---
title: "Rotary dial dialing time calculation"
subject: "Telecommunications"
chapter: 1
key: "semester_8/telecommunications:rotary-dial-time-calculation"
source: https://www.bctengineer.com/q/semester_8/telecommunications/rotary-dial-time-calculation
site: BCT Engineering
---

# Rotary dial dialing time calculation

Telecommunications · Chapter 1: Telecommunication Networks

- Asked in: 2079 Bhadra, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/rotary-dial-time-calculation
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-1

## Question

Calculate the time required to dial the number 011-91-44-414630 using a rotary dial telephone. Assume the subscriber takes 600 milliseconds on average to rotate the dial for a single digit; the pulse rate is 10 pulses per second with a 10% tolerance, the inter-digit gap is 200 milliseconds, and the duty ratio of a pulse is 33%.

## Short answer

Total time = rotation time (13 digits × 600 ms = 7800 ms) + pulse time (58 pulses × 100 ms = 5800 ms) + inter-digit gaps (12 × 200 ms = 2400 ms) = 16.0 s at nominal 10 pps. Worst case (9 pps, period 111.1 ms) total = 16.64 s.

## Answer

The total time = (dial rotation time for every digit) + (pulse time for every digit) + (inter-digit gaps). The 33% duty ratio only fixes how each pulse period is split into make (33%) and break (67%); it does not change the pulse period.

**Digits and pulses** (number 0119144414630, 13 digits; digit 0 gives 10 pulses):

| Digit | 0 | 1 | 1 | 9 | 1 | 4 | 4 | 4 | 1 | 4 | 6 | 3 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pulses | 10 | 1 | 1 | 9 | 1 | 4 | 4 | 4 | 1 | 4 | 6 | 3 | 10 |

Total pulses $= 58$.

**Nominal rate (10 pps):** pulse period $T = 1/10 = 100$ ms (make 33.3 ms, break 66.7 ms).
$$
\begin{aligned}
t &= 13 \times 600 + 58 \times 100 + 12 \times 200 \\
&= 7800 + 5800 + 2400 \\
&= 16000\ \text{ms} = 16.0\ \text{s}
\end{aligned}
$$

**Worst case (slowest rate, 10% tolerance → 9 pps):** $T = 1/9 = 111.1$ ms.
$$
\begin{aligned}
t_{max} &= 7800 + 58 \times 111.1 + 2400 \\
&= 7800 + 6444.4 + 2400 = 16644.4\ \text{ms}
\end{aligned}
$$

(At the fastest rate, 11 pps, $T = 90.9$ ms and $t_{min} = 15472.7$ ms.)

**Answer:** about **16.0 s** at the nominal 10 pps; up to **16.64 s** in the worst case (9 pps). (12 inter-digit gaps are counted, between the 13 digits.)

## Check yourself

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

1. How many pulses are in 011-91-44-414630?
   A. 48
   B. 58
   C. 13
   D. 60
   Answer: B. Digits 0,1,1,9,1,4,4,4,1,4,6,3,0 with 0 as 10 pulses give 58. (Key point: Total pulses)

2. How many inter-digit gaps are counted for the 13 digits?
   A. 13
   B. 14
   C. 12
   D. 11
   Answer: C. Gaps lie between digits, so 13 digits give 12. (Key point: Gap count)

3. What is the total time at nominal 10 pps?
   A. 13.0 s
   B. 18.4 s
   C. 16.64 s
   D. 16.0 s (7800 + 5800 + 2400 ms)
   Answer: D. 13 x 600 + 58 x 100 + 12 x 200 = 16000 ms. (Key point: Nominal time)

4. What is the role of the 33% duty ratio?
   A. It only splits each pulse period into make and break; it does not change the period
   B. It reduces the pulse period to 33 ms
   C. It adds 33% to the total time
   D. It sets the inter-digit gap
   Answer: A. The period stays 1/rate. (Key point: Duty ratio)

## Related in Telecommunications

- [Pulse dialing waveform for number 401](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apulse-dialing-waveform-401) — Telecommunications, chapter 1
- [Role of exchange and rotary dial operation](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aexchange-role-rotary-dial) — Telecommunications, chapter 1
- [DTMF vs pulse dialing and DTMF design](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adtmf-vs-pulse-design) — Telecommunications, chapter 1, asked 2×
- [Subscriber loop or line plant](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Asubscriber-loop-line-plant) — Telecommunications, chapter 1
- [Device holding time and calls per hour](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adevice-holding-time-calls) — Telecommunications, chapter 6
- [Traffic numerical: 600 calls, 40 lost, 120 s](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Agos-600-calls-120s) — Telecommunications, chapter 6, asked 5×

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