Digital Logic Toolkit — Home
Type or paste anything — an expression, a truth table, a minterm list, a binary number, a line of text. This page works out what it is and shows you every other form of it.
AND is · * & or juxtaposition (AB); OR is + or |; NOT is ¬ ~ ! or a trailing ′; ^ is XOR, never a power; | is OR, never NAND. Paste a truth table, a Σm list, a number in any base, or plain text.
Read as ((A · B) + (¬A · C) + (B · C))
The function written in algebra, reduced as far as it goes.
A′ · C + A · B
Minimal SOP: 2 terms / 4 literals — verified exact (Quine–McCluskey, unique minimum).
One row per input combination; the output column is the function.
| A | B | C | F |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
8 rows · 4 ones · 0 don't-cares
The same table laid out so that adjacent cells differ in one variable.
2 groups · 2×4 map
The minimal expression built out of physical gates.
4 gates · 7 gate inputs
Every minterm and every maxterm written out in full.
Σm(1, 3, 6, 7) · ΠM(0, 2, 4, 5)
The function as two lists of row indices.
m = 1, 3, 6, 7
Turn one expression into every other form of itself, and reduce it with named laws.
Simplify any expression to its minimal SOP and POS, one named law at a time.
Turn an expression into a full truth table, with a column for every sub-expression.
Group a 2- to 6-variable map yourself and have every group marked right or wrong.
Minimise past the K-map limit with the full tabular method and Petrick’s step.
Every law, both duals, each with a truth-table proof you can check.
Push a negation through any expression and see both forms side by side.
Expand to canonical minterms and maxterms, and convert between the two.
What each gate does, in both symbol standards, and how to build circuits out of them.
Draw an expression as a gate schematic in IEEE or IEC symbols and copy it as an image.
Wire up gates and read the Boolean expression and truth table back out.
Every gate in both symbol standards, side by side, on a printable one-page chart.
Truth table, symbol and algebraic form for A·B, with a live two-input toggle.
Truth table, symbol and algebraic form for A + B, with a live two-input toggle.
Truth table, symbol and algebraic form for the inverter, Ā.
Truth table, symbol and algebraic form for (A·B)′, the universal gate.
Truth table, symbol and algebraic form for (A + B)′, the other universal gate.
Truth table, symbol and algebraic form for A ⊕ B, the difference detector.
Truth table, symbol and algebraic form for A ⊙ B, the equality detector.
Truth table, symbol and algebraic form for the non-inverting buffer, and what it is for.
Rebuild any of the other gates using only NAND, or only NOR, with the gate count.
Truth tables, K-maps and circuits for both adders, and the ripple-carry chain.
SR, D, JK and T: characteristic tables, excitation tables and timing diagrams.
Multiplexers from 2:1 to 16:1 and decoders from 2:4 to 4:16, with the selection logic derived.
Convert between bases and representations, and check the codes that detect and fix errors.
Convert between any two bases, integers and fractions, with the positional working.
Convert text to binary and back, byte by byte, with the full UTF-8 breakdown.
Encode and decode signed binary at any width, with overflow and sign extension.
Add, subtract, multiply and divide in binary with every carry and borrow shown.
Convert binary to reflected Gray code and back, and build the sequence by reflection.
Pack and unpack binary-coded decimal, and add with the +6 correction shown.
Encode, inject an error, and watch the syndrome point straight at the flipped bit.
Even and odd parity, one’s-complement sums and the Internet checksum, step by step.
Build the tree from text or from frequencies, with the merge order and canonical codes.
Bits per symbol for any distribution, with the surprisal of each symbol shown.
Every tool here shows its working. When you simplify an expression you get the minimal form and the named law applied at each step — Absorption, Consensus, De Morgan — because you are usually being graded on the method, not the result. When you group a Karnaugh map, the grouping is drawn, and your own grouping is marked correct, redundant or invalid. When you convert a number, the positional arithmetic is written out.
Where a canonical algorithm exists we name it and use it: Quine–McCluskey with Petrick’s method for exact minimisation, so an answer is never a guess that ran out of rewrite rules. Where a function has more than one equally minimal form, you get all of them, rather than one silently chosen and presented as if it were the only one. Nothing is behind an account, a paywall, or a “click to calculate” button, and every page keeps working with no network after your first visit.
In 1937 a twenty-one-year-old master’s student at MIT noticed that the algebra George Boole had built to describe the laws of thought was the same algebra that describes a network of relay switches — a claim Claude Shannon published the following year as A Symbolic Analysis of Relay and Switching Circuits (Transactions of the AIEE 57(12), 713–723, 1938). That single observation is why a truth table, a Karnaugh map and a circuit diagram are three views of one object, and it is the reason every tool on this site can hand its input to every other.