Position measurement system comprising a number of 2^χ position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4), where x is a positive integer, and a position computer (20, 120), wherein the position computer (20, 120) comprises a system interface (24, 124), a serial arithmetic unit (25, 125) and a computer interface (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) for each position sensor (10.1, 10.2, 100.1, 100.2, 100.3, 100.4), wherein • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are connected, via data transmission channels (14.1, 14.2, 114.1, 114.2, 114.3, 114.4), to corresponding device interfaces (12.1, 12.2, 112.1, 112.2, 112.3, 112.4) of the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4) for the purpose of transmitting data, • the system interface (24, 124) can be connected to a control device via an external data transmission channel and is configured to forward external position request commands, which arrive from the control device, to the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) and to serially output averaged position values to the control device, • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are configured, as a result of an external position request command arriving, to in turn send position request commands (RA, RB, RC, RD) to the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4), • the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4) are configured, as a result of a position request command (RA, RB, RC, RD) arriving, to generate a position value (A, B, C, D) with a word length of n bits and to serially output it to the position computer (20, 120) via the device interface (12.1, 12.2, 112.1, 112.2, 112.3, 112.4), • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are further configured to receive the position value (A, B, C, D) and to serially output it to the serial arithmetic unit (25, 125), and • the serial arithmetic unit (25, 125) is configured to serially calculate the averaged position value from the position values (A, B, C, D) and to serially output it to the system interface (24, 124) for output to the control device. • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are connected, via data transmission channels (14.1, 14.2, 114.1, 114.2, 114.3, 114.4), to corresponding device interfaces (12.1, 12.2, 112.1, 112.2, 112.3, 112.4) of the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4) for the purpose of transmitting data, • the system interface (24, 124) can be connected to a control device via an external data transmission channel and is configured to forward external position request commands, which arrive from the control device, to the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) and to serially output averaged position values to the control device, • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are configured, as a result of an external position request command arriving, to in turn send position request commands (RA, RB, RC, RD) to the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4), • the position sensors (10.1, 10.2, 100.1, 100.2, 100.3, 100.4) are configured, as a result of a position request command (RA, RB, RC, RD) arriving, to generate a position value (A, B, C, D) with a word length of n bits and to serially output it to the position computer (20, 120) via the device interface (12.1, 12.2, 112.1, 112.2, 112.3, 112.4), • the computer interfaces (22.1, 22.2, 122.1, 122.2, 122.3, 122.4) are further configured to receive the position value (A, B, C, D) and to serially output it to the serial arithmetic unit (25, 125), and • the serial arithmetic unit (25, 125) is configured to serially calculate the averaged position value from the position values (A, B, C, D) and to serially output it to the system interface (24, 124) for output to the control device.