Machine instructions, referred to herein as a long Convert from Zoned instruction (CDZT) and extended Convert from Zoned instruction (CXZT), are provided that read EBCDIC or ASCII data from memory, convert it to the appropriate decimal floating point format, and write it to a target floating point register or floating point register pair. Further, machine instructions, referred to herein as a long Convert to Zoned instruction (CZDT) and extended Convert to Zoned instruction (CZXT), are provided that convert a decimal floating point (DFP) operand in a source floating point register or floating point register pair to EBCDIC or ASCII data and store it to a target memory location.