1.4 Map simplification(1) - minterm

Minterm(최소항)

: 모든 항이 들어가는 조합(AND)

 

SOP(Some of Products)

: OR로 연결된 AND

 

[예시]

F = Y' + XY + X'Y'Z'

 

---

POS(Product of Sums)

: AND로 연결된 OR

 

[예시]

F = Y'(X + Y)(X' + Y' + Z')

 

Sum of minterms

: OR로 연결된 minterm

F(x, y, z) = y’ + xy + x’yz’
                = y’(x + x’) + xy(z + z’) + x’yz’
                = xy’ + x’y’ + xyz + xyz’ + x’yz’
                = xy’(z + z’) + x’y’(z + z’) + xyz + xyz’ + x’yz’
                = xy’z + xy’z’ + x’y’z + x’y’z’ + xyz + xyz’ + x’yz’
                = m5 + m4 + m1 + m0 + m7 + m6 + m2
                = m0 + m1 + m2 + m4 + m5 + m6 + m7

 

대략적인 계층

 

[Standard form]

• Sum of products
  
  • Sum of minterm(Canonical SOP)
• Product of sums
  • Product of maxterms

 

[Canonical form]

• Sum of minterm(Canonical SOP)
• Product of maxterms(Canonical POS)