---
title: "2's complement: 15 − 20"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:two-complement-15-20"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-15-20
site: BCT Engineering
---

# 2's complement: 15 − 20

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2069 Bhadra, 2 marks
- Video: [1's complement and 2's complement | Signed Binary Numbers Explained](https://www.youtube.com/watch?v=MuUnffIpX7Y) — ALL ABOUT ELECTRONICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-15-20
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Find: (15)10 − (20)10 = ?, use 2's complement method.

## Short answer

8-bit: 15 = 00001111, 20 = 00010100. 2's complement of 20 = 11101100. Add: 00001111 + 11101100 = 11111011, no carry, negative. 2's complement of result gives 00000101 = 5, so 15 − 20 = −5.

## Answer

Use 8-bit numbers.

- 15 = 00001111
- 20 = 00010100

1. 1's complement of 20 = 11101011; add 1 gives the 2's complement **11101100**.
2. Add:

```text
   00001111   (15)
 + 11101100   (2's complement of 20)
 ----------
   11111011
```

3. No end carry, so the result is negative.
4. Magnitude: 2's complement of 11111011 = 00000100 + 1 = 00000101 = 5.

**Answer: 15 − 20 = −5**

## Check yourself

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

1. With 8 bits, the 2's complement of 20 (00010100) is:
   A. 11101100
   B. 11101011
   C. 00010101
   D. 11101101
   Answer: A. The answer states this: 11101100. (Key point: 2's complement of 20)

2. 00001111 + 11101100 equals:
   A. 11111100
   B. 11111011
   C. 00000101
   D. 11101111
   Answer: B. The answer states this: 11111011. (Key point: Sum)

3. To get the magnitude of a negative result 11111011, we:
   A. Subtract 1 only
   B. Take its 1's complement without adding 1
   C. Take its 2's complement
   D. Read it directly as unsigned
   Answer: C. The answer states this: Take its 2's complement. (Key point: Finding magnitude)

4. 15 - 20 equals:
   A. +5
   B. -35
   C. -4
   D. -5
   Answer: D. The answer states this: -5. (Key point: Final answer)

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