Laws and Normal Forms

K-Map Simplify

A tiny K-map shows that all true cells share B=1.

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

Example

A tiny K-map shows that all true cells share B=1.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0\begin{array}{c|c}\text{AB=00 C=0}&\hlmath{\text{F=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\hlmath{\text{F=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\hlmath{\text{F=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\hlmath{\text{F=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1AB=11 C=0F=1\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\text{F=1}\\\text{AB=11 C=0}&\hlmath{\text{F=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1AB=11 C=0F=1AB=11 C=1F=1\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\text{F=1}\\\text{AB=11 C=0}&\text{F=1}\\\text{AB=11 C=1}&\hlmath{\text{F=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1AB=11 C=0F=1AB=11 C=1F=1AB=10 C=0F=0\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\text{F=1}\\\text{AB=11 C=0}&\text{F=1}\\\text{AB=11 C=1}&\text{F=1}\\\text{AB=10 C=0}&\hlmath{\text{F=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1AB=11 C=0F=1AB=11 C=1F=1AB=10 C=0F=0AB=10 C=1F=0\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\text{F=1}\\\text{AB=11 C=0}&\text{F=1}\\\text{AB=11 C=1}&\text{F=1}\\\text{AB=10 C=0}&\text{F=0}\\\text{AB=10 C=1}&\hlmath{\text{F=0}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

AB=00 C=0F=0AB=00 C=1F=0AB=01 C=0F=1AB=01 C=1F=1AB=11 C=0F=1AB=11 C=1F=1AB=10 C=0F=0AB=10 C=1F=0verdictsimplified formula is B\begin{array}{c|c}\text{AB=00 C=0}&\text{F=0}\\\text{AB=00 C=1}&\text{F=0}\\\text{AB=01 C=0}&\text{F=1}\\\text{AB=01 C=1}&\text{F=1}\\\text{AB=11 C=0}&\text{F=1}\\\text{AB=11 C=1}&\text{F=1}\\\text{AB=10 C=0}&\text{F=0}\\\text{AB=10 C=1}&\text{F=0}\\\text{verdict}&\hlmath{\text{simplified formula is B}}\end{array}