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Truth Table

A systematic table listing all possible input combinations for a Boolean function and the corresponding output value, defining the function's behavior.
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The statement of the theorem

Let f:{0,1}n→{0,1}f: \{0, 1\}^n \to \{0, 1\} be a Boolean function mapping an nn-bit input vector x=(x1,…,xn)\mathbf{x} = (x_1, \dots, x_n) to a single output bit. The truth table is a systematic enumeration of the 2n2^n possible input assignments xi\mathbf{x}_i (where ii ranges from 00 to 2n−12^n-1) and the corresponding output value f(xi)f(\mathbf{x}_i), thereby defining the function's complete behavior: f(x)=∑i=02n−1f(xi)⋅Minterm(xi)f(\mathbf{x}) = \sum_{i=0}^{2^n-1} f(\mathbf{x}_i) \cdot \text{Minterm}(\mathbf{x}_i).