Building Arithmetic

D Latch State Table

A tiny memory cell is a next-state table with the old state as input.

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

Example

A tiny memory cell is a next-state table with the old state as input.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\hlmath{\text{Qnext=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\hlmath{\text{Qnext=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\hlmath{\text{Qnext=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\hlmath{\text{Qnext=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1E=1 D=0 Qprev=0Qnext=0\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\text{Qnext=1}\\\text{E=1 D=0 Qprev=0}&\hlmath{\text{Qnext=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1E=1 D=0 Qprev=0Qnext=0E=1 D=0 Qprev=1Qnext=0\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\text{Qnext=1}\\\text{E=1 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=1 D=0 Qprev=1}&\hlmath{\text{Qnext=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1E=1 D=0 Qprev=0Qnext=0E=1 D=0 Qprev=1Qnext=0E=1 D=1 Qprev=0Qnext=1\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\text{Qnext=1}\\\text{E=1 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=1 D=0 Qprev=1}&\text{Qnext=0}\\\text{E=1 D=1 Qprev=0}&\hlmath{\text{Qnext=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1E=1 D=0 Qprev=0Qnext=0E=1 D=0 Qprev=1Qnext=0E=1 D=1 Qprev=0Qnext=1E=1 D=1 Qprev=1Qnext=1\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\text{Qnext=1}\\\text{E=1 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=1 D=0 Qprev=1}&\text{Qnext=0}\\\text{E=1 D=1 Qprev=0}&\text{Qnext=1}\\\text{E=1 D=1 Qprev=1}&\hlmath{\text{Qnext=1}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

E=0 D=0 Qprev=0Qnext=0E=0 D=0 Qprev=1Qnext=1E=0 D=1 Qprev=0Qnext=0E=0 D=1 Qprev=1Qnext=1E=1 D=0 Qprev=0Qnext=0E=1 D=0 Qprev=1Qnext=0E=1 D=1 Qprev=0Qnext=1E=1 D=1 Qprev=1Qnext=1verdictenable=0 holds, enable=1 copies D\begin{array}{c|c}\text{E=0 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=0 Qprev=1}&\text{Qnext=1}\\\text{E=0 D=1 Qprev=0}&\text{Qnext=0}\\\text{E=0 D=1 Qprev=1}&\text{Qnext=1}\\\text{E=1 D=0 Qprev=0}&\text{Qnext=0}\\\text{E=1 D=0 Qprev=1}&\text{Qnext=0}\\\text{E=1 D=1 Qprev=0}&\text{Qnext=1}\\\text{E=1 D=1 Qprev=1}&\text{Qnext=1}\\\text{verdict}&\hlmath{\text{enable=0 holds, enable=1 copies D}}\end{array}