---
title: "Processor types and revenue loss"
subject: "Embedded System"
chapter: 1
key: "semester_6/embedded_system:spp-gpp-asp-revenue-loss"
source: https://www.bctengineer.com/q/semester_6/embedded_system/spp-gpp-asp-revenue-loss
site: BCT Engineering
---

# Processor types and revenue loss

Embedded System · Chapter 1: Introduction to Embedded System

- Asked in: 2070 Bhadra, 2+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/embedded_system/spp-gpp-asp-revenue-loss
- Whole chapter: https://www.bctengineer.com/md/semester_6/embedded_system/chapter-1

## Question

Differentiate between single-purpose processors, general-purpose processors, and application-specific processors. Using the simplified revenue model, derive the percentage revenue loss equation for any rise angle, rather than just for 45 degrees.

## Short answer

Single-purpose processors are custom hardware for one program, offering highest performance and lowest power but no flexibility; general-purpose processors run any program; application-specific processors are programmable but optimized for a domain. Revenue loss for a delayed product is D(3W−D)/(2W²) × 100%, independent of rise angle.

## Answer

#### Processor types
| Point | Single-purpose processor (SPP) | General-purpose processor (GPP) | Application-specific processor (ASIP) |
|---|---|---|---|
| Function | Performs exactly one program (custom digital circuit) | Runs any program (microprocessor) | Optimised for a class of applications (DSP, microcontroller) |
| Design | Custom datapath + FSM; no program memory | Standard datapath, program memory, generic ALU | Programmable, with special datapath/instructions for the domain |
| Performance and power | Fastest, lowest power, small | Moderate, higher power | Good for its domain |
| Flexibility | None | Highest | Medium |
| NRE / unit cost | High NRE, low unit cost for large volume | Low NRE, higher unit cost | Medium |
| Time-to-market | Long | Short | Medium |
| Example | Fibonacci hardware, JPEG codec | Intel/ARM CPU | DSP, microcontroller, network processor |

#### Percentage revenue loss (simplified model)
Assume a market window of total length 2W with peak revenue at time W. The product's revenue rises linearly with rise angle θ and falls to zero at 2W.
- On-time product: triangle, base 2W, peak height W·tanθ, area = ½ × 2W × W·tanθ = W²·tanθ.
- Product delayed by D: starts at D, peak at W with height (W − D)·tanθ (same slope), ends at 2W. Area = ½ × (2W − D) × (W − D)·tanθ.

Loss = (on-time area − delayed area) / on-time area:
```text
Loss = 1 - (2W - D)(W - D) / (2W²)
     = (2W² - (2W² - 3WD + D²)) / (2W²)
     = D(3W - D) / (2W²)
```
**Answer: percentage revenue loss = D(3W − D) / (2W²) × 100 %.** tanθ appears in both areas and cancels, so the loss is the same for any rise angle, not just 45° (for 45°, tanθ = 1 and the heights equal W and W − D). Example: W = 26 weeks, D = 4 weeks gives 4(78 − 4)/(2 × 676) = 21.9 %.

## Check yourself

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

1. Which describes a single-purpose processor?
   A. Runs any program, highest flexibility
   B. Executes exactly one program in a custom circuit, fastest and lowest power but high NRE
   C. Medium flexibility with DSP instructions
   D. Needs large program memory
   Answer: B. An SPP is a custom datapath + FSM with no program memory: fast, low power, high NRE. (Key point: SPP characteristics)

2. Which is an ASIP example?
   A. Intel Core
   B. Fibonacci hardware
   C. DSP or microcontroller
   D. JPEG codec circuit
   Answer: C. ASIPs such as DSPs and microcontrollers are optimised for a class of applications. (Key point: GPP vs ASIP)

3. In the revenue model, the delayed product (delay D) has area:
   A. 1/2 x 2W x W tan(theta)
   B. W^2 tan(theta)
   C. D x W
   D. 1/2 x (2W - D) x (W - D) x tan(theta)
   Answer: D. Delayed triangle base is 2W - D and peak height (W - D) tan(theta); the on-time area is W^2 tan(theta). (Key point: Delayed-product area)

4. What is the percentage revenue loss for delay D and half-window W?
   A. D(3W - D)/(2W^2) x 100%
   B. D/W x 100%
   C. D^2/(2W^2) x 100%
   D. (W - D)/W x 100%
   Answer: A. Loss = 1 - (2W - D)(W - D)/(2W^2) = D(3W - D)/(2W^2). (Key point: Revenue loss formula)

5. Why is the loss the same for any rise angle?
   A. The angle is always 45 degrees
   B. tan(theta) cancels because it appears in both areas
   C. Delay D depends on angle
   D. W depends on angle
   Answer: B. Both areas contain tan(theta), so it cancels in the ratio. (Key point: Rise angle independence)

## Related in Embedded System

- [ASIP versus general purpose processor](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aasip-vs-gpp) — Embedded System, chapter 2
- [Optimization of single-purpose processors](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aspp-optimization) — Embedded System, chapter 2, asked 6×
- [Fibonacci single-purpose processor](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aspp-fibonacci) — Embedded System, chapter 2, asked 2×
- [Single-purpose processor for power](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aspp-power) — Embedded System, chapter 2, asked 2×
- [Factorial single-purpose processor](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aspp-factorial) — Embedded System, chapter 2
- [Design LCM single-purpose processor](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Aspp-lcm-datapath-controller) — Embedded System, chapter 2

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