## What are logic functions?

Logic functions are used in spreadsheets to check whether a situation is true or false. Depending on the results of the test, you can choose to do one thing or another. These decisions can be used to present information, perform various variable calculations, or perform other tests.

## What is a Logic function gate?

In the binary lesson, the switches inside a computer. A logic gate is a switch that opens or closes based on what the user is doing. They are the building blocks for how computers work.

Type of logic function gates are: NOT, AND, OR, and XOR gates, these are the main gates. There are other exclusive gates NAND, NOR, and XNOR. These are also called the Boolean logic gate.

## NOT Gate

There is no reasonable gateway to convert digital input signals. For this reason, the NOT gate is sometimes called an inverter (not to be confused with a power converter). If the input value is low (logic 0), the NOT gate always has a high output (logic 1). Conversely, a logical NOT gate always has a low output (logic 0) if the input is high (logic 1).

If the binary input gate NOT input is considered A, then the binary output gateway will be Ā. Since the inactivity icon is a bar or overline (-). If the value of A is 1. then Ā = 0 and vice versa.

Its Boolean Expression is usually denoted by a bar or overline (¯) the input symbol that represents the function of the inverter, (hence the name inverter).

## AND Gate

AND GATE is a logical gateway with two or more outputs and one input. AND Gate operates with reasonable repetition rules. At this gate, if the other input is low (0), then the output is also low. If all inputs are high (1), the output is also high. The 2 inputs and 3 input AND gates are the most common.

The logical equation of AND gate can be represented as Z = AB, All multiplication combinations of A and B can be represented in the form of a table in the truth table. The truth table lists the output of a particular digital logic function circuit in all possible combinations of its inputs.

## OR Gate

The gate OR has two or more inputs and one exit signal. It is called a gate OR because the exit signal will only be high if any or all of the input signals are high.

It can be seen from the truth table that when the input of the OR gate is low, that is, 0, the output will be 0. If either or both inputs of the OR gate are 1, that is, it is high, and the output will be high, that is 1.

## NOR Gate

The NOR gate is a combination of the NOT gate and the OR gate. Also called negative OR gate. The NOR gate provides true or high output only when both the output is low or false. Logic NOR Gate is a retractable or “compatible” method of integrated gate OR seen before.

## NAND Gate

The NAND gate is a combination of the AND gate and the NOT gate. They are connected in the form of a cascade. Also called negative AND gate. The NAND gate provides false or low output only when both the output is high or true. The NAND gate is important because different types of Boolean operations are done through its use.

The NAND gate has a fully functional area. Completeness of functions means that any type of gate can be operated using the NAND gate. Using different combinations, it can perform the functions of NOT, OR, and AND gateways.

## Example to understand the logic function

In order to understand the logic of the Logic Gates operating system, let us consider the example of a street lighting system.

Switch: On = 1, Off = 0

Light Sensor: Dark = 0, Bright = 1 Street Light: On = 1, Off = 0

## Uses of logic function

• De Morgan's theory allows the large bars in Boolean expressions to be split into smaller bars for each variable. In order to minimize the conversation with the large bar, the bar should be separated first. This means that in some cases, the first step in reducing the logical expression is to apply De Morgan's theory.
• The K-map method for solving logical expressions is called the image method for simplifying Boolean extensions. K-map is also called a 2 dimensional truth table because each K-map is just a separate format that represents the value that exists in a one-dimensional truth table.
• Boolean functions, commonly known as logical functions, are expressions expressed algebraically with binary variables, logical operation symbols, parentheses, and equal signs. Boolean algebra is fundamental to the operation of an FPGA. Boolean algebra describes operations in which the input and output values are true or false (1 or 0, respectively).
• They are basically used in logic circuits that include calculations and processing.
• They are also used to change the pressure button. E.g., Door to Door.
• They are used for the operation of street lights.
• They are also used for TTL, MOSFET (Transistor-Transistor Logic), and CMOS rotation.

## Common Mistakes

These are important digital devices that are mainly based on the Boolean function. Logic gates are used to perform logic operations on single or multiple binary inputs and give a binary output. Simply put, a logic gate is an electronic circuit in a digital system.

## Context and Applications

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used for:

• Bachelor of technology in the electrical and electronic department
• Bachelor of Science in physics
• Master of Science in physics
• Boolean algebra
• Karnaugh map

## Practice Problems

Q1.  A full adder logic circuit will have __________.

a) Two inputs and one output

b) Three inputs and three outputs

c) Two inputs and two outputs

d) Three inputs and two outputs

Correct option - (d)

Explanation - The full adder circuit will add two bits and will also calculate the load insertion generated in the previous section. So, three inputs and two outputs (sum and carry) can be used. In the case of a half adder loop, there are only two input bits and two outputs (SUM and CARRY).

Q2.  Which of the following are known as universal gates?

a) NAND & NOR

b) AND & OR

c) XOR & OR

d) EX-NOR & XOR

Correct option - (a)

Explanation - NAND and NOR Gates are called international gates, because any digital circuit can use any of these two gates to run completely, and can generate 3 basic gates AND, OR, and NOT.

Q3.  The gates required to build a half adder are __________.

a) Exclusive-OR gate and NOR gate

b) EX-OR gate and OR gate

c) EX-OR gate and AND gate

d) EX-NOR gate and AND gate

Correct option - (c)

Explanation - The gates required to build a half adder are an EX-OR gate and a gate. EX-OR removes SUM for two bits of input and AND releases CARRY for two bits of input.

Q4. How many truth table entries are necessary for a four-input circuit?

a) 16

b) 4

c) 9

d) 64

Correct option- (a)

Explanation - Calculate the number of entries:

$\begin{array}{rcl}{2}^{n}& =& {2}^{4}\\ & =& 16\end{array}$

Q5.  The basic logic gate whose output is the complement of the input is the ___________

a) OR gate

b) AND gate

c) INVERTER gate

d) XOR gate

Correct option - (c)

Explanation - Also called NOT gate and it simply converts input, so that 1 becomes 0 and 0 becomes 1.

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