Derivation of Canonical Forms (2)

• Alternative: Use Theorem 6 to add missing literals.

• Example: f(A,B,C) = AB + AC' + A'C to canonical SOP form.

  • AB = ABC' + ABC = m6 + m7
  • AC' = AB'C' + ABC' = m4 + m6
  • A'C = A'B'C + A'BC = m1 + m3
  • Therefore,
    f(A,B,C) = (m6 + m7) + (m4 + m6) + (m1 + m3) = ?m(1, 3, 4, 6, 7)
    
    

• Example: f(A,B,C) = A(A + C') to canonical POS form.

  • A = (A+B')(A+B) = (A+B'+C')(A+B'+C)(A+B+C')(A+B+C)
    = M3M2M1M0
    
  • (A+C')= (A+B'+C')(A+B+C') = M3M1
  • Therefore,
    f(A,B,C) = (M3M2M1M0)(M3M1) = ?M(0, 1, 2, 3)
    

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