Gates to Circuits

NAND Is Universal

NOT, AND, and OR can be built from only NAND gates.

Example

NOT, AND, and OR can be built from only NAND gates.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0\begin{array}{c|c}\text{A=0 B=0}&\hlmath{\text{NOTA=1 AND=0 OR=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0A=0 B=1NOTA=1 AND=0 OR=1\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0}\\\text{A=0 B=1}&\hlmath{\text{NOTA=1 AND=0 OR=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0A=0 B=1NOTA=1 AND=0 OR=1A=1 B=0NOTA=0 AND=0 OR=1\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0}\\\text{A=0 B=1}&\text{NOTA=1 AND=0 OR=1}\\\text{A=1 B=0}&\hlmath{\text{NOTA=0 AND=0 OR=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0A=0 B=1NOTA=1 AND=0 OR=1A=1 B=0NOTA=0 AND=0 OR=1A=1 B=1NOTA=0 AND=1 OR=1\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0}\\\text{A=0 B=1}&\text{NOTA=1 AND=0 OR=1}\\\text{A=1 B=0}&\text{NOTA=0 AND=0 OR=1}\\\text{A=1 B=1}&\hlmath{\text{NOTA=0 AND=1 OR=1}}\end{array}

Read the table verdict

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0A=0 B=1NOTA=1 AND=0 OR=1A=1 B=0NOTA=0 AND=0 OR=1A=1 B=1NOTA=0 AND=1 OR=1verdictNAND can build the basic gates\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0}\\\text{A=0 B=1}&\text{NOTA=1 AND=0 OR=1}\\\text{A=1 B=0}&\text{NOTA=0 AND=0 OR=1}\\\text{A=1 B=1}&\text{NOTA=0 AND=1 OR=1}\\\text{verdict}&\hlmath{\text{NAND can build the basic gates}}\end{array}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.