---
title: "Convert (1011011)₂ to BCD"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-1011011-bcd"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-1011011-bcd
site: BCT Engineering
---

# Convert (1011011)₂ to BCD

Digital Logic · Chapter 1: Introduction

- Asked in: 2078 Kartik, 2 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-1011011-bcd
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert (1011011)₂ = (?)BCD.

## Short answer

Convert binary 1011011 to decimal 91. Encode each decimal digit in 4-bit BCD: 9 → 1001, 1 → 0001; result 1001 0001 (BCD).

## Answer

BCD codes each decimal digit separately in 4 bits, so first convert the binary number to decimal.

**Step 1: Binary to decimal**

$$
\begin{aligned} (1011011)_2 &= 1\cdot 2^6 + 0\cdot 2^5 + 1\cdot 2^4 + 1\cdot 2^3 + 0\cdot 2^2 + 1\cdot 2^1 + 1\cdot 2^0 \\ &= 64 + 16 + 8 + 2 + 1 \\ &= (91)_{10} \end{aligned}
$$

**Step 2: Each decimal digit to 4-bit BCD**

| Decimal digit | 9 | 1 |
|---|---|---|
| BCD | 1001 | 0001 |

**Answer:** $(1011011)_2 = (91)_{10} = (1001\ 0001)_{BCD}$

## Check yourself

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

1. How do we convert binary to BCD?
   A. Convert to decimal, then code each decimal digit in 4 bits
   B. Group the binary bits in fours directly
   C. Add 3 to each bit
   D. Invert all the bits
   Answer: A. BCD represents decimal digits, so decimal comes first. (Key point: Method)

2. What is (1011011)2 in decimal?
   A. 91
   B. 89
   C. 93
   D. 107
   Answer: A. 64 + 16 + 8 + 2 + 1 = 91. (Key point: Decimal value)

3. What is 91 in BCD?
   A. 0001 1001
   B. 1011 0001
   C. 0101 1011
   D. 1001 0001
   Answer: D. 9 = 1001 and 1 = 0001. (Key point: BCD result)

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