---
title: "Number conversions (10101.101)2 etc."
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:number-conversion-2071-bhadra"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/number-conversion-2071-bhadra
site: BCT Engineering
---

# Number conversions (10101.101)2 etc.

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2071 Bhadra, 1×3 marks
- Video: [Binary to Decimal and Decimal to Binary Conversion | Learn Coding](https://www.youtube.com/watch?v=pHRVViY3sPM) — Learn Coding
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/number-conversion-2071-bhadra
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

(a) (10101.101)2 = (?)10  (b) (9001180)10 = (?)BCD  (c) (2AB.5E)16 = (?)8

## Short answer

(a) 1×16+0+1×4+0+1=21, fraction 0.5+0.125=0.625 → 21.625. (b) 9001180 BCD: 1001 0000 0000 0001 0001 1000 0000. (c) Hex to binary then groups of three: (1253.274)₈.

## Answer

#### (a) (10101.101)₂ to decimal

Integer: 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 21
Fraction: 1×2⁻¹ + 0×2⁻² + 1×2⁻³ = 0.5 + 0.125 = 0.625

**(10101.101)₂ = (21.625)₁₀**

#### (b) (9001180)₁₀ to BCD

9 = 1001, 0 = 0000, 0 = 0000, 1 = 0001, 1 = 0001, 8 = 1000, 0 = 0000

**(9001180)₁₀ = (1001 0000 0000 0001 0001 1000 0000)BCD**

#### (c) (2AB.5E)₁₆ to octal

Convert each hex digit to 4 bits, then regroup in 3 bits.

```text
2    A    B   .  5    E
0010 1010 1011 . 0101 1110

Integer: 001 010 101 011   = 1 2 5 3
Fraction: 010 111 100      = 2 7 4   (padded with a zero)
```

**(2AB.5E)₁₆ = (1253.274)₈**

## Check yourself

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

1. (10101.101)2 equals:
   A. 21.625
   B. 21.5
   C. 20.625
   D. 21.125
   Answer: A. The answer states this: 21.625. (Key point: (10101.101) to decimal)

2. Each decimal digit in BCD is written as:
   A. A 3-bit binary number
   B. A 4-bit binary number
   C. A single bit
   D. The full number in binary
   Answer: B. The answer states this: A 4-bit binary number. (Key point: BCD of 9001180)

3. To convert hex to octal, we:
   A. Divide by 8 repeatedly
   B. Convert each digit to decimal and add
   C. Write each hex digit in 4 bits and regroup in 3 bits
   D. Write each digit in 3 bits only
   Answer: C. The answer states this: Write each hex digit in 4 bits and regroup in 3 bits. (Key point: Hex to octal method)

4. (2AB.5E)16 equals:
   A. 1253.724
   B. 1523.274
   C. 2531.274
   D. 1253.274
   Answer: D. The answer states this: 1253.274. (Key point: Result of hex to octal)

## Related in Basic Electronics Engineering

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## Related in other subjects

- [Conversions: (21)₈, (671)₁₀ to BCD, (110101.011)₂](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Anumber-conversions-21-671) — Digital Logic, chapter 1
- [(10.001)₂ − (11.101)₂ by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Atwos-complement-binary-subtraction) — Digital Logic, chapter 5