Laws and Normal Forms

Sum of Products

Build a formula from the rows where the output is one.

logic-computation Every row is intentionally ordered and pinned to the lesson specification.

Example

Build a formula from the rows where the output is one.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0output=0 no minterm\begin{array}{c|c}\text{A=0 B=0}&\hlmath{\text{output=0 no minterm}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0output=0 no mintermA=0 B=1output=1 term=notA_and_B\begin{array}{c|c}\text{A=0 B=0}&\text{output=0 no minterm}\\\text{A=0 B=1}&\hlmath{\text{output=1 term=notA\_and\_B}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0output=0 no mintermA=0 B=1output=1 term=notA_and_BA=1 B=0output=1 term=A_and_notB\begin{array}{c|c}\text{A=0 B=0}&\text{output=0 no minterm}\\\text{A=0 B=1}&\text{output=1 term=notA\_and\_B}\\\text{A=1 B=0}&\hlmath{\text{output=1 term=A\_and\_notB}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0output=0 no mintermA=0 B=1output=1 term=notA_and_BA=1 B=0output=1 term=A_and_notBA=1 B=1output=0 no minterm\begin{array}{c|c}\text{A=0 B=0}&\text{output=0 no minterm}\\\text{A=0 B=1}&\text{output=1 term=notA\_and\_B}\\\text{A=1 B=0}&\text{output=1 term=A\_and\_notB}\\\text{A=1 B=1}&\hlmath{\text{output=0 no minterm}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

A=0 B=0output=0 no mintermA=0 B=1output=1 term=notA_and_BA=1 B=0output=1 term=A_and_notBA=1 B=1output=0 no mintermverdictnotA_and_B OR A_and_notB\begin{array}{c|c}\text{A=0 B=0}&\text{output=0 no minterm}\\\text{A=0 B=1}&\text{output=1 term=notA\_and\_B}\\\text{A=1 B=0}&\text{output=1 term=A\_and\_notB}\\\text{A=1 B=1}&\text{output=0 no minterm}\\\text{verdict}&\hlmath{\text{notA\_and\_B OR A\_and\_notB}}\end{array}