In a computer system the instruction decoding unit for translating program instructions to microcode instructions operates dynamically. Thus the unit receives state signals indicating the state of the computer, such as a trace enabling signal, influencing the translation process in the instruction decoding unit. These state signals are added to the operation code of the program instruction to be decoded, the operation code of the program instruction thus being extended and used as input to a translating table, the extended operation code of the program instruction being taken as an address of a field in the table. The addresses and thus the contents of the fields addressed for the same operation code of a program instruction can then be different for different values of the state signals. Thus generally, the state signals cause the instruction decoder to change its translating algorithm so that the decoder can decode an operation code differently depending on the state which the signals adopt. The dynamic decoding can for a trace enabling signal be used for switching on and off a trace function. In the normal case, when tracing is not desired, no microinstructions supporting the trace function have to executed and thereby the performance and in particular the speed of the computer system will be increased.