Advanced Truth Table Generator
π 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 XOR gates. These are 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.
XOR Gate: While not fully universal alone, XOR gates are fundamental in arithmetic circuits, parity generation, and cryptography. Many functions can be efficiently implemented using XOR gates.
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, Β·, &, && | Logical conjunction |
| OR | OR, +, |, || | Logical disjunction |
| NOT | NOT, -, ~, ! | Logical negation |
| XOR | XOR, β | Exclusive OR |
| NAND | NAND | Not AND |
| NOR | NOR | Not OR |
| IMPLIES | IMPLIES, β, => | Logical implication |
Gate Conversion Features
The tool can convert any boolean expression to use only specific gate types:
- NAND Gate Conversion: Convert any expression to use only NAND gates (universal gate)
- XOR Gate Conversion: Optimize expressions using XOR gates for arithmetic and parity functions
- Step-by-step conversion: See how each operator is converted to the target gate type
Universal Gate Properties
| Gate | Universal? | Common Uses |
|---|---|---|
| NAND | Yes | CMOS technology, basic logic circuits |
| NOR | Yes | NMOS technology, memory circuits |
| XOR | No (with NOT) | Arithmetic, parity, cryptography |
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
- Integrated into larger digital systems
Auto-Generation Features
Quickly generate common boolean expressions with different complexity levels:
- Basic: Simple gates and combinations
- Intermediate: Multi-gate circuits and common logic
- Advanced: Complex expressions and real-world examples
Examples
a AND b- Logical ANDa OR (NOT b)- a OR NOT b(a AND b) OR c- a AND b OR ca IMPLIES b- If a then ba XOR b- Exclusive OR
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