---
title: "Number conversions 33 to binary etc."
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:number-conversion-2067-chaitra"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/number-conversion-2067-chaitra
site: BCT Engineering
---

# Number conversions 33 to binary etc.

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2067 Chaitra, 3 marks
- Video: [How To Convert Decimal to Binary](https://www.youtube.com/watch?v=rsxT4FfRBaM) — The Organic Chemistry Tutor
- 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-chaitra
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Convert the following: i) 33(10) to binary  ii) (1100 0011)2 to decimal  iii) Add (1001)2 and (0111)2

## Short answer

33 decimal is 100001 binary. (11000011)₂ equals 195 decimal. (1001)₂ + (0111)₂ = (10000)₂, which is 16 decimal.

## Answer

#### i) 33₁₀ to binary

33 ÷ 2 = 16 r1, 16 → 8 r0, 8 → 4 r0, 4 → 2 r0, 2 → 1 r0, 1 → 0 r1. Read upward: 100001.

**(33)₁₀ = (100001)₂**

#### ii) (1100 0011)₂ to decimal

128 + 64 + 2 + 1 = 195

**(11000011)₂ = (195)₁₀**

#### iii) (1001)₂ + (0111)₂

```text
   1001   (9)
 + 0111   (7)
 ------
  10000   (16)
```

Bit by bit: 1+1 = 0 carry 1; 0+1+1 = 0 carry 1; 0+1+1 = 0 carry 1; 1+0+1 = 0 carry 1; final carry 1.

**Answer: (10000)₂ = 16₁₀**

## Check yourself

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

1. (33)10 in binary is:
   A. 100001
   B. 100011
   C. 10001
   D. 110001
   Answer: A. The answer states this: 100001. (Key point: 33 to binary)

2. (11000011)2 equals:
   A. 193
   B. 195
   C. 197
   D. 205
   Answer: B. The answer states this: 195. (Key point: Binary to decimal)

3. 1001 + 0111 equals:
   A. 1111
   B. 10001
   C. 10000
   D. 1110
   Answer: C. The answer states this: 10000. (Key point: Binary addition)

4. 1001 + 0111 in decimal is 9 + 7 =
   A. 15
   B. 17
   C. 14
   D. 16
   Answer: D. The answer states this: 16. (Key point: Decimal check)

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