Explain the maxterm and minterm in computer
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Each row of a truth table can be associated with a minterm and a maxterm.
A minterm l is a product (AND) of all variables in the function, in direct or complemented form. A minterm has the property that it is equal to 1 on exactly one row of the truth table.
A maxterm is a sum (OR) of all the variables in the function, in direct or complemented form. A maxterm has the property that it is equal to 0 on exactly one row of the truth table.
\begin{tabular}{c|c|c|c}\begin{tabular}{c|c|c|c}
A & B & C & F\\A & B & C & F\\
0 & 0 & 0 & 1\\0 & 0 & 0 & 1\\
0 & 0 & 1 & 0\\0 & 0 & 1 & 0\\
0 & 1 & 0 & 0\\0 & 1 & 0 & 0\\
0 & 1 & 1 & 0\\0 & 1 & 1 & 0\\
1 & 0 & 0 & 1\\1 & 0 & 0 & 1\\
1 & 0 & 1 & 0\\1 & 0 & 1 & 0\\
1 & 1 & 0 & 0\\1 & 1 & 0 & 0\\
1 & 1 & 1 & 11 & 1 & 1 & 1
\end{tabular}\end{tabular}
In minterms we can indicate that
F=m0+m4+m7=a′b′c′+ab′c′+abcF=m0+m4+m7=a′b′c′+ab′c′+abc
Or we can use maxterms as
F=M1⋅M2⋅M3⋅M5⋅M6=(a+b+c′)(a+b′+c)(a+b′+c′)(a′+b+c′)(a′+b′+c)F=M1⋅M2⋅M3⋅M5⋅M6=(a+b+c′)(a+b′+c)(a+b′+c′)(a′+b+c′)(a′+b′+c)
It’s just two ways to view the problem.
A minterm l is a product (AND) of all variables in the function, in direct or complemented form. A minterm has the property that it is equal to 1 on exactly one row of the truth table.
A maxterm is a sum (OR) of all the variables in the function, in direct or complemented form. A maxterm has the property that it is equal to 0 on exactly one row of the truth table.
\begin{tabular}{c|c|c|c}\begin{tabular}{c|c|c|c}
A & B & C & F\\A & B & C & F\\
0 & 0 & 0 & 1\\0 & 0 & 0 & 1\\
0 & 0 & 1 & 0\\0 & 0 & 1 & 0\\
0 & 1 & 0 & 0\\0 & 1 & 0 & 0\\
0 & 1 & 1 & 0\\0 & 1 & 1 & 0\\
1 & 0 & 0 & 1\\1 & 0 & 0 & 1\\
1 & 0 & 1 & 0\\1 & 0 & 1 & 0\\
1 & 1 & 0 & 0\\1 & 1 & 0 & 0\\
1 & 1 & 1 & 11 & 1 & 1 & 1
\end{tabular}\end{tabular}
In minterms we can indicate that
F=m0+m4+m7=a′b′c′+ab′c′+abcF=m0+m4+m7=a′b′c′+ab′c′+abc
Or we can use maxterms as
F=M1⋅M2⋅M3⋅M5⋅M6=(a+b+c′)(a+b′+c)(a+b′+c′)(a′+b+c′)(a′+b′+c)F=M1⋅M2⋅M3⋅M5⋅M6=(a+b+c′)(a+b′+c)(a+b′+c′)(a′+b+c′)(a′+b′+c)
It’s just two ways to view the problem.
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