---
title: "Convert (BD.1A)₁₆ to decimal"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-bd-1a-decimal"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-bd-1a-decimal
site: BCT Engineering
---

# Convert (BD.1A)₁₆ to decimal

Digital Logic · Chapter 1: Introduction

- Asked in: 2079 Bhadra, 1.5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-bd-1a-decimal
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (BD.1A)₁₆ = (?)₁₀.

## Short answer

B=11, D=13, 1=1, A=10. Value = 11×16 + 13 + 1/16 + 10/256 = 176+13+0.0625+0.0390625 = 189.1015625. Result: (189.1015625)₁₀.

## Answer

$$
\begin{aligned}
(BD.1A)_{16} &= 11\times16 + 13\times1 + 1\times16^{-1} + 10\times16^{-2} \\
&= 176 + 13 + 0.0625 + 0.0390625 \\
&= 189.1015625
\end{aligned}
$$

**Answer: $(BD.1A)_{16} = (189.1015625)_{10}$**

## Check yourself

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

1. What are the weights of the fractional digits 1 and A in (BD.1A)16?
   A. 8^-1 and 8^-2
   B. 16^-1 and 16^-2
   C. 16^1 and 16^2
   D. 10^-1 and 10^-2
   Answer: B. After the point, the weights are 16^-1, 16^-2, and so on. (Key point: Positional weights)

2. What decimal values are B and D?
   A. 11 and 13
   B. 12 and 14
   C. 10 and 12
   D. 11 and 14
   Answer: A. A = 10, B = 11, C = 12, D = 13. (Key point: Hex digit values)

3. What is (BD.1A)16 in decimal?
   A. 189.26
   B. 190.1015625
   C. 176.1015625
   D. 189.1015625
   Answer: D. 11x16 + 13 = 189, and 1/16 + 10/256 = 0.1015625. (Key point: Final result)

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