---
title: "Convert (615)₈ to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-615-octal-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-615-octal-bcd
site: BCT Engineering
---

# Convert (615)₈ to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2075 Chaitra, 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-615-octal-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (615)₈ = (?)BCD.

## Short answer

First convert octal to decimal: (615)₈ = 397. Then encode each decimal digit in 4-bit BCD: 3→0011, 9→1001, 7→0111, giving 0011 1001 0111.

## Answer

BCD codes decimal digits, so first convert octal to decimal.

**Step 1: Octal to decimal**

$$
\begin{aligned} (615)_8 &= 6 \times 8^2 + 1 \times 8^1 + 5 \times 8^0 \\ &= 384 + 8 + 5 \\ &= (397)_{10} \end{aligned}
$$

**Step 2: Each decimal digit in 4 bits**

| Digit | 3 | 9 | 7 |
|---|---|---|---|
| BCD | 0011 | 1001 | 0111 |

**Answer:** $(615)_8 = (397)_{10} = (0011\ 1001\ 0111)_{BCD}$

## Check yourself

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

1. Why convert octal to decimal first?
   A. BCD codes octal digits
   B. Octal has no binary
   C. BCD codes decimal digits
   D. BCD needs hex
   Answer: C. BCD is a decimal-digit code. (Key point: Route)

2. (615)8 in decimal?
   A. 413
   B. 389
   C. 397
   D. 415
   Answer: C. 6x64 + 1x8 + 5 = 397. (Key point: Decimal value)

3. 397 in BCD?
   A. 0011 1001 0101
   B. 0011 1001 0111
   C. 0110 0001 0101
   D. 1100 0100 1010
   Answer: B. 3=0011, 9=1001, 7=0111. (Key point: BCD)

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