Digital Logic Toolkit

Digital Logic Toolkit — Truth table generator

Source
https://digitallogictoolkit.com/truth-table/
Printed

P·P̄ — truth table

exam standardcontradiction: 0 on every row

Answer

2 rows, 0 true ()

Why this example is worth doing

The law of non-contradiction, in two rows. It is deliberately the shortest table on the site because it shows what a constant-false column looks like before you meet one accidentally in a real problem. The page makes the practical point that in synthesis a contradiction means a wire tied to ground and an entire cone of logic that can be deleted, and that a K-map with no 1s in it is not an error state the tool should refuse to draw.

Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.

How the answer is reached

Truth table

Truth table — columns #, P, P · P′
#PP · P′
000
110

Compare with

Open this example in the Truth table generator

The field arrives filled in with this example’s input.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • In a minterm index the first variable is the most significant bit, so over [A, B, C] minterm 5 is A·B̄·C.

Sources

  • Boole, An Investigation of the Laws of Thought (1854)
  • Shannon, “A Symbolic Analysis of Relay and Switching Circuits” (1938)