---
title: "Analog vs digital signal; convert A2.64H"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:analog-digital-convert-a264h"
source: https://www.bctengineer.com/q/semester_3/digital_logic/analog-digital-convert-a264h
site: BCT Engineering
---

# Analog vs digital signal; convert A2.64H

Digital Logic · Chapter 1: Introduction

- Asked in: 2075 Asoj, 2+4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/analog-digital-convert-a264h
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Describe in your own words the characteristics of an analog and a digital signal. Convert A2.64H into its octal and decimal equivalents.

## Short answer

Analog signals are continuous with infinite values, while digital signals are discrete and noise‑immune. Convert A2.64₁₆: write hex digits in 4 bits (A=1010, 2=0010, 6=0110, 4=0100) → 1010 0010.0110 0100, regroup in 3‑bit groups → 242.31₈. Decimal: 10×16¹ + 2×16⁰ + 6×16⁻¹ + 4×16⁻² = 162.390625.

## Answer

#### Characteristics of analog and digital signals

| Analog signal | Digital signal |
|---|---|
| Continuous in time and amplitude | Discrete levels (usually 0 and 1) |
| Infinite possible values in a range | Finite set of values |
| Example: sine wave, voice | Example: clock pulses, computer data |
| Easily affected by noise | High noise immunity |
| Hard to store without loss | Stored and copied exactly |

#### Convert $(A2.64)_{16}$ to octal
Write each hex digit in 4 bits:

$A = 1010,\ 2 = 0010,\ 6 = 0110,\ 4 = 0100$

$(A2.64)_{16} = (1010\ 0010\ .\ 0110\ 0100)_2$

Regroup into 3-bit groups from the binary point (left for integer, right for fraction), padding with zeros:

```text
 Integer : 010 100 010   ->  2 4 2
 Fraction: 011 001 000   ->  3 1 0
```

**Answer: $(A2.64)_{16} = (242.31)_8$**

#### Convert $(A2.64)_{16}$ to decimal

$$
\begin{aligned}
(A2.64)_{16} &= 10\times16^1 + 2\times16^0 + 6\times16^{-1} + 4\times16^{-2} \\
&= 160 + 2 + 0.375 + 0.015625 \\
&= 162.390625
\end{aligned}
$$

Check from octal: $2\times64 + 4\times8 + 2 + 3/8 + 1/64 = 162.390625$.

**Answer: $(A2.64)_{16} = (162.390625)_{10}$**

## Check yourself

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

1. How do analog and digital signals compare in noise effect?
   A. Digital is easily affected; analog is immune
   B. Analog is easily affected by noise; digital has high noise immunity
   C. Both are equally affected
   D. Neither is affected by noise
   Answer: B. Discrete levels let digital signals reject small noise. (Key point: Noise behaviour)

2. How is hex converted to octal?
   A. Multiply each hex digit by 8
   B. Divide by 8 repeatedly
   C. Hex to 4-bit binary, then regroup in 3 bits from the binary point
   D. Hex digits map directly to octal digits
   Answer: C. Binary is the common intermediate. (Key point: Hex to octal method)

3. What is (A2.64) hex in octal?
   A. 122.64
   B. 242.62
   C. 162.31
   D. 242.31
   Answer: D. 1010 0010 . 0110 0100 regrouped is 010 100 010 . 011 001 000 = 242.310. (Key point: Octal result)

4. What is (A2.64) hex in decimal?
   A. 162.390625
   B. 162.64
   C. 160.375
   D. 162.6
   Answer: A. 160 + 2 + 6/16 + 4/256 = 162.390625. (Key point: Decimal result)

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