Error detection code generation circuits of semiconductor devices, memory controllers including the same and semiconductor memory devices including the same

An error detection code generation circuit of a semiconductor device includes a first cyclic redundancy check (CRC) engine, a second CRC engine and an output selection engine. The first CRC engine generates first error detection code bits using a first generation matrix, based on a plurality of first unit data and first DBI bits in response to a mode signal. The second CRC engine generates second error detection code bits using a second generation matrix, based on a plurality second unit data and second DBI bits, in response to the mode signal. The output selection engine generates final error detection code bits by merging the first error detection code bits and the second error detection code bits in response to the mode signal. The first generation matrix is the same as the second generation matrix.