Gates to Circuits

Gate Truth Tables

A gate is a small table from input bits to output bits.

Example

A gate is a small table from input bits to output bits.

highlighted = computed this step

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1\begin{array}{c|c}\text{A=0 B=0}&\hlmath{\text{NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1A=0 B=1NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1}\\\text{A=0 B=1}&\hlmath{\text{NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1A=0 B=1NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0A=1 B=0NOTA=0 AND=0 OR=1 XOR=1 NAND=1 NOR=0\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1}\\\text{A=0 B=1}&\text{NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0}\\\text{A=1 B=0}&\hlmath{\text{NOTA=0 AND=0 OR=1 XOR=1 NAND=1 NOR=0}}\end{array}

Build the concrete table

Compute the highlighted logic-table value.

A=0 B=0NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1A=0 B=1NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0A=1 B=0NOTA=0 AND=0 OR=1 XOR=1 NAND=1 NOR=0A=1 B=1NOTA=0 AND=1 OR=1 XOR=0 NAND=0 NOR=0\begin{array}{c|c}\text{A=0 B=0}&\text{NOTA=1 AND=0 OR=0 XOR=0 NAND=1 NOR=1}\\\text{A=0 B=1}&\text{NOTA=1 AND=0 OR=1 XOR=1 NAND=1 NOR=0}\\\text{A=1 B=0}&\text{NOTA=0 AND=0 OR=1 XOR=1 NAND=1 NOR=0}\\\text{A=1 B=1}&\hlmath{\text{NOTA=0 AND=1 OR=1 XOR=0 NAND=0 NOR=0}}\end{array}
logic-computation Every row is intentionally ordered and pinned to the lesson specification.