Boolean Algebra Calculator is a tool that helps you simplify logical expressions easily using basic rules of Boolean algebra.
Instead of solving long expressions by hand, you can just enter them into this calculator—like (A + B)(A + !B)(!A + C)—and it will….
- Show you the Boolean algebra simplification result
- Generate the truth table
- Give you SOP (Sum of Products) and POS (Product of Sums) forms
- Explain the steps clearly
How to Use Boolean Algebra Calculator ?
- Enter Your Boolean Expression, In the input box, type your Boolean expression. You can use….
⊕for XOR (optional)+for OR•for AND (or simply write two variables together likeAB)!AorA'for NOT A()for grouping terms
For Example : (A + B)(A + !B)(!A + C)
2. Then Click on Calculate
3. What Will Be the Outputs?
Once Simplify Boolean Expressions Online, you will get Output as
Simplified Expression (Y = …) : A shorter version of your input using Boolean rules.
For example: A•C
Truth Table : A table that shows every possible input combination and the result (0 or 1) for each.
SOP (Sum of Products) : A form where output is 1, written as OR of multiple AND terms.
Example: A•!B + !A•C
POS (Product of Sums) : A form where output is 0, written as AND of multiple OR terms.
Example: (A + B)(!A + C)
Sharing Options : You can share the result on WhatsApp or Email directly, with one click.
Boolean Algebra Calculator
Examples of Boolean Expressions and Results
Below are the result of Boolean Algebra Simplification, by choosing Boolean Expression Simplifier
- (A + B)(A + BÌ…)(AÌ… + C)
- Simplified Expression (Y):
A•C - SOP (Sum of Products):
A•C - POS (Product of Sums):
(A + B)(A + !B)(!A + C) - Truth Table
| A | B | C | Y (Output) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
2. (A + B’) • (B + C)
- Simplified Expression (Y):
A•C + B'•C + A•B - SOP:
A•C + B'•C + A•B - POS:
(A + !B)(B + C) - Truth Table
| A | B | C | Y (Output) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Why SOP and POS Are Useful?
SOP (Sum of Products) and POS (Product of Sums) are ways to simplify your Boolean expression.
Why is simplification important? 1. It’s easier to solve questions in exams or build digital circuits practically
2. It helps you understand the logic more clearly
3. It makes your circuit design smaller and faster
FAQs
What is the role of Boolean Algebra in digital electronics
Boolean Algebra is like the language of digital electronics. It helps us write, simplify, and understand how digital circuits work using just 1s and 0s.
Can I simplify expressions with 4 or more variables?
Yes, the calculator supports multiple variables like A, B, C, D, and even more. It automatically generates the full truth table and shows the simplified output for any expression.
What is Boolean algebra used for
Use of Boolean Algebra : 1.Digital Electronics and Circuit Design, 2.Simplifying Logical Expressions, 3.Programming and Algorithms, 4.Computer Science and AI, 5.Mathematics (Discrete Math).
What is 1+1 in Boolean algebra
Boolean Algebra 1 + 1 = 1
1+1=1 Theory name
In Boolean Algebra , 1+1=1
a’+1 in Boolean algebra
Any value OR 1 = 1, so A’ + 1 = 1
a + a’b = a+b in Boolean algebra
a + a’b = a + b is absolutely correct. You can check it in calculator by adding left and right expression one by one
A’B+AB’ simplify
This is a classic expression known as the Exclusive OR (XOR) function. This matches the output of A ⊕ B. You can check in above Boolean Algebra calculator.
(A+B)(A+B’) Boolean
(A + B)(A + B′) = A+BB’ = A
