We propose a biological computation paradigm based on parallel computing across cellular consortia. Parallel computation requires more data intensive communication channels, which is not possible with diffusible small molecules as done before. We use DNA as signalling molecule, which is packaged into a phagemid. We have developed a genetic platform relying on phagemid particles and regulatory circuits based on CRISPR single guide RNAs (sgRNAs) to encode logic operations in bacterial populations. This relies on a carefully fine-tuned system of orthogonal sgRNAs, dCas9, inteins, split T7 RNA polymerase, M13 phagemid and fluorescent reporters. Boolean functions are implemented by decomposing them into elementary logic gates encoded in different cells, creating consortia of bacterial strains. Parallel computing offers distinct advantages of division of labour, insulation, modularity, scalability, diversity, and fault tolerance. Our computing paradigm is demonstrated by implementing in live bacteria an algorithm for playing the game of Tic-Tac-Toe. This system is composed of 8 cell types that report user moves through a red fluorescence signal, and another 25 cell types that process user moves and respond to indicate the counter-move of the bacterial automaton through a green fluorescence signal. Since we use orthogonal genetic parts our system can be generalised to other organisms, including higher eukaryotes.