In which waveform is logic 1 represented by a half-bit wide pulse and logic 0 by the absence of a pulse?

The correct choice is unipolar RZ (Return-to-Zero) waveform. In this type of signaling, logic 1 is represented by a pulse that lasts for half the duration of the bit period, while logic 0 is indicated by the absence of any pulse. This results in a clear distinction between the presence and absence of a signal.

Unipolar RZ is unique in that it relies solely on a single polarity for the signal, using a positive voltage to represent logic 1 and 0 volts for logic 0. The return-to-zero aspect implies that after sending a pulse for logic 1, the waveform returns to zero voltage for the rest of that bit period, clearly delineating the states.

The other options involve different signaling schemes. Manchester coding, for example, encodes both logic states with a transition in the middle of the bit period, which affects how pulses are represented. RZ-AMI and bipolar RZ also incorporate signaling features that differ from the straightforward representation in unipolar RZ. Thus, unipolar RZ accurately matches the description where logic 1 is represented by a half-bit wide pulse.