A sort-and-delay time-to-digital converter (TDC) is provided, made up of a plurality of serially connected sort-and-delay circuits. Each sort-and-delay circuit accepts a time-differential input signal with a first edge separated from a second edge by an input duration of time. The first and second edges are selectively routed as a time-differential output signal with a delayed edge separated from a trailing edge by an output duration of time representing a compression of the input duration of time. Each sort-and-delay circuit also supplies a TDC coded bit (e.g., Gray code) indicating the order in which the first and second edges are routed as leading and trailing edges. The TDC outputs a digital output signal representing the initial input duration of time associated with the initial time-differential input signal received by the initial sort-and-delay circuit. Associated TDC, sort-and-delay, and time amplification methods are also provided.