Advanced Truth Table Generator
🔄 Auto-Generate Boolean Formulas
Quickly generate common boolean expressions:
Quick Formulas
Expanded Formula
Truth Table
Universal Gate Conversion
Convert any boolean expression to use only NAND gates or only NOR gates. These are the two Universal Gates that can implement any boolean function.
About Universal Gates
NAND Gate: Known as a universal gate because any boolean function can be implemented using only NAND gates. This is widely used in CMOS technology.
NOR Gate: The other universal gate. Like NAND, any logic circuit (AND, OR, NOT) can be built using only NOR gates. It is essential in technologies like NMOS.
Note: XOR is NOT a universal gate on its own, but it is very useful for arithmetic operations.
Verilog Code Generator
Generate Verilog HDL code from your boolean expression for digital circuit simulation.
How to Use
Enter a boolean formula using logical operators and specify the variables to generate a truth table.
Supported Operators
| Operator | Symbols | Description |
|---|---|---|
| AND | AND, ·, &, && | Logical conjunction |
| OR | OR, +, |, || | Logical disjunction |
| NOT | NOT, -, ~, ! | Logical negation |
| XOR | XOR, ⊕ | Exclusive OR |
| NAND | NAND | Not AND |
| NOR | NOR | Not OR |
| XNOR | XNOR | Exclusive NOR (Inverse of XOR) |
| IMPLIES | IMPLIES, →, => | Logical implication |
Gate Conversion Features
The tool can convert boolean expressions to use specific gate types:
- NAND Gate Conversion: Convert to use only NAND gates (Universal).
- NOR Gate Conversion: Convert to use only NOR gates (Universal).
- XOR Optimization: Uses XOR gates for efficiency in arithmetic/parity logic.
Universal Gate Properties
| Gate | Universal? | Common Uses |
|---|---|---|
| NAND | Yes | CMOS technology, basic logic circuits |
| NOR | Yes | NMOS technology, memory circuits |
| XOR | No | Arithmetic, parity, cryptography |
Note on XNOR Gates
XNOR (Exclusive-NOR) is the inverse of XOR. It outputs true (1) only when both inputs are the same (both 0 or both 1). Like XOR, XNOR is not a universal gate, but it is extremely useful in "Equality Detectors" and digital comparators.
Verilog Code Generation
The tool can generate Verilog HDL code for your boolean expressions that can be:
- Simulated in DigitalJS online simulator
- Used in FPGA/ASIC design workflows
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