--- title: "Switching functions and three-stage crosspoints" subject: "Telecommunications" chapter: 4 key: "semester_8/telecommunications:switching-functions-crosspoints-4x4" source: https://www.bctengineer.com/q/semester_8/telecommunications/switching-functions-crosspoints-4x4 site: BCT Engineering --- # Switching functions and three-stage crosspoints Telecommunications · Chapter 4: Digital Switching - Asked in: 2072 Chaitra, 3+5 marks - Video: [Switching Engineering - Cross-points and Number of Switches - Calculations](https://www.youtube.com/watch?v=Bbm3lKI7O5Y) — KINEMARC - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/telecommunications/switching-functions-crosspoints-4x4 - Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4 ## Question What are the basic switching functions? Calculate and draw, how many cross points are found in three stage switching system, whereas 3 stage array of 4 input lines and 4 second stages array. ## Short answer Basic switching functions: off-hook detection, digit reception/analysis, busy testing, path setup, alerting, supervision, signaling, charging. For 12 inlets (3 arrays of 4 inputs) and 4 middle arrays, total crosspoints = 3×(4×4) + 4×(3×3) + 3×(4×4) = 48+36+48 = 132. ## Answer #### Basic switching functions 1. **Attending:** detect a call request (off-hook) and identify the calling line. 2. **Information receiving:** send dial tone and receive the dialled digits. 3. **Information processing:** analyse the digits to find the called party and route. 4. **Busy testing:** check that the called line or a trunk is free. 5. **Interconnection:** set up a path through the switching network. 6. **Alerting:** ring the called party and send ring-back tone to the caller. 7. **Supervision:** detect answer and clear-down; release the path. 8. **Information sending:** send signals to other exchanges for outgoing calls. 9. **Charging:** record call details for billing. #### Crosspoints in the three-stage switch **Reading of the data:** 3 first-stage arrays with 4 input lines each, so $N = 3 \times 4 = 12$, $n = 4$; 4 second-stage arrays, $k = 4$. - Stage 1: 3 arrays of $4 \times 4$ - Stage 2: 4 arrays of $3 \times 3$ - Stage 3: 3 arrays of $4 \times 4$ ```text 4 in [4x4] \ / [4x4] 4 out 4 in [4x4] --> 4 x [3x3] --> [4x4] 4 out 4 in [4x4] / middle \ [4x4] 4 out (12 inputs) (12 outputs) each outer array has one link to each of the 4 middle arrays ``` $$ \begin{aligned} N_1 &= 3 \times (4 \times 4) = 48 \\ N_2 &= 4 \times (3 \times 3) = 36 \\ N_3 &= 3 \times (4 \times 4) = 48 \\ N_x &= 48 + 36 + 48 = 132 \end{aligned} $$ Check with the formula: $N_x = 2Nk + k(N/n)^2 = 2(12)(4) + 4(3)^2 = 96 + 36 = 132$. A single-stage $12 \times 12$ switch needs $12^2 = 144$ crosspoints, so the saving is 12 crosspoints. Since $k = 4 < 2n - 1 = 7$, the network is **blocking**; 7 middle arrays would make it strictly non-blocking. **Answer:** total crosspoints = **132**. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the alerting function? A. Ringing the called party and sending ring-back tone to the caller B. Identifying the calling line C. Releasing the path D. Counting digits Answer: A. Alerting rings the called party and gives ring-back tone. (Key point: Alerting) 2. What is done in information processing? A. Dial tone is sent B. Digits are analysed to find called party and route C. Billing records are made D. Ringing is applied Answer: B. The dialled digits are analysed to determine destination and route. (Key point: Information processing) 3. With 3 first-stage arrays of 4 inputs and 4 middle arrays, what are the middle array sizes? A. 4 x 4 B. 3 x 3 C. 12 x 12 D. 4 x 3 Answer: B. N/n = 3 first-stage arrays, so each middle array is 3 x 3. (Key point: Stage sizes) 4. Total crosspoints for this three-stage switch? A. 132 B. 144 C. 96 D. 36 Answer: A. 48 + 36 + 48 = 132 = 2(12)(4) + 4(3)^2. (Key point: Total crosspoints) ## Close variants set in other exams - [Crosspoints in three-stage switch (4 inputs, 5 arrays)](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Acrosspoints-4-input-5-second) — Telecommunications, chapter 4, asked 2× ## Related in Telecommunications - [PCM switching and three-stage crosspoints](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Apcm-switching-crosspoints-4x5) — Telecommunications, chapter 4 - [Crosspoints and three-stage switching](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Acrosspoint-switching-array) — Telecommunications, chapter 4 - [Digital exchange and three-stage crosspoints](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-exchange-crosspoints) — Telecommunications, chapter 4 - [TST vs STS and three-stage design](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atst-sts-design-crosspoints) — Telecommunications, chapter 4 - [Design 200×200 three-stage switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Athree-stage-200x200-clos) — Telecommunications, chapter 4 - [Digital switching system and its functions](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Adigital-switching-functions) — Telecommunications, chapter 4