Logic gates are the basic building block of computers. Logic gates are basic circuit that have at least one and usually more input and exactly one output. Input and output are the logical values TRUE and FALSE. In computer architecture it is common to use 0 for FALSE and 1 for TRUE. The values of output depends only on the current value of input. Useful way of describing the relationship between input of gates and output of gates at their truth table. In truth table, the values of each input is tabulated for every possible combination of input values.
Table of Contents
Different types of Logic Gates
We usually consider three basic kinds of gates as AND, OR and NOT gates. Firstly, let’s talk about the AND Gate.
AND Gate:
The output of AND gate is true when all the inputs are true otherwise output will be false. The AND operation usually shown by dot(.) between variables. It is written as X=A.B
The symbol and truth table of AND gate with two inputs are given below:
| Input | Input | Output |
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
OR Gate:
OR gate is a logical gate that performs a logical conjunction based on the combination of its input. The output of OR gate is TRUE only when one or more inputs are TRUE. If all the inputs are FALSE then all the output is false. It is written as X=A+B.
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The symbol and truth table of OR gate with two inputs are given below:
| Input | Input | Output |
| A | B | Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
NOT Gate:
NOT gate is a logic gate with one input and one output that performs inverter operation of the input. The output of NOT gate is the reverse of input. When the input of NOT gate is TRUE then the output is FALSE and vice-versa. The Boolean expression for NOT gate is X=A
The symbol and truth table of NOT gate with one input is given below:
| Input | Output |
| A | X |
| 0 | 1 |
| 1 | 0 |
Derived Gate
Simply, NAND gate produce false output when all the inputs are true otherwise the output is true. NAND gate is the complement of AND gate.
NAND Gate:
The symbol and truth table of NAND gate with two inputs are given below:
| Input | Input | Output |
| A | B | X |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR Gate:
NOR gate give positive output when both the inputs are negative.
The symbol and truth table of NOR gate with two inputs are given below:
| Input | Input | Output |
| A | B | X |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
X-OR Gate:
X-OR gate is pronounced as exclusive OR gate. It is a gate which gives true output only when both the inputs are art opposite logic level. In other words, X OR gate produces true output when the number of two input is odd.
| Input | Input | Output |
| A | B | X |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
X-NOR Gate:
X-NOR gate is exclusive NOR gate which has two or more inputs and one output that performs logical equally. The output of X-NOR gate is true only if all of its inputs are true or if all its inputs are false. In other words, the X-NOR gate produces true output only when both inputs are of same logic level.
| Input | Input | Output |
| A | B | X |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
UNIVERSAL GATE:
Universal gate is a gate which can implement any Boolean function without need to use any other gate type. The NAND and NOR gates are universal gates. In practice, this is advantageous since NAND and NOR gate are economical and easier to use and are basic gate used in IC digital logic family.
NAND gate as a universal gate:
Any Boolean function can be implemented using only NAND gate. Hence, NAND gate is known as universal gate. We will show that the AND, OR, NOR operation can be performed only these gates.
Implementing an inverter using only NAND gate:
Implementing an AND gate using NAND gate:
Implementing an OR gate using NAND gate:
Overall, this article is all about the logic gates with it’s different types like AND Gate, OR Gate, NOT Gate also Derived gate NAND Gate and NOR Gate, X-OR AND X-NOR Gate as well. After that we discuss about the Universal Gates and it’s implementation like the NAND Gate implementation using AND Gate and OR Gate with clear diagram. I hope all of the above theory and the diagram makes you clear about the Logic Gates and their types.
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