Boolean Algebra & Logic Gates Lab
Build and analyze Boolean expressions with interactive truth tables and circuit diagrams. Explore logic gates, verify Boolean algebra laws, and convert between Sum of Products and Product of Sums canonical forms.
Guided Experiment: De Morgan's Theorem Verification
De Morgan's theorem states that NOT(A AND B) = NOT(A) OR NOT(B), and NOT(A OR B) = NOT(A) AND NOT(B). How can you verify these identities using truth tables?
Write your hypothesis in the Lab Report panel, then click Next.
Circuit Diagram
Controls
· or & AND+ or | OR′ or ! NOT⊕ or ^ XORVariables: A B C DResults
| A | B | Out |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Data Table
(0 rows)| # | Expression | Variables | Minterms | Gate Count | Simplified |
|---|
Reference Guide
Basic Logic Gates
Logic gates are the building blocks of digital circuits. Each gate performs a specific Boolean operation on one or more binary inputs.
| Gate | Symbol | Output = 1 when |
|---|---|---|
| AND | A · B | Both inputs are 1 |
| OR | A + B | At least one input is 1 |
| NOT | A′ | Input is 0 |
| NAND | (A · B)′ | Not both inputs are 1 |
| NOR | (A + B)′ | Both inputs are 0 |
| XOR | A ⊕ B | Inputs differ |
| XNOR | (A ⊕ B)′ | Inputs are the same |
NAND and NOR are called universal gates because any other gate can be built from them alone.
Boolean Algebra Laws
Boolean algebra follows a set of laws that let you simplify and transform expressions while preserving their truth tables.
| Identity | A + 0 = A | A · 1 = A |
| Null | A + 1 = 1 | A · 0 = 0 |
| Idempotent | A + A = A | A · A = A |
| Complement | A + A′ = 1 | A · A′ = 0 |
| Commutative | A + B = B + A | A · B = B · A |
| Distributive | A · (B + C) = AB + AC | |
| Absorption | A + AB = A | |
De Morgan's Theorems
De Morgan's theorems describe how NOT distributes over AND and OR. They are essential for converting between gate types and simplifying circuits.
Use the Laws Explorer tab to verify these theorems with side-by-side truth tables.
SOP and POS Forms
Every Boolean function can be represented in two standard canonical forms.
OR of AND terms (minterms). Each product term includes every variable, either complemented or uncomplemented.
F = A′B′ + A′B + AB′ = Σm(0,1,2)
AND of OR terms (maxterms). Each sum term includes every variable.
F = (A + B) = ΠM(3)
SOP is preferred when there are fewer 1s in the output. POS is preferred when there are fewer 0s.