---
title: "Number conversions (25.5)10, (EAB)16"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:number-conversion-2073-magh"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/number-conversion-2073-magh
site: BCT Engineering
---

# Number conversions (25.5)10, (EAB)16

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2073 Magh, 3 marks
- Video: [Lec-2: Convert Decimal to Any Other Base(Binary, Octal, Hex etc) | Number System](https://www.youtube.com/watch?v=M6c6Xw5mt90) — Gate Smashers
- 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-2073-magh
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Convert the following number system. (a) (25.5)10 = (?)2  (b) (EAB)16 = (?)10  (c) (9180)10 = (?)BCD

## Short answer

(a) Integer 25 to binary by repeated division gives 11001, fraction 0.5×2=1.0 → .1, so (11001.1)₂. (b) EAB hex: 14×256+10×16+11 = 3755. (c) 9180 BCD: 1001 0001 1000 0000.

## Answer

#### (a) (25.5)₁₀ to binary

Integer 25: divide by 2 repeatedly.
25 → 12 r1, 12 → 6 r0, 6 → 3 r0, 3 → 1 r1, 1 → 0 r1. Read upwards: **11001**.
Fraction 0.5 × 2 = 1.0, so the fraction is **.1**.

**(25.5)₁₀ = (11001.1)₂**

#### (b) (EAB)₁₆ to decimal

E = 14, A = 10, B = 11.
14 × 16² + 10 × 16 + 11 = 3584 + 160 + 11 = 3755

**(EAB)₁₆ = (3755)₁₀**

#### (c) (9180)₁₀ to BCD

Write each decimal digit as a 4-bit binary number:
9 = 1001, 1 = 0001, 8 = 1000, 0 = 0000

**(9180)₁₀ = (1001 0001 1000 0000)BCD**

## Check yourself

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

1. (25.5)10 in binary is:
   A. 11001.1
   B. 10011.1
   C. 11001.01
   D. 11101.1
   Answer: A. The answer states this: 11001.1. (Key point: (25.5) to binary)

2. (EAB)16 equals:
   A. 3745
   B. 3755
   C. 3575
   D. 2755
   Answer: B. The answer states this: 3755. (Key point: (EAB) hex to decimal)

3. 0.5 in binary is:
   A. .01
   B. .11
   C. .1
   D. .101
   Answer: C. The answer states this: .1. (Key point: Fraction conversion)

4. (9180)10 in BCD is:
   A. 1001 0001 1000 0001
   B. 1001 0001 0111 0000
   C. 10011111011100
   D. 1001 0001 1000 0000
   Answer: D. The answer states this: 1001 0001 1000 0000. (Key point: BCD conversion)

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