---
title: "Space switch design with connection memory"
subject: "Telecommunications"
chapter: 4
key: "semester_8/telecommunications:space-switch-connection-memory"
source: https://www.bctengineer.com/q/semester_8/telecommunications/space-switch-connection-memory
site: BCT Engineering
---

# Space switch design with connection memory

Telecommunications · Chapter 4: Digital Switching

- Asked in: 2074 Asoj, 5+1+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/telecommunications/space-switch-connection-memory
- Whole chapter: https://www.bctengineer.com/md/semester_8/telecommunications/chapter-4

## Question

Design space switch with following input trunks, output trunks and connection memory. How many virtual paths are required in this switch? Write down each output channels of output trunks in time t0 to t3, with respect to decode logic.

Input trunks and their channels:

| Input trunk | I1 | I2 | I3 | I4 | I5 |
|---|---|---|---|---|---|
| Channels | A4 A3 A2 A1 | B4 B3 B2 B1 | C4 C3 C2 C1 | D4 D3 D2 D1 | E4 E3 E2 E1 |

Connection memory (5 bits per output trunk, feeding the decode logic):

| Time | O1 | O2 | O3 | O4 |
|---|---|---|---|---|
| t0 | 0 0 1 0 0 | 0 1 0 0 0 | 1 0 0 0 0 | 0 0 0 1 0 |
| t1 | 1 0 0 0 0 | 0 0 1 0 0 | 0 1 0 0 0 | 0 0 0 0 1 |
| t2 | 0 0 0 0 1 | 0 0 0 1 0 | 0 0 1 0 0 | 1 0 0 0 0 |
| t3 | 0 1 0 0 0 | 1 0 0 0 0 | 0 0 0 1 0 | 0 0 1 0 0 |

## Short answer

Design a 5x4 time-multiplexed space switch with one-hot 5-bit connection memory per output column. It has 80 possible virtual paths; the given memory sets up 16 virtual paths per frame. Outputs: O1 B4 E3 A2 C1, O2 A4 D3 C2 B1, O3 D4 C3 B2 A1, O4 C4 A3 E2 D1.

## Answer

**Assumptions:** each 5-bit connection-memory word is a one-hot select for the decode logic, with the bits in the order I1 I2 I3 I4 I5 (left to right). Channel 1 of each trunk arrives first (in $t_0$), channel 2 in $t_1$, and so on, as the channels are written right-to-left ("A4 A3 A2 A1").

#### Design of the space switch
This is a **time-multiplexed space switch** with 5 input trunks (rows) and 4 output trunks (columns), with 4 time slots per frame.

```text
          O1    O2    O3    O4
 I1 ----- x --- x --- x --- x
 I2 ----- x --- x --- x --- x
 I3 ----- x --- x --- x --- x
 I4 ----- x --- x --- x --- x
 I5 ----- x --- x --- x --- x
          |     |     |     |
       [CM1] [CM2] [CM3] [CM4]
       decode logic per column
       (4 words x 5 bits each)
```
- Each output column has its own control memory with 4 words (one per time slot) of 5 bits.
- In each time slot the decoder of a column closes the one crosspoint whose bit is 1, connecting that input trunk to the output trunk for that slot only.
- The switch has $5 \times 4 = 20$ crosspoints and $4 \times 4 = 16$ control words.

#### Number of virtual paths
Each crosspoint can carry a different connection in each time slot:
$$
\text{virtual paths} = 5 \times 4 \times 4 = 80
$$
In each time slot at most 4 connections exist (one per output), so in one frame at most $4 \times 4 = 16$ of these paths can be in use. The given connection memory sets up all 16, so the switch must provide **16 virtual paths** per frame (out of 80 possible).

#### Decoding the connection memory

| Time | O1 | O2 | O3 | O4 |
|---|---|---|---|---|
| $t_0$ | 00100 → I3 | 01000 → I2 | 10000 → I1 | 00010 → I4 |
| $t_1$ | 10000 → I1 | 00100 → I3 | 01000 → I2 | 00001 → I5 |
| $t_2$ | 00001 → I5 | 00010 → I4 | 00100 → I3 | 10000 → I1 |
| $t_3$ | 01000 → I2 | 10000 → I1 | 00010 → I4 | 00100 → I3 |

#### Output channels in $t_0$ to $t_3$

| Time | O1 | O2 | O3 | O4 |
|---|---|---|---|---|
| $t_0$ | C1 | B1 | A1 | D1 |
| $t_1$ | A2 | C2 | B2 | E2 |
| $t_2$ | E3 | D3 | C3 | A3 |
| $t_3$ | B4 | A4 | D4 | C4 |

Written in the same style as the input trunks (latest on the left):
- O1: B4 E3 A2 C1
- O2: A4 D3 C2 B1
- O3: D4 C3 B2 A1
- O4: C4 A3 E2 D1

A space switch does not change the time slot of a sample: channel $m$ always leaves in time slot $t_{m-1}$. Changing slots needs a time switch, which is why practical exchanges use TST.

## Check yourself

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

1. How many virtual paths does the 5-input, 4-output space switch with 4 time slots provide?
   A. 20
   B. 16
   C. 80
   D. 9
   Answer: C. Each of the 5 x 4 = 20 crosspoints can carry a different connection in each of 4 slots, so 5 x 4 x 4 = 80. (Key point: Virtual paths)

2. In the connection memory, the word 00100 for O1 at t0 selects which input trunk (bits in order I1 to I5)?
   A. I1
   B. I2
   C. I3
   D. I5
   Answer: C. The third bit is 1, so the decoder closes the crosspoint for I3. (Key point: Decoding one-hot words)

3. At t1, O3 has word 01000 (I2). Which output channel appears on O3 at t1?
   A. B1
   B. B2
   C. C2
   D. A2
   Answer: B. I2 carries trunk B, and a space switch keeps the slot, so slot t1 is channel 2: B2. (Key point: Slot is preserved)

4. Why does channel m always leave in time slot t(m-1) in this switch?
   A. The decode logic delays samples by one slot
   B. A space switch changes the highway but not the time slot
   C. The connection memory stores slot numbers
   D. Output trunks are slower than input trunks
   Answer: B. Only a time switch can change slots; a space switch just closes crosspoints during each slot. (Key point: Space switch limitation)

## Related in Telecommunications

- [Time division switching and space switch](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-division-space-switch) — Telecommunications, chapter 4
- [Time and space switch drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-space-switch-drawbacks) — Telecommunications, chapter 4
- [Space switch and two-stage S-T drawbacks](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-two-stage-st) — Telecommunications, chapter 4
- [Space switch and why TST is used](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-switch-why-tst) — Telecommunications, chapter 4
- [Time switch and two-stage T-S network](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Atime-switch-two-stage-ts) — Telecommunications, chapter 4
- [Space and time switches; STS vs TST](https://www.bctengineer.com/question.md?key=semester_8%2Ftelecommunications%3Aspace-time-switch-sts-tst) — Telecommunications, chapter 4

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