1. A bus interface circuit for coherently transferring digital signals as words of a specified number of bits formatted in messages with each message having a specified maximum number of words between a signal processor and an asynchronous serial data bus, comprising: remote terminal interface (RTI) means, responsive to incoming digital signals in serial form from the serial data bus for transferring said incoming serial signals in parallel form, and responsive to outgoing digital signals in parallel form from the signal processor for transferring said outgoing parallel signals in serial form to the serial data bus; wraparound receive memory means, responsive to said incoming serial signals in parallel form from said RTI for sequentially storing received messages at successive memory addresses starting at the beginning of said wraparound memory and then continuing regardless of message number until the end of said wraparound memory is reached and then continuing sequential storing at the beginning again of said wraparound memory, said wraparound memory providing read access to stored words to the signal processor; transmit memory means, having its memory addresses organized in predefined message blocks with each block having a selected number of word storage addresses greater than the specified maximum number in a message each block for storing more than one message, each block organized for utilization as a separate wraparound transmit memory responsive to said outgoing parallel signals from the signal processor for sequentially storing message words at successive memory addresses starting at the beginning of a wraparound transmit memory block and then continuing until the end of said block is reached and then continuing sequential storing at the beginning again of said block, read access to each of said blocks to said RTI being confined to a signal processor specified completed message in the block; and terminal controller (TC) means, responsive to said incoming serial signals in parallel form from said RTI for providing start and stop addresses of complete and valid messages to the signal processor for algorithmically preventing signal processor read access to an individual message stored in wraparound receive memory until said individual message has been entirely and correctly received, said TC responsive to said outgoing signals in parallel form for providing to said RTI read access to said transmit memory but only to the signal process specified message in a block and for algorithmically preventing signal processor write access to the latest message in an individual block in said transmit memory if said RTI is read accessing said latest message and for otherwise being responsive to the storing of a word of a new message by said signal processor for transmission in said individual block and preventing RTI read access to said new message until said first word for transmission is stored by said signal processor in said individual block.