Gates to Circuits

Full Adder

A full adder adds two bits plus an incoming carry.

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

Example

A full adder adds two bits plus an incoming carry.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\hlmath{\text{total=0 sum=0 carry=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\hlmath{\text{total=1 sum=1 carry=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\hlmath{\text{total=1 sum=1 carry=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0A=0 B=1 Cin=1total=2 sum=0 carry=1\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=1}&\hlmath{\text{total=2 sum=0 carry=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0A=0 B=1 Cin=1total=2 sum=0 carry=1A=1 B=0 Cin=0total=1 sum=1 carry=0\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=0 Cin=0}&\hlmath{\text{total=1 sum=1 carry=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0A=0 B=1 Cin=1total=2 sum=0 carry=1A=1 B=0 Cin=0total=1 sum=1 carry=0A=1 B=0 Cin=1total=2 sum=0 carry=1\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=0 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=1 B=0 Cin=1}&\hlmath{\text{total=2 sum=0 carry=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0A=0 B=1 Cin=1total=2 sum=0 carry=1A=1 B=0 Cin=0total=1 sum=1 carry=0A=1 B=0 Cin=1total=2 sum=0 carry=1A=1 B=1 Cin=0total=2 sum=0 carry=1\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=0 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=1 B=0 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=1 Cin=0}&\hlmath{\text{total=2 sum=0 carry=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0 Cin=0total=0 sum=0 carry=0A=0 B=0 Cin=1total=1 sum=1 carry=0A=0 B=1 Cin=0total=1 sum=1 carry=0A=0 B=1 Cin=1total=2 sum=0 carry=1A=1 B=0 Cin=0total=1 sum=1 carry=0A=1 B=0 Cin=1total=2 sum=0 carry=1A=1 B=1 Cin=0total=2 sum=0 carry=1A=1 B=1 Cin=1total=3 sum=1 carry=1\begin{array}{c|c}\text{A=0 B=0 Cin=0}&\text{total=0 sum=0 carry=0}\\\text{A=0 B=0 Cin=1}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=0 B=1 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=0 Cin=0}&\text{total=1 sum=1 carry=0}\\\text{A=1 B=0 Cin=1}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=1 Cin=0}&\text{total=2 sum=0 carry=1}\\\text{A=1 B=1 Cin=1}&\hlmath{\text{total=3 sum=1 carry=1}}\end{array}