Truth table
A tabular method for evaluating logical expressions.
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments. It provides a graphical representation of a truth function, showing for each combination of input values the result of a logical operation. Truth tables are fundamental in logic, digital electronics, and computer science for specifying and analyzing Boolean functions.
- field
- Logic, Boolean algebra, digital electronics
- known_for
- Graphical representation of truth functions; used to show logical validity and prove equivalences
Lore & Background
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Reader's Guide
Truth tables are a simple and straightforward way to encode Boolean functions, with one column for each input variable and a final column for the result. Each row represents a possible configuration of inputs. They can be used to prove logical equivalences, such as that p → q is equivalent to ¬p ∨ q. In digital logic, truth tables specify the function of hardware look-up tables (LUTs); for an n-input LUT, the table has 2^n rows. Truth table values can be encoded as integer bits in electronic design automation software. However, due to exponential growth in size as inputs increase, truth tables are not suitable for functions with many inputs; other representations like text equations and binary decision diagrams are more memory efficient. In digital electronics, truth tables can reduce basic Boolean operations to simple input-output correlations, as in half-adders and full-adders.
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