# Truth Tables Calculator + Online Solver With Free Steps

The **Truth Tables Calculator** is used to find out the Truth Tables of Boolean Logic Gates. Boolean Algebra is an old branch of algebra, it was invented by the great **George Boole** for Logic design and testing.

**Logic Gates** run the world nowadays. Everything from computers to calculators, TVs to smartphones, etc. — all of them have some logic gate combination running inside of them. **Boolean Algebra** is used to solve a lot of daily life engineering problems faced by people, so having a **Calculator** such as this is the ultimate plus in the arsenal.

## What Is the Truth Tables Calculator?

**The Truth Tables Calculator is an online calculator designed to solve Boolean Algebra-based Logic Gate problems and provide their Truth Tables.**

This **Calculator** is special as it belongs to the Boolean family of calculators. Also, it works in your **browser** and does not require anything to be installed or downloaded.

This **Calculator** can be used at any point in time and any place by just connecting with the internet. Providing information on the **Truth Tables** for logic gates is very useful as it comes in handy for engineers working with problems involving **Boolean Algebra**.

## How to Use the Truth Tables Calculator?

To use the **Truth Tables Calculator**, we first select the variables we want to use, and then we select the Logic Gate we would like to find the Truth Table for. This **Calculator** comes in handy when working with Logical problems.

It can quickly provide you with the **Truth Table** of any Logic Gate you need, and thus it can be very helpful when solving **Boolean Algebra**.

Now, an in-depth step-by-step guide to using this calculator is given as follows:

### Step 1

You begin by entering the name you want to give your first variable, and this is done in the input box labeled “proposition 1”.

### Step 2

You follow up by entering the name you want to give the second variable in this table, and this is carried out by entering that name in the input box labeled “proposition 2”.

### Step 3

Once all of that is done, you go to the setting labeled “logical operation” and select the **Boolean Logic Operation** you would like to get the Truth Table of as a result. It may be noted that this **Calculator** will provide the solution in terms of the variables you add, which is very helpful.

### Step 4

Finally, you move forward by pressing the button labeled “Submit”, as this button will open up a new interactable window and display the **Solution** to your problem. And if you would like to solve similar questions, you can do so by simply entering your newer **Problems** in the new interactable window.

An important note regarding the calculator would be that it does not support the Truth Tables for **Secondary Logic Gates**, them being the ones made from the primary ones. It only shows the Truth tables of **Primary Logical Operations**.

As we know, every logical operation can be made from the three primary logic gates, but there are a lot of logical operations possible. This **Calculator** would have been overloaded dealing with them all, so you can use this calculator’s help to solve your complicated Boolean problems by using its database of **Primary Boolean Operations**.

## How Does the Truth Tables Calculator Work?

The **Truth Tables Calculator** works by solving the Truth Table for a given Boolean Operation and showing the results in the format of a **Truth Table**. There are several Boolean operations, as there is a whole domain of mathematics called **Boolean Algebra** associated with it.

To learn about how a **Truth Tables Calculator** works deep down inside, we must first begin by giving an overview of what makes **Boolean Algebra**.

### Boolean Algebra

Named after the great **George Boole**, Boolean Algebra is defined as the type of algebra in which we deal with Binary Values for variables. This means that we deal only with true or false logic values when working with such an **Algebraic Expression**.

Now, there are only a set of three major **Boolean Operations** that take place between variables in Boolean Algebra, and these are Union, Intersection, and Inversion. Another important piece of information regarding Boolean Algebra would be that it works independently of numbers.

Therefore, in **Boolean Algebra** all we deal with are variables representing possible input-output signals.

### Applications of Boolean Algebra

**Boolean Algebra** is very frequently used in engineering for solving problems involving Digital Logic, and Logic Gates. As **Logic Gates** are a big part of the computer engineering world, Boolean Algebra is at the very core of that.

Now, **Boolean Logic** is most commonly expressed using a Truth Table. A **Truth Table** can be described as a list of all possible outcomes of a logical operation or a Boolean Expression. As one variable can either have a true or false value, the number of **Combinations** for a **Truth Table **is dictated by the number of input variables n of the expression:

\[ 2^n \]

### Boolean Logic of Primary Operations

Now the three primary **Logic Operations:** Union, Intersection, and Inversion, are usually referred to as OR, AND, and NOT, respectively. These operations are called **Logic Gates**, and the whole of computer engineering relies on these for its functioning.

The Logic Gate AND is defined as the one in which if both inputs of the gate are true, only then is the output true. The OR gate is defined as the gate which has a true answer for every input combination but both false, and the NOT gate is just known for reversing the logic of any input.

An important fact about these gates is that using these three gates, we can make any circuit diagram and any logical operation in the fields of **Electrical** and **Computer Engineering**.

### Solving for Truth Tables

To solve for a Truth Table, we require the **Boolean Algebraic Expression** of the problem or a schematic diagram. As a schematic diagram is yet to have the expression extracted from it, we have to solve it into a simplified **Boolean Expression**.

Once we have our hands on an expression, then we just make $2^n$ number of **Combinations** for n number of inputs. And then we calculate the output value based on the logic provided by the **Expression** itself.

Hence, a Truth Table for AND gate looks like this:

\begin{array}{C|C|C} p & q & p\land q \\ \hline T & T & T \\ T & F & F \\ F & T & F \\ F & F & F \end{array}

## Solved Examples

To get a better understanding of this concept, let’s look at some examples.

### Example 1

Solve the Truth Table for the Boolean Operation OR acting between two variables a and b.

### Solution

We begin by first setting up the two variables given to us a and b, then we use the formula $2^n$ which would result in:

\[ 2^n = 2^2 = 4 \]

Hence, we would have four rows for the Truth Table, and we would place them using the following combination:

\begin{array}{C|C} a & b \\ \hline T & T \\ T & F \\ F & T \\ F & F \end{array}

So now we must solve this using the logic behind the OR gate. The **Logic Gate** defined as OR is known for two input logic. And the logic states that when either or both inputs are true, so is the output.

When neither input is true, the output is false. So replicating that in this Truth Table would look like this:

\begin{array}{C|C|C} a & b & a\lor b \\ \hline T & T & T \\ T & F & T \\ F & T & T \\ F & F & F \end{array}

### Example 2

Solve for the AND gate between p and q and get the Truth Table.

### Solution

We begin by checking the number of inputs, which is two, so now running through the formula known to us $2^n$, we will get:

\[ 2^n = 2^2 = 4 \]

Hence, four rows are to be set up for the Truth Table and they would be expressed as:

\begin{array}{C|C} p & q \\ \hline T & T \\ T & F \\ F & T \\ F & F \end{array}

Now, we will look at the logic for the AND gate. As we have two inputs for this gate, the logic proceeds in such a way that if both inputs are **True**, so is the output otherwise for any other case it will be **False**.

As we know that there are four cases of this logic gate, now we look at them in the Truth Table:

\begin{array}{C|C|C} p & q & p \land q \\ \hline T & T & T \\ T & F & F \\ F & T & F \\ F & F & F \end{array}