Cheat Sheet : Logic Gates (AND, OR and NOT) and Combinational Logic Circuits

“AND” gate

The “AND” logical operation produces a “High” output if all of its input are “1s”. If one or multiples of its inputs are “0s”, the output of the “AND” logic gate will be a zero. We could have more than two inputs with an “AND” gate but there will always be only one output. The 3 or more inputs “AND” gate follows the same rule as the 2 inputs “AND” gate. The “AND” logical operation produces a “High” output if all of its input are “1s”. If one or multiples of its inputs are “0s”, the output of the “AND” logic gate will be a zero.

For a 2-inputs “AND” gate, we have the following truth table:

$\begin{array}{c c|c} A & B & Output\\ \hline 0 & 0 & 0 \\ 0 & 1 & 0 \\ 1&0&0 \\ 1 & 1 & 1\end{array}$

“OR” gate

The “OR” logical operation produces a “Low” output if all of its input are “0s”. If one or multiples of its inputs are “1s”, the output of the “OR” logic gate will be a “1”. We could have more than two inputs with an “OR” gate but there will always be only one output. The 3 or more inputs “OR” gate follows the same rule as the 2 inputs “OR” gate. The “OR” logical operation produces a “Low” output if all of its input are “0s”. If one or multiples of its inputs are “1s”, the output of the “OR” logic gate will be a “1”.

For a 2-inputs “OR” gate, we have the following truth table:

$\begin{array}{c c|c} A & B & Output\\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1&0&1 \\ 1 & 1 & 1\end{array}$

“NOT” gate

The “NOT” gate is often called the inverting gate and will invert the input. If the input is Low “0”, the output is gonna be High “1”. If the input is High “1”, the output is gonna be Low “0”.

For the “NOT” gate, we have the following truth table:

$\begin{array}{c|c} Input & Output\\ \hline 0 & 1 \\ 1 & 0 \end{array}$

Combinational Logic Circuits

To solve a combinational logic circuits, you need to find the output of every logic gates. For this, you need to have the value of all inputs of the logic gate you are analyzing to find its output. It is generally recommended to start with the logic gates which haves the inputs signal since the inputs value of these logic gates are known. You can work your way until you reach the last logic gate and find the resulting output of the combinational logic circuit.