---
title: "PCM and analog-to-digital conversion"
subject: "Data Communication"
chapter: 5
key: "semester_5/data_communication:pcm-working"
source: https://www.bctengineer.com/q/semester_5/data_communication/pcm-working
site: BCT Engineering
---

# PCM and analog-to-digital conversion

Data Communication · Chapter 5: Data Encoding and Modulation

- Asked in: 2078 Kartik, 5 marks; 2076 Chaitra, 6 marks; 2071 Chaitra, 4 marks; 2068 Chaitra, 6 marks (asked 4 times)
- Video: [PCM - Analog to digital conversion](https://www.youtube.com/watch?v=HlGJ6xxbz8s) — Sunny Classroom
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/pcm-working
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-5

## Question

Explain the working of Pulse Code Modulation (PCM), i.e. the steps involved in converting an analog signal to a digital signal.

## Short answer

PCM converts analog to digital via sampling at ≥2fm, quantizing each sample to L=2ⁿ levels, and encoding each level as an n-bit binary word. For telephone voice, fs=8 kHz, n=8, giving 64 kbps.

## Answer

Pulse Code Modulation (PCM) converts an analog signal to a digital (binary) one. The steps are sampling, quantization and encoding.

```text
Analog  +---------+ +----------+ +---------+  bits
 input->| Sampler |->|Quantizer |->| Encoder |-> 0101 ...
        +---------+ +----------+ +---------+
        (low-pass filter first, fs >= 2 fm)
```

#### 1. Low-pass filtering
The input is limited to its highest frequency fm (4 kHz for telephone speech) to avoid aliasing.

#### 2. Sampling
The signal is measured at regular intervals Ts = 1/fs. By the **sampling theorem**, fs ≥ 2fm. Telephone speech uses fs = 8000 samples/s. The result is a PAM signal.

#### 3. Quantization
Each sample amplitude is rounded to the nearest of L discrete levels (L = 2ⁿ). The step size is Δ = (Vmax - Vmin)/L. The rounding error is the **quantization noise** (maximum ±Δ/2); more levels mean less noise. The SNR is about 6n + 1.8 dB for an n-bit uniform quantizer. Non-uniform quantization (companding, μ-law/A-law) improves weak signals.

#### 4. Encoding
Each quantized level is represented by an n-bit binary code word, for example 8 bits give 256 levels.

#### Bit rate
Bit rate = fs × n = 8000 × 8 = 64 kbps for one telephone voice channel (DS0).

#### Receiver
The decoder converts code words back to levels (D/A), and a low-pass filter reconstructs the analog signal.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What are the main steps of PCM?
   A. Modulation, detection, decoding
   B. Sampling, quantization, encoding
   C. Filtering, mixing, amplifying
   D. Sampling, multiplexing, scrambling
   Answer: B. Preceded by low-pass filtering. (Key point: PCM steps)

2. Minimum sampling rate for fm = 4 kHz:
   A. 4000 samples/s
   B. 8000 samples/s
   C. 2000 samples/s
   D. 16000 samples/s
   Answer: B. fs >= 2fm. (Key point: Sampling theorem)

3. What does more levels do?
   A. Increases noise
   B. Reduces bit rate
   C. Reduces quantization noise
   D. Removes aliasing
   Answer: C. Step size shrinks. (Key point: Quantization)

4. Bit rate of one voice channel with 8 bits and fs = 8000:
   A. 8 kbps
   B. 32 kbps
   C. 128 kbps
   D. 64 kbps
   Answer: D. fs x n = 8000 x 8. (Key point: Bit rate)

## Related in Data Communication

- [Define analog and digital signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aanalog-digital-signal-define) — Data Communication, chapter 1
- [Advantages of digital over analog systems](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adigital-vs-analog-advantages) — Data Communication, chapter 1, asked 5×
- [Compare analog and digital communication](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adigital-vs-analog-comparison) — Data Communication, chapter 1, asked 4×
- [Short note: Analog vs digital mux hierarchy](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aanalog-vs-digital-mux-hierarchy) — Data Communication, chapter 6
- [Digital vs analog spread spectrum](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aspread-spectrum-digital-vs-analog) — Data Communication, chapter 6
- [Data representation; analog vs digital system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adata-representation-analog-digital) — Data Communication, chapter 1

## Related in other subjects

- [Short note: Digital to analog conversion](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Ashort-note-dac) — Digital Control System, chapter 1
- [Digital vs analog modulation; GMSK](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adigital-modulation-gmsk) — Wireless Communication, chapter 4
- [Analog vs digital signal; convert A2.64H](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aanalog-digital-convert-a264h) — Digital Logic, chapter 1
- [Digital signal and Gray code](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Adigital-signal-gray-code) — Digital Logic, chapter 1, asked 2×