# Intro to Logic Gates

**Logic gates**

**Logic gates** are the **basic** building blocks of any digital system. It is an electronic **circuit** having one or more than one input and only one output. The relationship between the input and the output is based on a certain **logic**. These gates are the AND, OR, NOT, NAND, NOR EXOR and EXNOR gates. The basic operations are described below with the aid of truth tables.

**AND gate**

The AND gate is an electronic circuit that gives a **high** output (1) only if **all** its inputs are high. A dot (.) is used to show the AND operation i.e. A.B. Bear in mind that this dot is sometimes omitted i.e. AB

**OR gate**

The OR gate is an electronic circuit that gives a high output (1) if **one or more** of its inputs are high. A plus (+) is used to show the OR operation.

**NOT gate**

The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an *inverter*. If the input variable is A, the inverted output is known as NOT A. This is also shown as A’, or A with a bar over the top, as shown at the outputs. The diagrams below show two ways that the NAND logic gate can be configured to produce a NOT gate. It can also be done using NOR logic gates in the same way.

**NAND gate**

This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate. The outputs of all NAND gates are high if **any** of the inputs are low. The symbol is an AND gate with a small circle on the output. The small circle represents inversion.

**NOR gate**

This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The outputs of all NOR gates are low if **any** of the inputs are high.

The symbol is an OR gate with a small circle on the output. The small circle represents inversion.

**EXOR gate**

The ‘**Exclusive-OR**‘ gate is a circuit which will give a high output if **either, but not both**, of its two inputs are high. An encircled plus sign () is used to show the EOR operation.

**EXNOR gate**

The ‘**Exclusive-NOR’ **gate circuit does the opposite to the EOR gate. It will give a low output if **either, but not both**, of its two inputs are high. The symbol is an EXOR gate with a small circle on the output. The small circle represents inversion.

The NAND and NOR gates are called *universal functions* since with either one the AND and OR functions and NOT can be generated.

Note:

A function in *sum of products* form can be implemented using NAND gates by replacing all AND and OR gates by NAND gates.

A function in *product of sums* form can be implemented using NOR gates by replacing all AND and OR gates by NOR gates.

**Table 1: Logic gate symbols**

Table 2 is a summary truth table of the input/output combinations for the NOT gate together with all possible input/output combinations for the other gate functions. Also note that truth table with ‘n’ inputs has 2^{n} rows. You can compare the outputs of different gates.

**Table 2: Logic gates representation using the Truth table**