Digital logic tools
Twenty-one calculators for the things you actually have to work out, from truth tables, simplification and Karnaugh maps to logic proofs, number bases and text encodings. Each one shows its working, and all of them are free and run in your browser, with nothing uploaded.
Boolean algebra and circuits
Truth table generator
Type an expression, or several for a multi-output circuit, and get the full truth table, plus the tables of all seven basic gates.
Open →Boolean algebra calculator
Simplify to an irredundant sum of products, or check whether two expressions are equivalent.
Open →Karnaugh map solver
Draws the K-map with every group highlighted, for two to six variables.
Open →Sum of products calculator
Minterms, maxterms, and all four forms: canonical and minimal, SOP and POS.
Open →NAND and NOR converter
Rewrite any expression using only NAND gates, or only NOR gates, with the gate count.
Open →Circuit diagram generator
Draws one expression, or several outputs at once, as a gate diagram you can click through, with live signal colours.
Open →Worksheet generator
A printable set of questions with an answer key, rebuilt from the number in the link.
Open →Logic statements and sets
Logic statement truth tables
Truth tables for p → q, ↔ and ¬ with every step shown, plus tautology, equivalence and argument validity checks.
Open →Logical equivalence calculator
Step-by-step proofs that two logic statements are equivalent, one named law per line, or a counterexample when they are not.
Open →Expression tree generator
Draw the parse tree of a logic expression and see every part's value for any row of its truth table.
Open →Venn diagram generator
Shade any set expression of up to three sets, or click regions to get the expression, with the truth table.
Open →Numbers and binary arithmetic
Binary converter
Decimal, binary, hex and octal at a fixed width, with two's complement and BCD.
Open →Gray code converter
Convert between binary and Gray code, with the full sequence for any width.
Open →Hex to decimal converter
Hex to decimal and back, with the place-value sum and the repeated division written out.
Open →Hex to binary converter
Hex to binary and back, nibble by nibble, and octal in groups of three bits.
Open →Binary calculator
Add, subtract, multiply and divide in binary with every carry and borrow shown, plus bitwise operations.
Open →Hex calculator
Hex arithmetic with column working, carries at 16, and the full hex addition table.
Open →IEEE 754 converter
Decimal to float and double bits: sign, exponent and fraction, the exact value stored and the rounding error.
Open →Text and encodings
Binary translator
Text to binary and binary to text, with each character broken down into its code point and UTF-8 bytes.
Open →ASCII table
All 128 ASCII codes in decimal, hex and binary, with the control characters named and explained.
Open →Base64 encode and decode
Encode text to Base64 or decode it, with every 3 bytes shown becoming 4 characters, bit by bit.
Open →Which one do I want?
| If you have | And you want | Use |
|---|---|---|
| An expression | every input combination listed | Truth table generator |
| A long expression | the shortest equivalent | Boolean algebra calculator |
| Two expressions | to know whether they match | Boolean algebra calculator |
| A homework K-map | the groups drawn and named | Karnaugh map solver |
| A truth table | minterms, maxterms, SOP or POS | Sum of products calculator |
| A circuit design | it rebuilt from one gate type | NAND and NOR converter |
| A counter or encoder | a one-bit-at-a-time sequence | Gray code converter |
| A number | it in another base, or in two's complement | Binary converter |
| A class to teach | a printable question sheet with answers | Worksheet generator |
| An idea | to build and run it | The simulator |
The expression tools share one engine
The same parser and minimiser sits behind every tool here that takes an expression, so what you type into one means exactly the same thing in the next. (The binary and Gray code converters work on bit patterns rather than expressions, so they are their own thing.) It accepts whichever notation you use — a·b, a&b, a∧b, ab — and the simplification is Quine-McCluskey, the same algorithm whether you see it as algebra or as groups on a map.