1. A computer system interface adapter for connection between a host computer bus and an input/output SCSI bus for interconnecting a host computer to a SCSI peripheral device, said adapter comprising: an internal interface data bus; a main FIFO buffer coupled to said internal interface data bus; a first interface means comprising an input/output FIFO coupled to said SCSI bus and to said internal interface data bus; a second interface means coupled to said host computer bus and to said internal interface data bus; control means for causing data communicated between said SCSI bus and said first interface means to flow onto said internal interface data bus and to further flow from said internal interface data bus into said main FIFO buffer; data counter means for monitoring the quantity of data in said main FIFO buffer and for generating a numerical value, in real time, indicating the quantity of data stored in said main FIFO buffer; interrupt logic means responsive to said main FIFO buffer for generating an interrupt signal to said host computer bus to inform said host computer that said main FIFO buffer is full; and FIFO control means responsive to said numerical value generated by said data counter means for controlling transfers of data blocks to said main FIFO buffer from said input/output FIFO such that a variable block size is transmitted to said main FIFO buffer with each data transfer without overflowing said main FIFO buffer, said variable block size being limited to a maximum block size transmittable over said internal interface data bus.