Relation between function of minterm and function of maxterm
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Minterms:
Standard "products"Contain each literal in the function in primed or unprimed formFor a function of N variables, there are 2N minterms (one for each line in truth table)For each line in a truth table of a function where that function is 1, the function is said to "contain" that minterm.
F(x,y,z) = xy + x'z
xyzmintermmaxtermF[`F]000m0 Û x'y'z'M0 Û (x+y+z)01001m1 Û x'y'zM1 Û (x+y+z')10010m2 Û x'yz'M2 Û (x+y'+z)01011m3 Û x'yzM3 Û (x+y'+z')10100m4 Û xy'z'M4 Û (x'+y+z)01101m5 Û xy'zM5 Û (x'+y+z')01110m6 Û xyz'M6 Û (x'+y'+z)10111m7 Û xyzM7 Û (x'+y'+z')10
Maxterms:
Standard "sums"Contain each literal in the function in primed or unprimed formFor a function of N variables, there are 2N maxtermsA maxterm is the complement of the corresponding mintermFor each line in a truth table of a function where that function is 0, the function is said to "contain" that maxterm.
Standard "products"Contain each literal in the function in primed or unprimed formFor a function of N variables, there are 2N minterms (one for each line in truth table)For each line in a truth table of a function where that function is 1, the function is said to "contain" that minterm.
F(x,y,z) = xy + x'z
xyzmintermmaxtermF[`F]000m0 Û x'y'z'M0 Û (x+y+z)01001m1 Û x'y'zM1 Û (x+y+z')10010m2 Û x'yz'M2 Û (x+y'+z)01011m3 Û x'yzM3 Û (x+y'+z')10100m4 Û xy'z'M4 Û (x'+y+z)01101m5 Û xy'zM5 Û (x'+y+z')01110m6 Û xyz'M6 Û (x'+y'+z)10111m7 Û xyzM7 Û (x'+y'+z')10
Maxterms:
Standard "sums"Contain each literal in the function in primed or unprimed formFor a function of N variables, there are 2N maxtermsA maxterm is the complement of the corresponding mintermFor each line in a truth table of a function where that function is 0, the function is said to "contain" that maxterm.
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