Abstract: Algorithms and optical processor architectures for implementing a two-dimensional truth-table look-up processor are disclosed. An optical holographic medium stores the spectral expansion coefficients that map two-dimensional digital inputs of a binary truth-table into two-dimensional outputs of that binary truth table. Several algorithms are described using discrete orthogonal transforms such as one of the Walsh transforms (the Walsh-Hadamard transform, the Rademacher-Walsh transform, the Walsh-Kaczmarz transform) or the Haar transform. These transforms are used to find the corresponding spectral vectors and the corresponding boolean basis vector. The inner product multiplication of the spectral vector with the boolean basis vector yields the digital outputs of the binary truth-table. Another algorithm uses the Reed-Muller expansion which is a non-orthogonal transform. Various architectures of digital optic two-dimensional truth-table look-up processors are also disclosed.