# Truth table, Boolean expression and Logic gates

### Truth table and Boolean expression:

The truth table is a table of all possible combinations of the variables showing the relation between the values that variables may take and the result of the operation. The table used to represent the Boolean expression of a logic gate function called a truth table. A truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of input. To represent a function in truth table, there should be the list of the combination of the binary variables. An expression that results in a Boolean value i.e. in a value of either true or false, which takes several forms.

The examples of truth table of different gates are as follows

#### Logic gates:

A logic gate is an electronic circuit that operates on one or more input signals to produce an output signal. A logic gate is also known building block of a digital circuit. Mostly, the logic gate consists of two inputs and one output. Gates produce the signals 1 or 0 if input requirements are satisfied. Digital computer uses different types of logical gates. Each gate has a specific function and graphical symbol. The function of the gate is expressed by means of an algebraic expression. The basic gates are described below:

**AND Gate:**

The AND Gate contain two or more than to input values which produce only one output value. AND gate produces 1 output when all inputs are 1, otherwise the output will be 0. It can be explained with the help of two switches connected in series. In AND gate, current is flowing in the circuit only when both switches, A and B, are closed.

The switch contains two states which are ON or OFF. The ON means the logic 1 and the OFF means the logic 0. So, when both switches are ON, the output is 1 and when any of the switches are OFF, the output is 0.

The graphical symbol, logical circuit, algebraic expression and truth table of AND gate is shown below:

**OR Gate:**

The OR Gate contains two or more than two input values which produce only one output value. OR gate produces 1 output, when one of the inputs is 1. If inputs are 0, then the output will be also 0. It can be explained by taking an example of two switches connected in parallel.

The graphical symbol, algebraic expression and truth table of OR gate is as shown below:

**NOT Gate:**

The NOT Gate contains only one input value which produces only one output value. This gate is also known as an inverter. So, this circuit inverts the logical sense of a binary signal. It produces the complemented function. If the input is 1, then this gate will produce 0 as output and vice-versa. The graphical symbol, algebraic expression and truth table of a NOT gate is given below.

**NAND Gate:**

The NAND Gate contains two or more than two input values which produce only one output value. This gate is the combination of AND and NOT gates. This gate is a complement of AND function. This gate produces output 0, when all inputs are 1, otherwise, output will be 1.

The graphical symbol, algebraic expression and truth table of NAND gate is shown below:

**NOR Gate:**

The NOR Gate contains two or more than two input values which produce only one output value. This gate is a combination of OR and NOT gate. This gate is the complement of the OR function. This gate produces 1 output, when all inputs are 0 otherwise output will 0.

The graphical symbol, algebraic expression and truth table of NOR gate are given below

**Exclusive OR (X-OR) Gate:**

This gate contains two or more than two input values which produce only one output value. The graphical symbol of X-OR gate is similar to OR gate except for the additional curve line on the input side. This gate produces 1 as output, if any input is 1 and 0 if both inputs are either 1 or 0, otherwise its output is 0.

The graphical symbol, algebraic expression and truth table of X-OR gate is given below:

**Exclusive NOR (X-NOR) Gate:**

This gate contains two or more than two input values which produce only one output value. The X-NOR is the complement of the X-OR, as indicated by the small circle in the graphical symbol. This gate produces 1 output, when all inputs are either 0 or 1, otherwise its output value is 0.

The graphical symbol, algebraic expression and truth table of X-NOR gate is shown below:

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