What are the uses of truth table?

Answer 1

A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. Truth tables can be used to prove many other logical equivalences. Truth tables are also used to specify the function of hardware look-up tables (LUTs) in digital logic circuitry. For an n-input LUT, the truth table will have 2^nvalues (or rows in the above tabular format), completely specifying a boolean function for the LUT. By representing each boolean value as a bit in a binary number, truth table values can be efficiently encoded as integer values in electronic design automation (EDA) software. For example, a 32-bit integer can encode the truth table for a LUT with up to 5 inputs. Truth tables are a simple and straightforward way to encode boolean functions, however, given the exponential growth in size as the number of inputs increase, they are not suitable for functions with a large number of inputs. Other representations which are more memory efficient are text equations and binary decision diagrams.