Building Arithmetic

Mux and Decoder

A selector chooses a data input or turns one bit into one-hot wires.

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

Example

A selector chooses a data input or turns one bit into one-hot wires.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

S=0 D0=1 D1=0mux output=1\begin{array}{c|c}\text{S=0 D0=1 D1=0}&\hlmath{\text{mux output=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

S=0 D0=1 D1=0mux output=1S=1 D0=1 D1=0mux output=0\begin{array}{c|c}\text{S=0 D0=1 D1=0}&\text{mux output=1}\\\text{S=1 D0=1 D1=0}&\hlmath{\text{mux output=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

S=0 D0=1 D1=0mux output=1S=1 D0=1 D1=0mux output=0S=0decoder=(1,0)\begin{array}{c|c}\text{S=0 D0=1 D1=0}&\text{mux output=1}\\\text{S=1 D0=1 D1=0}&\text{mux output=0}\\\text{S=0}&\hlmath{\text{decoder=(1,0)}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

S=0 D0=1 D1=0mux output=1S=1 D0=1 D1=0mux output=0S=0decoder=(1,0)S=1decoder=(0,1)\begin{array}{c|c}\text{S=0 D0=1 D1=0}&\text{mux output=1}\\\text{S=1 D0=1 D1=0}&\text{mux output=0}\\\text{S=0}&\text{decoder=(1,0)}\\\text{S=1}&\hlmath{\text{decoder=(0,1)}}\end{array}