---
title: "Convert (101101.011)₂ to decimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-101101-011-decimal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-101101-011-decimal
site: BCT Engineering
---

# Convert (101101.011)₂ to decimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2080 Baisakh, 1.5 marks
- Video: [How To Convert Binary To Decimal - Computer Science](https://www.youtube.com/watch?v=VLflTjd3lWA) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-101101-011-decimal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (101101.011)₂ = (?)₁₀.

## Short answer

Add powers of two for each 1: 32+8+4+1+0.25+0.125 = 45.375. Result is (45.375)₁₀.

## Answer

$$
\begin{aligned}
(101101.011)_2 &= 2^5 + 2^3 + 2^2 + 2^0 + 2^{-2} + 2^{-3} \\
&= 32 + 8 + 4 + 1 + 0.25 + 0.125 \\
&= 45.375
\end{aligned}
$$

**Answer: $(101101.011)_2 = (45.375)_{10}$**

## Check yourself

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

1. What is 101101 in decimal?
   A. 43
   B. 35
   C. 53
   D. 45
   Answer: D. 32 + 8 + 4 + 1. (Key point: Integer part)

2. What is .011 in decimal?
   A. 0.375
   B. 0.75
   C. 0.11
   D. 0.3
   Answer: A. 0.25 + 0.125. (Key point: Fraction part)

3. (101101.011) binary equals?
   A. 45.75
   B. 45.375
   C. 44.375
   D. 53.375
   Answer: B. 45 + 0.375. (Key point: Final answer)

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