Up-counter driving a 4-bit DAC: “When the inputs of a 4-bit D/A converter are driven by a binary up-counter, the analog output looks like an upward sloping line.” Evaluate this description.

Introduction / Context:A binary up-counter feeding a DAC is the basis of a staircase generator. Many texts informally say it “ramps up,” but the precise shape at the DAC output is key for understanding quantization effects and reconstruction filtering.

Given Data / Assumptions:

• 4-bit DAC, ideal behavior.
• Binary up-counter increments by 1 code per tick.
• No post-DAC low-pass smoothing unless stated.

Concept / Approach:The DAC maps each successive code to a discrete analog level separated by one LSB. As the counter increments, the output steps upward by fixed increments, forming a staircase, not a continuous sloped line. A continuous ramp can be approximated only after low-pass filtering (reconstruction), which smooths the steps by integrating high-frequency components from the sampling process.

Step-by-Step Solution:

Verification / Alternative check:Oscilloscope traces of DAC outputs driven by counters show step-and-hold behavior. Applying an RC or active low-pass can make the envelope look like a ramp, but the raw output remains quantized steps.

Why Other Options Are Wrong:

• Correct: Ignores quantized nature of DAC output.
• Only true after heavy filtering: That caveat is accurate, but the stem did not include it; as written, the claim is false.
• Ambiguous: Update rate does not change the stepped nature without filtering.

Common Pitfalls:Equating “monotonic increasing” with “line”; forgetting LSB granularity; assuming infinite update rate eliminates steps (it does not).

Final Answer:Incorrect