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We describe a magnetic nanofabric, which may provide a route to building reconfigurable spin-based logic circuits compatible with conventional electron-based devices. A distinctive feature of magnetic nanofabric is that a bit of information is encoded into the phase of the spin wave signal. This makes it possible to transmit information without the use of electric current and to utilize wave interference for useful logic functionality. The basic elements include voltage-to-spin-wave and wave-to-voltage converters, spin waveguides, a spin wave modulator, and a magnetoelectric cell. We illustrate the performance of the basic elements by experimental data and the results of numerical modeling. The combination of the basic elements leads us to construct magnetic circuits for NOT and majority logic gates. Logic gates such as AND, OR, NAND, and NOR are shown as the combination of NOT and reconfigurable majority gates. Examples of computational architectures such as a multibit processor and a cellular nonlinear network are described. The main advantage of the proposed magnetic nanofabric is its ability to realize logic gates with fewer devices than in CMOS-based circuits. Potentially, the area of the elementary reconfigurable majority gate can be scaled down to 0.1 mum2. We also discuss the disadvantages and limitations of the magnetic nanofabric.