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Premium experiment • Boolean truth structure

COMPUTER SCIENCE & TECHNOLOGY • DIGITAL LOGIC

Logic Gates Interactive Lab

Drive binary inputs through real gate symbols, watch the output change, step through every truth-table row and compare Boolean behavior across seven fundamental gates.

● LIVE BOOLEAN LABLogic Gates
Output Y—
Gate—
Input A—
Input B—
Gate family—
Truth-table density—

TRUTH TABLE

Complete input → output map

Current row highlighted
ABY

Reasoning inspector

live model state
Gate—
Current inputs—
Current output—
Truth pattern—
True rows—
Expression—
Gate family—

Build intuition with every gate

Use manual inputs when you want to test a specific case. Use Step or Play when you want the simulator to enumerate the complete truth table and expose the pattern automatically.

What the signal strip shows

The lower canvas keeps a short history of recent A, B and Y states. It is a logical state history—not an electrical timing or propagation-delay model.

LEARN WITH THE SIMULATION

Understand Logic Gates by experimenting.

START HERE

Logic gates implement Boolean functions by mapping discrete input states to an output. A single input setting is only one row of that function, so this laboratory pairs the live gate drawing with the complete truth-pattern signature for AND, OR, XOR, NAND, NOR, XNOR and NOT. The premium inspector shows the current expression, current output, number of true rows and the entire output pattern so learners can reason about a gate as a function rather than memorizing isolated examples.

BUILD THE IDEA

What you should understand first

  • Read a truth table as the complete definition of a Boolean gate.
  • Distinguish inclusive OR from XOR and identify XNOR as the complement of XOR.
  • Explain NAND and NOR as complemented gates and why each is functionally universal.
  • Treat NOT as a unary gate whose output depends only on A.

TRY IT YOURSELF

How can two gates agree on one input row but still represent different Boolean functions?

  1. Choose AND and set A=0, B=0; record the output and truth pattern.
  2. Switch to OR while keeping the same input row and note that the current output may still agree.
  3. Compare the full truth patterns across all four two-input rows.
  4. Repeat with XOR and XNOR and identify how every row is complemented.
Read the visual:

One matching row does not make two Boolean functions equivalent. A truth table compares the complete mapping. Complementary gates invert every output row, while gates such as AND and OR differ only on particular input combinations.

WHY IT WORKS 01

A truth table is the full behavioral specification

For two Boolean inputs there are four possible input rows: 00, 01, 10 and 11. Listing the output for all four completely defines a two-input Boolean function. Looking at only the current A and B values can hide important differences because several gates may produce the same output on one row while differing elsewhere.

WHY IT WORKS 02

Complemented gates come in useful pairs

NAND is NOT-AND, NOR is NOT-OR and XNOR is NOT-XOR. Their truth patterns are bitwise complements of the underlying gate's pattern. NAND and NOR are especially important because either one alone can be combined repeatedly to construct NOT, AND, OR and therefore any Boolean function.

WHY IT WORKS 03

XOR is a parity detector, not another spelling of OR

XOR outputs one when exactly one of two inputs is one, giving the pattern associated with odd parity for two bits. XNOR outputs one when the inputs match. This equality-versus-difference interpretation makes XOR/XNOR useful for adders, checksums, comparison logic and controlled bit toggling.

DO NOT MIX THESE UP

Common misconception

OR is inclusive, so 1 OR 1 is 1; XOR is the gate that is true only when the two inputs differ. NOT is unary even if an interface displays another input nearby. Logic levels are abstract 0/1 states in this model, not fixed real-world voltages or propagation-delay behavior.

PRACTICE CHALLENGE

Can you predict the entire truth pattern of a selected gate before testing individual input rows?

  • Choose a gate and write the expected outputs in 00, 01, 10, 11 order.
  • Use the premium inspector to reveal its truth pattern.
  • Change A and B through the rows and verify each prediction.
  • Choose a complementary gate and predict its pattern by flipping every previous output bit.
Reveal the reasoning

A two-input gate is identified by all four outputs, not by one sample. Complementary gates reverse each row: NAND complements AND, NOR complements OR and XNOR complements XOR. NOT is unary and therefore needs only the two A rows 0 and 1.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Inputs and outputs are ideal binary logic levels 0 or 1.
  • Gate behavior is instantaneous and follows ideal Boolean truth tables.
  • Signal voltage, current and timing details are abstracted away.

Model limitations

  • Propagation delay, noise margins, metastability, fan-out and electrical loading are not modeled.
  • Real digital circuits can exhibit hazards and timing-dependent behavior absent from ideal Boolean logic.

CONNECT IT

Where this matters

  • Digital arithmetic and processors
  • Combinational control circuits
  • Boolean simplification
  • Foundation for multiplexers, adders and state machines

WORDS THAT MATTER

Key vocabulary

Boolean function
Mapping from binary input values to a binary output.
Truth table
Complete list of outputs for every possible input combination.
XOR
Exclusive-OR gate that outputs one when its two inputs differ.
Universal gate
Gate type such as NAND or NOR from which any Boolean function can be constructed.
Complement
Logical inversion that changes 0 to 1 and 1 to 0.