---
title: "Number conversions (10111.101)2 etc."
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:number-conversion-2067-mangsir"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/number-conversion-2067-mangsir
site: BCT Engineering
---

# Number conversions (10111.101)2 etc.

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2067 Mangsir, 6 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-2067-mangsir
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Perform the conversion of the following: i) (10111.101)2 = (?)10  ii) (AFC.00)16 = (?)8  iii) (901)10 = (?)BCD

## Short answer

i) 10111.101 binary = 23.625 decimal (sum of powers). ii) AFC.00 hex to octal via binary: 5374. iii) 901 BCD: 1001 0000 0001.

## Answer

#### i) (10111.101)₂ to decimal

Integer: 1×16 + 0×8 + 1×4 + 1×2 + 1×1 = 23
Fraction: 1×0.5 + 0×0.25 + 1×0.125 = 0.625

**(10111.101)₂ = (23.625)₁₀**

#### ii) (AFC.00)₁₆ to octal

```text
A    F    C   .  0    0
1010 1111 1100 . 0000 0000

Integer: 101 011 111 100  = 5 3 7 4
Fraction: 000 000 00(0)   = 0 0 0
```

**(AFC.00)₁₆ = (5374)₈**, since the fractional part is zero.

#### iii) (901)₁₀ to BCD

9 = 1001, 0 = 0000, 1 = 0001

**(901)₁₀ = (1001 0000 0001)BCD**

## Check yourself

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

1. (10111.101)2 equals:
   A. 23.625
   B. 23.5
   C. 22.625
   D. 23.125
   Answer: A. The answer states this: 23.625. (Key point: Binary to decimal)

2. (AFC.00)16 equals:
   A. 5734
   B. 5374
   C. 5347
   D. 12274
   Answer: B. The answer states this: 5374. (Key point: Hex to octal)

3. In (AFC.00)16 the fractional part is zero, so the octal result:
   A. Has fraction .1
   B. Has fraction .4
   C. Has no fractional part
   D. Needs another digit
   Answer: C. The answer states this: Has no fractional part. (Key point: Zero fraction)

4. (901)10 in BCD is:
   A. 1001 0000 0000
   B. 1001 0001
   C. 1110000101
   D. 1001 0000 0001
   Answer: D. The answer states this: 1001 0000 0001. (Key point: BCD)

## Related in Basic Electronics Engineering

- [Number conversions (903)10 to BCD etc.](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Anumber-conversion-2068-magh) — Basic Electronics Engineering, chapter 6, asked 3×
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- [Number conversions (25.5)10, (EAB)16](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Anumber-conversion-2073-magh) — Basic Electronics Engineering, chapter 6
- [Number conversions (375.37)8 etc.](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Anumber-conversion-2071-magh) — Basic Electronics Engineering, chapter 6, asked 3×
- [Number conversions 33 to binary etc.](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Anumber-conversion-2067-chaitra) — Basic Electronics Engineering, chapter 6

## 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
- [Code conversions: (41.8125)₁₀, (1000)₂, (19)₁₀](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Acode-conversions-41-8125) — Digital Logic, chapter 1