Logic Gates and Number System

Logic Gates form the basis of today’s digital infrastructure and are immensely important. They form a salient part of our digital world thus helping in making day-to-day tasks easier and less time-consuming. The term logic gates is made up of two words logic and gate, the former means operators who produce a result based on a logical equation whose answer is either yes or no, and the latter is used because these operators are usually used for gatekeeping in the electrical industries. Thus we can conclude that logic gates are operators like logical and gates. 

They are mainly based on two binary digits, 1 and 0 which each represent ON and OFF functioning of the devices. Based on this binary system we have various different types of logic gates performing different calculations thus having various different applications. Some examples of logic gates are: NOT Gate which works as an inverter, OR gate, AND gate, NOR gate, NAND gate, XOR gate, etc. 

Truth Table and Logic Gates

The Truth Table is the visual representation of all the combinations of inputs and the outputs thereof, stored in a tabular format. They uncomplicated working with the Logic Gates. 

Tautology: When the output is true(1)

Fallacy: When the output is False(0)

Example of a Truth Table

Logical Operators

1. NOT or Negation:

It is the only operator which works with only one variable at a time thus is termed as an Unary Operator. Its most common symbol is ~. It returns 1 for 0 and 0 for 1, that is it negates. 

The truth table for the operator is:

Symbol and Truth Table for NOT Operator

2. AND or Conjunction Operator:

It is a binary operator that is it works on two variables at a time, it may work with even more than two operands at a time. Its mathematical basis is A.B that is multiplication. It is represented by the symbol: “.”

Symbol and Truth Table for AND Operator

3. OR or Disjunction Operator:

It is another example of a binary operator but it can also work with more than two operands at a time. Its mathematical basis is addition of the two operands. Its symbol is +

The Truth Table is given as:

Symbol and Truth Table for OR Gate

Logical Expression for NAND Gate

The NAND Gate is the combination of AND and NOT gate. In this section we will talk about the logical expression for NAND gate.

Mathematically, it first multiplies the two operands and then inverts the answer, for example: if our two inputs are 1 and 1 then it will first perform 1x1=1 followed by inverting it to 0 thus our final result will be 0.

State the logical expression for nand gate:

The logical expression for nand gate is: \[]\bar{A.B}\

Symbol and Truth Table for NAND Gate

Summary 

The logic gates form the fundamental part of digital devices and are responsible for performing the basic calculation behind the working of the devices. They follow the binary system of numbers which include 1 and 0 representing ON and OFF states of the devices, respectively. We have different types of logic gates like NOT, OR, AND, NAND, NOR, etc.

Sample Questions

1. Write the truth table for the following logical operators:

• AND

• NAND

Ans: 

• AND Gate:

AND Gate

• NAND Gate:

NAND Gate

2. Give the symbol representing the following logic operators:

• NOT

• OR

Ans:

• NOT Gate:

NOT Gate

• OR Gate:

OR Gate

Practice Questions

Calculate the output for the inputs in the NAND Gate:

1. A=1; B=0

2. A=1; B=1

Answers:

1. 1

2. 0

State the type of gates based on the data given:

1. Input: A=1; B=0, Output: Y=0

2. Input: A=0; B=0, Output: Y=1

Answers:

1. NOR Gate

2. NAND Gate