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We study the magnetic and thermodynamic properties of a spin- 1 ∕ 2 Ising system containing three layers, each of which is composed exclusively of one out of two possible types of atoms, A or B. The A-A and B-B bonds are ferromagnetic while the A-B bonds are antiferromagnetic. The study is performed through Monte Carlo simulations using the Wolff algorithm and the data are analyzed with the aid of the multiple-histogram reweighting technique and finite-size scaling tools. We verify the occurrence of a compensation phenomenon and obtain the compensation and critical temperatures of the model as functions of the Hamiltonian parameters. The influence of each parameter on the overall behavior of the system is discussed in detail and we present our results in the form of phase diagrams dividing the parameter space in regions where the compensation phenomenon is present or absent. Our results may provide invaluable information for experimentalists seeking to build materials with desired characteristics. • Ferrimagnetic spin-1/2 Ising trilayer is studied. • Each layer can only have atoms of one out of two types (A or B). • Only A-B couplings are antiferromagnetic. • Magnetic properties of the system are studied through Monte Carlo simulations. • Compensation phenomenon is found and phase diagrams are obtained. [ABSTRACT FROM AUTHOR]