---
title: "Discrete vs continuous signal; convert (25.25)₁₀"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:discrete-continuous-convert-25-25"
source: https://www.bctengineer.com/q/semester_3/digital_logic/discrete-continuous-convert-25-25
site: BCT Engineering
---

# Discrete vs continuous signal; convert (25.25)₁₀

Digital Logic · Chapter 1: Introduction

- Asked in: 2081 Baisakh, 2+4 marks
- Video: [Continuous and Discrete Time Signals](https://www.youtube.com/watch?v=H4hk6N5vC1Q) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/discrete-continuous-convert-25-25
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Differentiate between discrete and continuous signal with necessary figures and example. Convert (25.25)₁₀ to binary and octal equivalent.

## Short answer

Continuous signals exist at all times with any amplitude; discrete signals are defined only at sampling instants. (25.25)₁₀ to binary: integer 11001, fraction .01 → 11001.01₂; to octal: integer 31, fraction .2 → 31.2₈.

## Answer

#### Discrete vs continuous signal
A **continuous (analog) signal** is defined at every instant of time and can take any value in a range. A **discrete-time signal** is defined only at specific (sampled) instants; if its values are also limited to fixed levels, it is a digital signal.

```text
 Continuous x(t)          Discrete x[n]
    __                       |  |
   /  \      /             | |  | |
  /    \    /              | |  | |  |
 /      \__/            ---+-+--+-+--+--- n
---------------- t         0 1  2 3  4
```

| Continuous signal | Discrete signal |
|---|---|
| Defined for all time $t$ | Defined only at $t = nT$ |
| Written $x(t)$ | Written $x[n]$ |
| Example: voice, temperature | Example: daily rainfall, sampled audio |
| Processed by analog circuits | Processed by digital systems |

#### Convert $(25.25)_{10}$ to binary
Integer: 25 → 25/2 = 12 r1, 12/2 = 6 r0, 6/2 = 3 r0, 3/2 = 1 r1, 1/2 = 0 r1 → $11001$.
Fraction: 0.25 × 2 = 0.5 → 0; 0.5 × 2 = 1.0 → 1 → $.01$.

**Answer: $(25.25)_{10} = (11001.01)_2$**

#### Convert $(25.25)_{10}$ to octal
Integer: 25 ÷ 8 = 3 r 1; 3 ÷ 8 = 0 r 3 → $31$.
Fraction: 0.25 × 8 = 2.0 → 2.
(Check by grouping binary: 011 001 . 010 → 3 1 . 2.)

**Answer: $(25.25)_{10} = (31.2)_8$**

## Check yourself

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

1. How does a discrete signal differ from a continuous one?
   A. It is defined only at sampled instants, t = nT
   B. It is defined at every instant
   C. It has no values
   D. It is always digital
   Answer: A. Continuous is x(t); discrete is x[n]. (Key point: Continuous vs discrete)

2. What is (25.25) decimal in binary?
   A. 10011.01
   B. 11001.01
   C. 11001.1
   D. 11010.01
   Answer: B. 25 = 11001, 0.25 = .01. (Key point: Binary)

3. What is (25.25) decimal in octal?
   A. 25.25
   B. 32.1
   C. 31.2
   D. 31.4
   Answer: C. 25/8 = 3 r 1 gives 31; 0.25 x 8 = 2. (Key point: Octal)

## Related in Digital Logic

- [Convert octal 623.77 to decimal, binary, hex](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-octal-623-77) — Digital Logic, chapter 1
- [Octal-to-binary encoder; A+B'C canonical form](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aoctal-binary-encoder-canonical) — Digital Logic, 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
- [Convert (125.25)₁₀ to binary](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-125-25-binary) — Digital Logic, chapter 1
- [Gray vs binary code, convert (10110)₂ to Gray](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-vs-binary-convert-10110) — Digital Logic, chapter 1
- [Convert 37.432 decimal to binary](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-37-432-binary) — Digital Logic, chapter 1

## Related in other subjects

- [Continuous vs discrete variables, return period formulae](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acontinuous-discrete-variables-return-period) — Engineering Hydrology, chapter 6
- [Discrete vs continuous attributes](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adiscrete-vs-continuous) — Data Mining, chapter 2
- [Continuous-time vs discrete-time signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-vs-dt-signals) — Signals and Systems, chapter 1, asked 3×
- [Discrete and continuous random variables](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Adiscrete-continuous-rv-mean-variance) — Probability and Statistics, chapter 2