Logic Gate Truth Table

This tool generates complete truth tables for six fundamental logic gates (AND, OR, XOR, NAND, NOR, XNOR) based on user-specified binary inputs. It supports up to three inputs (A, B, and optional C), automatically handling both 2-input and 3-input configurations. The output displays all possible input combinations alongside corresponding gate outputs in an easy-to-read table format.

Engineers use it during digital logic verification—e.g., validating combinational logic behavior before PCB layout, debugging FPGA or ASIC behavioral models, teaching Boolean algebra concepts, or cross-checking hand-derived truth tables. It’s especially helpful when designing multiplexers, adders, parity generators, or control logic where gate interactions must be rigorously confirmed.

Inputs A and B are mandatory binary values (0 or 1). Input C is optional: entering -1 disables it, restricting calculations to 2-input gates; entering 0 or 1 enables 3-input operation (e.g., 3-input AND = A·B·C). The tool dynamically adjusts the truth table size (4 rows for 2 inputs, 8 rows for 3 inputs) and updates gate logic accordingly.

Valid inputs are integers: 0 or 1 for active signals; -1 only for disabling Input C. Entering non-integer, out-of-range, or NaN values (e.g., 2, -5, “abc”) will produce undefined or incorrect outputs. The calculator does not auto-correct—always verify inputs before clicking Calculate to ensure logical accuracy.

XOR is associative for even/odd parity: a 2-input XOR outputs 1 when inputs differ; a 3-input XOR (A⊕B⊕C) outputs 1 when an odd number of inputs are high—effectively implementing odd-parity detection. This matches standard IEEE logic conventions and is essential for error-detection circuits and arithmetic units.

NAND is the logical inverse of AND (output = NOT(A·B·C)), while NOR is the inverse of OR (output = NOT(A+B+C)). This tool computes them directly—not as cascaded gates—ensuring correct multi-input behavior. For example, a 3-input NAND outputs 0 only when all inputs are 1; otherwise, it outputs 1.

No—this version supports up to three inputs (A, B, C) to maintain clarity and usability for common educational and prototyping scenarios. For gates with >3 inputs, engineers typically decompose the logic into cascaded 2- or 3-input stages. The underlying Boolean formulas (e.g., AND = A·B·C) scale naturally, but manual extension or scripting is required beyond three variables.

XNOR is the complement of XOR: it outputs 1 when inputs are equal (even parity). For two inputs, XNOR = NOT(A⊕B); for three, XNOR = NOT(A⊕B⊕C), yielding 1 when zero or two inputs are high. This makes XNOR ideal for equality comparison and controlled inversion in bus interfaces and synchronization logic.

The dot (·) notation aligns with standard digital electronics textbooks and datasheets (e.g., TTL/CMOS logic families), emphasizing multiplication as logical AND. While ∧ and + are also valid, the chosen notation avoids ambiguity with arithmetic operators and mirrors industry practice—especially important when interfacing with SPICE simulators or HDL synthesis tools that use similar conventions.

First, ensure all inputs are integers (0, 1, or -1 for C). Next, confirm JavaScript is enabled and no browser console errors exist. If the #result div remains hidden, try refreshing the page or checking for conflicting scripts. Finally, verify that at least A and B are set—empty or non-numeric fields cause silent failures due to parseInt() returning NaN.

The truth table is the foundational input for both techniques: K-maps visually group minterms from the table to minimize expressions, while Boolean algebra uses the table to verify equivalences (e.g., proving (A·B)’ ≡ A’ + B’). Engineers often generate the truth table first, then apply minimization—making this tool a critical first step in optimizing gate count and propagation delay.

Yes—the result is rendered as semantic HTML

markup, which copies cleanly into Excel, Google Sheets, or Markdown editors (via paste-as-HTML or plain-text conversion). For programmatic use, developers can extract innerHTML from the #rt element or extend the calc() function to generate CSV/JSON output with minimal modification.