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Boolean Algebra Calculator
Insert the equation in the Boolean algebra calculator to know the truth table for Boolean expression.
Examples:
Click to evaluate Boolean expression(P*(-P+Q))+QP
(P*Q+P)
(P*(-P+Q))
(P*P+Q)
-(-P*Q)
(P*(-P+Q))+QP+P
Boolean Algebra Calculator
The Boolean algebra simplifier or expression calculator is an online tool that gives the truth table for boolean expressions and tells the nature of the expression.
Instead of typing And, Not, Nand e.t.c, you can simply use algebraic functions like +, -, *, e.t.c.
What is Boolean algebra?
Boolean algebra is the branch of algebra (mathematics) in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively.
We use Boolean algebra to analyze digital gates and circuits. It is being used in Finance and Digital computing now.
Boolean Expressions and Functions
| Name | Algebraic function |
| AND | F = A.B |
| OR | F = A + B |
| NOT | F = A |
| NAND | F = (AB) |
| NOR | F = (A + B) |
Example:
Find the truth table for the following boolean expression.
(A.B) +B
Solution:
Step 1: Break the expression into smaller operations.
- A.B = C
- C + B
Step 2: Solve these functions separately and combine them in one logic table.
| A | B | A.B = C | C + B |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
Truth Table for Binary Logical Operations
| p | q | F | NOR | ↚ | ¬p | ↛ | ¬q | XOR | NAND | AND | XNOR | q | → | p | ← | OR | T |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| T | T | F | F | F | F | F | F | F | F | T | T | T | T | T | T | T | T |
| T | F | F | F | F | F | T | T | T | T | F | F | F | F | T | T | T | T |
| F | T | F | F | T | T | F | F | T | T | F | F | T | T | F | F | T | T |
| F | F | F | T | F | T | F | T | F | T | F | T | F | T | F | T | F | T |
| Com | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||||||
| Assoc | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||||||
| Adj | F | NOR | ↛ | ¬q | ↚ | ¬p | XOR | NAND | AND | XNOR | p | ← | q | → | OR | T | |
| Neg | T | OR | ← | p | → | q | XNOR | AND | NAND | XOR | ¬q | ↛ | ¬p | ↚ | NOR | F | |
| Dual | T | NAND | → | ¬p | ← | ¬q | XNOR | NOR | OR | XOR | q | ↚ | p | ↛ | AND | F | |
| L id | F | F | T | T | T,F | T | F | ||||||||||
| R id | F | F | T | T | T,F | T | F | ||||||||||
Boolean Algebra Laws
Below you can find the rules of Boolean Algebra which are used to evaluate Boolean expressions.
| Laws Names | AND Form | OR Form |
| Commutative Law | A.B = B.A | A+B = B+A |
| Associative Law | (A.B).C = A.(B.C) | (A+B)+C = A+(B+C) |
| Identity Law | A.1 = A | A+0 = A |
| Zero and One Law | A.0 = 0 | A+1 = 1 |
| Inverse Law | A.A' = 0 | A+A' = 1 |
| Idempotent Law | A.A = A | A + A = A |
| Absorption Law | A(A+B) = A | A + A.B = A A + A'B = A+B |
| Distribution Law | (A.B)+C = (A+C).(B+C) | (A+B).C = (A.C)+(B.C) |
| De Morgan's Law | (A.B)' = A'+B' | (A+B)' = A'.B' |
| Double Complement Law | x̄̄̄ = x | |
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