + AB(C + ~C) + ~AB(C + ~C) + ~A~B(C + ~C)</p><p>= A~B + AB + ~AB + ~A~B</p><p>= A + ~A</p><p>= 1</p><p>(d) Sd = ~A~B~CD + ~A~BCD + A~BC~D + AB~C~D + ABC~D + ~ABC~D</p><p>= ~A~B~CD + ~A~BCD + ~ABC~D + A~BC~D + AB~C~D + ABC~D</p><p>= ~A~BD(~C + C) + ~ABC~D + A~BC~D + AB~D(~C + C)</p><p>= ~A~BD + ~ABC~D + A~BC~D + AB~D</p><p>(e) Se = AB~CD + ~A~BC~D + AB~C~D + ~ABC~D + ABC~D + A~BC~D + ABCD</p><p>= AB~CD + AB~C~D + ABC~D + ABCD + ~A~BC~D + ~ABC~D + A~BC~D</p><p>= AB(~CD + ~C~D + C~D + CD) + ~A~BC~D + ~ABC~D + A~BC~D</p><p>= AB(~C + C) + ~A~BC~D + ~ABC~D + A~BC~D</p><p>= AB + ~A~BC~D + ~ABC~D + A~BC~D</p><p>= AB + ~AC~D + A~BC~D</p><p>(f) Sf = AB~CD + ~AB~C~D + ~A~BC~D + AB~C~D + A~B~C~D + ~C~D + ~ABC~D + AB + ABC~D + AC~D</p><p>= ~D+AB</p><p>(g) Sg = ~[~(~B + ~C + ~D) ~(~A + B + C) + C] + ~A~BC + ~B~(A + C)</p><p>= ~C+~A~B</p><p>(h) Sh = A ~[~B ~(C + D) + ~A ~(B + C)] + C~D + A~BC + AB</p><p>= AB+AD+C~D</p><p>(i) Si = ~(A ⊕ B + ~BC~D) [~(~D + ~BC) + D ~(~A + B)] + ~A~D</p><p>= ~B+~A+~D</p><p>(j) Sj = ~(~(A ⊕ B + ~BC~D) ⊕ ~(~(AD) + ~BC~D + D)) ~[~(~B + ~AC) + ~AD ~(~A + B)] + ~(~BC)</p><p>= ~B+~A+~D</p><p>(k) Sk = ~A~BC~D + ~A~BCD + ~AB~C~D + A~B~C~D + A~BC~D + A~BCD + AB~C~D + ABCD</p><p>= ~C~DA+~C~DB+~BC~D+~BC~A+ACD</p><p>(l) Sl =~[~(B + C~D + ~D + AC) (A + ~B + ~C) + ~B ~(C + ~ABC + AC)] (A + B)</p><p>=	B+AC</p><p>(m) Sm = ~(~B + ~D) ~{~B + C ⊙ D + ~A ~[B~C + ~BC + A + B ~(~C + ~D)]}</p><p>= 0</p><p>(n) Sn = (~(D ⊙ C + ~AB) + B~C~D) [A~B + ~C~D + B ~(A~D + C)] + B~C~D</p><p>= ~CB+~C~D</p><p>(o) So = ~(~(~AB) + ~(C~D)) E + ~A (A~D~E + CDE)</p><p>= ~ACEB+~ACED</p><p>(p) Sp = ~((A ⊕ B) + (~BC~D))・~((~(~A + B) D) + ~BC + ~D) + (~A~D)</p><p>= ~A~BD~C~A~D</p><p>(q) Sq = AB~C + (B~C + ~BC) + A ⊙ B</p><p>= AB+C</p><p>3.2 Mapas de Karnaugh</p><p>3. Simplifique as expressões apresentadas a seguir utilizando Mapas de Karnaugh. Apresente a expressão simplificada e o circuito correspondente para cada uma:</p><p>(a) Sa = ~A~B~C~D + AB~CD + ~A~BC~D + AB~C~D + ~ABC~D + A~B~C~D + ABC~D + A~BC~D + ABCD</p><p>= ~DC+~D~B+AB</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>AB\CD</p><p>(b) Sb = ~A~B~C~D + AB~CD + ~A~BC~D + ~AB~CD + ~ABC~D + A~B~C~D + ABC~D + A~BC~D + ABCD</p><p>= ~DC+~D~B+BDA+BD~C</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>1</p><p>(c) Sc = ABCDEF + A~B~CD~EF + ~ABCDEF +AB~C~D~E~F + ~AB~C~DEF + ~A~B~CD~EF + ~A~B~CDE~F + A~B~C~DEF + ~AB~CDE~F + A~B~CD~E~F + ~AB~CD~EF + ~ABC~DEF + ~ABC~D~E~F + ~A~B~C~D~E~F</p><p>= A~B~CD~E + ~AB~CDF + ~AB~CEF + BCDEF + ~B~CD~EF + ~A~CDE~F + A~B~C~DEF + AB~C~D~E~F + ~ABC~D~E~F + ~A~B~C~D~E~F</p><p>(d) Sd = ABCDEF + A~BCD~EF + ~ABCDEF + AB~C~D~E~F + ABC~DE~F + ~AB~C~DEF + ~A~B~CD~EF + ~A~B~CDE~F + A~B~C~D~EF + A~B~C~DE~F + ~A~CDE~F + A~B~CD~E~F + ~AB~CD~EF + ~A~B~CD~EF + ~AB~C~DEF + ~ABC~D~E~F + ~A~B~C~D~E~F</p><p>(e) Se = ABCDEFG + A~BCD~EFG + AB~C~D~E~F~G + ABC~DE~F~G + A~B~C~D~EF~G + A~B~C~DE~FG + A~B~CD~E~FG + A~BC~D~EF~G + A~B~CDE~F~G + A~B~CD~E~FG + ABC~D~EF~G + A~BCDE~F~G + A~B~CD~EFG + ~ABCDEFG + ~AB~C~DEFG + ~A~B~CD~EFG + ~A~B~CDE~F~G + ~AB~C~DEFG + ~AB~CD~EFG + ~A~B~CDEF~G + ~AB~C~D~E~F~G + ~AB~CDEFG + ~A~B~CD~E~F~G + ~A~BCD~E~F~G + ~A~B~CDE~F~G + ~ABCD~E~F~G + ~A~B~CD~EF~G + ~A~B~CDEF~G + ~A~CDE~F~G + ~AB~CD~EFG + ~A~B~CD~EFG + ~AB~C~DEF~G + ~ABC~D~E~F~G + ~A~B~C~D~E~F~G</p><p>3.3 Circuito simplificado</p><p>4. Desenhe o circuito simplificado que executa a função explicitada nas seguintes tabelas verdade:</p><p>(a)</p><p>A.= S1: ~B~C+AC+~AB</p><p>S2: ~B+~C</p><p>S3: A~C+~BC</p><p>S4: B~C+A~C+AB+~A~BC</p><p>(b)</p><p>B. = S1: ~B+CD+~C~D</p><p>S2: ~A~D+BD+A~B~C</p><p>S3: B~CD+~AB~D+~BC~D</p><p>S4: ~AB~C+A~CD+ABC+~ACD</p><p>(c)</p><p>C. S1: ~AD+~A~C+~BC+AB~D</p><p>S2: ~A~D+BD+~B~C~D</p><p>S3: ~A~D+A~CD</p><p>S4: D</p><p>(d)</p><p>D.</p><p>image6.png</p><p>image7.png</p><p>image8.png</p><p>image9.png</p><p>image10.png</p><p>image11.png</p><p>image12.png</p><p>image13.png</p><p>image14.png</p><p>image15.png</p><p>image16.png</p><p>image17.png</p><p>image18.png</p><p>image19.png</p><p>image20.png</p><p>image21.png</p><p>image22.png</p><p>image23.png</p><p>image24.png</p><p>image25.png</p><p>image26.png</p><p>image27.png</p><p>image28.png</p><p>image29.png</p><p>image30.png</p><p>image1.png</p><p>image2.png</p><p>image3.png</p><p>image4.png</p><p>image5.png</p>