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We present a mathematical definition of hardware description language (HDL) that admits a semantics-preserving translation to a subset of VHDL. Our HDL includes the basic VHDL propagation delay mechanisms and gate-level circuit descriptions. We also develop formal procedures for deriving and verifying concise behavioral specifications of combinational and sequential devices. The HDL and the specification procedures have been formally encoded in the computational logic of Boyer and Moore, which provides a LISP implementation as well as a facility for mechanical proof-checking. As an application, we design, specify, and verify a circuit that achieves asynchronous communication by means of the biphase mark protocol.