All tools › Counting and logic

Truth table

A column for every sub-expression, and the normal forms

It runs entirely in this browser tab: what you type is never uploaded, and the arithmetic is exact — nothing here was ever a floating-point number.

Settings

Is what I type uploaded anywhere?: No. The whole application is carried as WebAssembly and runs on your own device. There is no server to send anything to, and none of these tools makes a network request while it works.
Why does it matter that there is no floating point?: Because these tools show their working. In floating point an elimination produces rows with 0.0000000000000002 where a zero belongs, and every step after it is decided by a tolerance somebody picked. In fractions the zero is a zero: the rank is a count, a determinant of a matrix of thirds is a third, and a matrix times its inverse is exactly the identity.
Can I use it in an exam or for homework?: That is between you and whoever set the work. What these give you is the method as well as the answer, which is usually what is being marked: the rule at each step, the substitution written out, the intermediate matrices, the table of values.
Why does a tool sometimes refuse instead of answering?: Because the honest answer is sometimes that there is none. An integral with no elementary antiderivative, a matrix with no inverse, a bisection over an interval with no sign change, a logarithm of zero: each is a fact rather than a failure, and a plausible number in its place would be worse than the refusal.

Combinations and permutations
Two questions decide the formula; the answer is exact

Binomial expansion
Every term, or just the one the question asks for

Pascal's triangle
The rows, the row sums, and the patterns hiding in it

Sequences and series
The nth term, the sum, and whether an infinite one converges

Set operations
Two pasted lists compared, with the counts in a Venn diagram

Boolean minimiser
Quine–McCluskey and a Karnaugh map, with the implicant table