---
title: "Convert (36.735)₈ to decimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-36-735-decimal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-36-735-decimal
site: BCT Engineering
---

# Convert (36.735)₈ to decimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Bhadra, 1.5 marks
- Video: [Octal to Decimal, Binary & Hexadecimal (Hindi) | Number system conversion | Digital electronics](https://www.youtube.com/watch?v=gUM2wWpDji0) — CS Engineering Gyan
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-36-735-decimal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (36.735)₈ = (?)₁₀.

## Short answer

Sum each digit multiplied by 8 raised to its position: 3×8 + 6×1 + 7×8⁻¹ + 3×8⁻² + 5×8⁻³ = 30.931640625. Result is (30.931640625)₁₀.

## Answer

$$
\begin{aligned}
(36.735)_8 &= 3\times8^1 + 6\times8^0 + 7\times8^{-1} + 3\times8^{-2} + 5\times8^{-3} \\
&= 24 + 6 + 0.875 + 0.046875 + 0.009765625 \\
&= 30.931640625
\end{aligned}
$$

**Answer: $(36.735)_8 = (30.931640625)_{10}$**

## Check yourself

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

1. What is the weight of the first digit after the octal point?
   A. 8^1
   B. 10^-1
   C. 8^-1
   D. 2^-1
   Answer: C. Place values are powers of 8. (Key point: Positional weights)

2. What is the integer part 36 octal in decimal?
   A. 36
   B. 24
   C. 6
   D. 30
   Answer: D. 3 x 8 + 6. (Key point: Integer part)

3. What is (36.735) octal in decimal?
   A. 30.931640625
   B. 36.735
   C. 30.735
   D. 30.875
   Answer: A. 30 + 0.875 + 0.046875 + 0.009765625. (Key point: Final answer)

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