Statements (A), (B) and (C) describe how a DSO works and what that buys; (D) claims a cost saving that does not exist — option 4.

(A), (B) and (C) are one process in three steps. The input is sampled and converted by a fast ADC, the samples are written into memory, and the display is then reconstructed from memory whenever it is wanted. Because the waveform exists as numbers rather than as a glowing trace, it can be held indefinitely, examined at leisure, scrolled through, expanded, measured automatically, or transferred to a computer.

The pre-trigger capability deserves emphasis, because an analogue scope simply cannot do it. The DSO writes into a circular buffer all the time, so when the trigger arrives the memory already contains what happened before it. Seeing the conditions that led up to a fault is often the whole reason for using the instrument.

(D) is false, and its reasoning is backwards. A digital storage oscilloscope contains everything an analogue instrument needs for its display plus a high-speed ADC, fast acquisition memory, a processor and firmware. Adding hardware cannot reduce cost. Historically DSOs were considerably more expensive than analogue scopes of the same bandwidth, and they displaced them because of capability, not price — although mass production has since made low-end DSOs cheap in absolute terms.

What limits a DSO is worth knowing alongside its advantages: the sampling rate must satisfy Nyquist, and a real instrument needs several samples per cycle rather than the theoretical two, so the usable bandwidth is well below half the sample rate. Undersampling produces aliasing — a false low-frequency waveform that looks entirely plausible. An analogue scope simply shows a dimming trace as it runs out of bandwidth, which is a more honest failure.

Hence, the correct statements are (A), (B) and (C).